The Wizard of Odds gives the odds, house edge, and proper strategy for the casino coin-op game Derby.

Enjoy!

To start viewing messages, select the forum that you want to visit from the selection below.

Either the wizard's math is wrong, or I'm making a mistake somewhere in calculating this: Basic strategy for a game with the 6 card charlie rule in effect.

congratulate, blackjack onlie answer is the wizard's strategy: So lets look at an example He says to hit a five card 17 v 2, but there are no numbers to explain his calculations S17 8 deck, The EV of STANDING on, for example, wizard of odds blackjack basic strategy calculator 2,3,4,5,3 v 2 is -0.

Im finding that almost all the examples of hitting 17 are wrong, and hitting 16 v 2-6 is always wrong What am i missing?

I'm hoping im miscalculating this somehow, but dont think that i am.

In eight decks, the standing e.

If you hit, you have exactly 0.

So, unless I'm missing something also, standing is clearly better.

FWIW, in wizard of odds blackjack basic strategy calculator Basic Blackjack, Wong also gives standing, so something seems to be wrong with Mike's chart.

I will write to him.

Don In eight decks, the standing e.

If you hit, you have exactly 0.

So, unless I'm missing something also, standing is clearly better.

FWIW, in his Basic Blackjack, Wong also gives standing, so something seems to be wrong with Mike's chart.

I will write to him.

DonI was using single deck for the hit, i may have mixed that with 8 deck to get the -0.

Here is our correspondence: Mike, One of the members of Norm's forum questioned the accuracy of your chart for 5- and 6-card Charlies, which can be found here: Specifically, he said that it made no sense to him that, for a six-card Charlie, which would be an automatic winner of one bet, you would hit 17 vs.

I verified in Wong's charts that, in fact, this was not a hit, but the math is rather simple to see.

I posted the following to the forum: In eight decks, the standing e.

If you hit, you have exactly 0.

So, unless I'm missing something also, standing is clearly better.

FWIW, in his Basic Blackjack, Wong also gives standing, so something seems to be wrong with Mike's chart.

I will write to him.

Don Hi Don, You make a good argument there.

I will remove for now given it obviously is flawed.

Thank you for bringing this to my attention.

Mike Mike, I have one more thought.

For the hand in question, there is obviously a big difference between a 5-card and 6-card Charlie, as the former pays double.

But https://clearadultskin.com/blackjack/blackjack-casinos-vegas.html have only one footnote, as if hitting 17 vs.

In fact, if you do the math, and Wong seems to agree Table 22, Basic Blackjackit's right to hit for the 5-card, but not the 6-card, Charlie.

You had separate charts for splitting but not for hitting and standing, so maybe you needed to distinguish between the two for that also.

Don I wrote to Mike.

Here is our correspondence: Mike, One of the members of Norm's forum questioned the wizard of odds blackjack basic strategy calculator of your chart for 5- and wizard of odds blackjack basic strategy calculator Charlies, which can be found here: Specifically, he said that it made no sense to him that, for a six-card Charlie, which would be an automatic winner of one bet, you would hit 17 vs.

I verified in Wong's charts that, in fact, this was not a hit, but the math is rather simple to see.

I posted the following to the forum: In eight decks, the standing e.

If you hit, you have exactly 0.

So, unless I'm missing something also, standing is clearly better.

FWIW, in his Basic Blackjack, Wong also gives standing, so something seems to be wrong with Mike's chart.

I will write to him.

Don Hi Don, You check this out a good argument there.

I will remove for now given it obviously is flawed.

Thank you for bringing this to my attention.

Mike Mike, I have one more thought.

For the hand in question, there is obviously a big difference between a 5-card and 6-card Charlie, as the former pays double.

But you have only one footnote, as if hitting 17 vs.

In fact, if you do the math, and Wong seems to agree Table 22, Basic Blackjackit's right to hit for the 5-card, but not the 6-card, Charlie.

You had separate charts for splitting but not for hitting and standing, so maybe you needed to distinguish between the two for that also.

The game i play has 6 card charlie and is single deck this is very important strategy i need to know, but i think that i have it all figured out perfectly.

The game i play has 6 card charlie and is single deck this is very important strategy i need to know, but i think that i have it all figured out perfectly.

Just go to the site where you orignally found the flawed one.

The game i play has 6 card charlie and is single deck this is very important strategy i need to know, but i think that i have it all figured out perfectly.

For 6 card auto winner you need to select the far right radio button in the auto winner section of rules options.

You can fill in whatever number of decks you would like along with any of the other available rules options.

For a player hand of 2-3-4-5-3 you simply click 2-3-4-5-3 under player cards.

When you are finished, click compute and the EVs for what you have entered will be displayed for the shoe composition that is displayed.

Shoe composition can also be input.

Reset removes all player cards.

Undeal removes the last player card.

If you click compute with no player cards entered or also 1 card, which displays EVs given player knows one of his cards prior to the hand being dealt an overall calculation for the shoe composition entered is done.

When 2 or more cards are entered the EVs for the player cards that were entered is displayed.

Although I have several ideas of additions to the website, I very rarely add anything because of time constraints.

That is, civil and considerate behavior for the mutual benefit of all involved.

The goal of advantage play is the legal extraction of funds from gaming establishments by gaining a mathematic advantage and developing the skills required to use that advantage.

To maximize our success, it is important to understand that we are all on the same side.

Personal conflicts simply get in the way of our goals.

Copyright Β© 2018All rights reserved.

Blackjack Forum is a message board.

Disclaimer: The views and opinions expressed in this forum are those of the authors and do not necessarily reflect the position of the management.

Software - MORE

Most players are bad enough at blackjack basic strategy to give up. You can make this calculation for any casino game, by the way β not just. you can flip the odds from being in the house's favor to being in your favor.

Enjoy!

The purpose of this video is to create the blackjack basic strategy from scratch in Excel starting with just a blank spreadsheet.

Why am I doing this?

Because I'm getting a little tired of hearing dealers say that the basic strategy is a myth, that it was created by Ed Thorp, Beat the Dealer fame back in 1962 on an old UNIVAC computer or whatever and he must've made a mistake somewhere and this mistake has been repeated for decades by other gambling writers who never once thought to confirm his work and we've all just been repeating his work like parrots.

Number one I'd like to correct something is actually, Ed Thorp was not the first person to publish the basic strategy.

There were four guys in the army wizard of odds blackjack basic strategy calculator the 50s who did it before him and published it in the American Statistical Journal.

However, Ed Thorp was the first one to write a book about it including addressing card counting and broke all kinds of new ground in the game.

I might also add that blackjack analysis has been repeated over and over by lots of gambling writers, including myself, and we all-- all the legitimate writers basically agree with each other.

Nevertheless, dealers will continue to say, "Well, I've seen players play by the book and lose lots of times.

But, as I always say, the more ridiculous a belief is, the more tenaciously it tends to be held, but let's quit talking and actually show you the basic strategy starting from nothing.

I'm going to use an assumption of an infinite number of decks of cards for the sake of simplicity.

The mathematics of the game are not tremendously different between eight decks and an infinite number of decks.

The basic strategy will be different in a couple borderline plays as we'll see later.

But let's jump in, shall we?

Let's call the first sheet in the spreadsheet, "the dealer sheet.

So, one of these things are going to happen to the dealer; he could bust, he could end up with 17, 18, 19, 20, or 21, and we're going to do this by American rules where the dealer peeks for blackjack and he exposes it, if he doesn't-- if he has it otherwise, the player is not drawing dead to a handy can't be.

We will factor in the blackjacks later on in another video where I show you how to calculate the house advantage.

There's 10 possible up cards the dealer can have, which we'll put across the first row.

This table up here will represent the possible probabilities under the American rules.

Again, it's a little tricky because in the-- again, because of this peeking rule.

So, let's do it underneath here according to the European rule where the dealer doesn't peek for a blackjack and let's consider all the possible totals all the way up to 31 which will make-- doing the spreadsheet a little bit easier and we also will look at the soft totals and we'll start there from a 12, also up to a 31.

What's a soft 31, you might ask?

That's the same thing as a hard 21.

For a soft 22 or more, just subtract 10 and it's the same thing as a hard total.

All right, if the dealer has a-- that's the 17.

There's a 100% chance he will end up with a 17 because he's going to stop and same thing with an 18 through a 21.

The dealer ends up with a 22 or more.

There's a 100% chance he's going to bust.

With the soft hands, let's assume the rule that the dealer stands on a soft 17.

We can do the same thing there.

With a soft 22, that's going to be the same thing as a hard 12.

Okay, let's start with looking at what is the probability of the dealer getting a 17 if he starts with a two?

Well, the next card could bring him up to a four all the way up to an 11, each with equal chance.

There's 4 chances he could end up with a 12 because there's four ranks in the deck that are 10 points, and one chance he could get to a soft 13.

We divide by 13 because there's 13 ranks.

This same formula is going to work all the way up to 16 for all the other possible totals.

Now, let's work on the soft hands.

The dealer starts with-- hit's a soft 12.

He could end up with a 13 up to a 21 each with equal chance, and four chances at a 22, copying paste that down.

Let's take the total to make sure it adds up to one.

Let's make sure it does for all the other outcomes.

Looks good so far.

All right, now, let's think about the American rules.

Blackjack is the same, all other things being equal in the US and Europe if the dealer's showing a two through nine because there's no chance a dealer can have a blackjack, so we can just refer to the European numbers for two through nine.

Let me add another row here for the total.

For the 10 and the ace, there's no chance the dealer has a blackjack because he already peeked for wizard of odds blackjack basic strategy calculator and again, we'll adjust for that later on when we figure out the house edge.

But if the dealer has a 10 showing and when he hits that, that could leave him with a 12 up through a 19, each with one chance and four chances of the 20, and we divide it by 12 because there's 12 ranks, not counting the ace.

Similar kind of logic with the ace, but there you can end up with a soft 12 up to a soft 20 and divide by 9, because there's only nine ranks that won't give them a blackjack.

There are all your dealer probabilities.

Let's save this before I forget.

We'll just call this "basic strategy.

Let's make our next sheet called "stand.

Let's do everything by the wizard of odds blackjack basic strategy calculator dealer wizard of odds blackjack basic strategy calculator cards.

Let's do all the player sheets according to having anywhere from a hard four all the way to 31 and a soft 12 all the way to 31.

Let me make the screen a little bigger for you.

I hope that helps so you can see what I'm doing.

What if the dealer stands on a four against a two?

The only way he's going to win is if the dealer busts.

His expected value is the probability of the dealer busting minus the probability of anything else happening.

So, he can expect to lose by standing on a four against a two of about 29.

That's the same number for standing on everything all the way through a 16 because a 16 is no better than a four or a zero.

Things start to get better with a 17 because now, a 17 is going to turn from a loss to a push, so the expected value there is the probability of the dealer busting minus the probability of an 18 through a 21.

We can ignore the dealer getting a 17 because that's going to result in a push with a player.

Eighteen, expected value is the probability of the bust or 17 minus the probability of a 19 to21.

With a 19, expected value is the probability of a dealer having a bust 17 or 18 minus a 20 or 21.

With a 20, it's a bust through a 19 minus a 21 and with a 21, it's anything except another 21 which would be a push.

So, the expected swim up blackjack of a 17 against a two is a expected loss of about 15.

If the dealer gets to 22 or more, these loss's expected value is negative one.

So, let's copy and paste that all over through to an ace.

Now, with the soft totals, it doesn't help wizard of odds blackjack basic strategy calculator player if it's soft if he's just going to stand on it.

We can just refer to the hard totals.

Soft 22 is the same thing as a soft 12 and expected value for standing.

There's our expected values of if the player stands.

link talk about hitting next.

We'll make a sheet called "hit" and let's also make one called "HS" which will represent the expected value of the better choice between hitting and standing because the player should make the choice with the higher expected value at every stage of the game.

Let's zoom this so you can see it better.

For the hit stand sheet, at any given stage of the game, the expected value is going to be the higher of the expected value for that state between hitting and standing.

We're going to need to reference that sheet when we talk about hitting because after the player hits, he can still keep hitting.

So, if the player hits a hard four against the two for example, he might be left with anywhere from a six through a 13, each with equal chance, four chances at a 14 and one chance at a soft 15 and divide it by 13 and just copy and paste.

The player hits a 21, he's going to bust, so his expected value is negative one, or if the player hits a soft 12, well, then he can have anywhere from a soft 13 to 21, four chances at the soft 22 which is the same thing as a 12, and again, divide by 13.

Copy and paste that down through 21.

As usual, a soft 22 is the same thing as a 12, so we can refer to the hard totals there.

So, there's our expected values for hitting.

Now, let's see what the basic strategy looks like if the player is only limited to hitting and standing which is the case very d alembert blackjack thank three or more cards.

If this greater expected value is the same as standing, let's put an S, otherwise an H for hitting.

Now, let's color that in.

Blackjack writers seem to always use red for hitting, I think it comes from Lawrence Revere, and yellow for standing.

Here's what it looks like.

Take it from me, this is correct.

Any legitimate blackjack book will show you this is the correct strategy for hitting and standing for any possible situation.

Let's talk about doubling next.

Let's make a new sheet called "double.

The doubling sheet is going to be based on the stand sheet, because when you double, you get one card only.

There's no option to hit after that.

So, if the player doubles on a four against the two, he could end up with a six through a 13 or four chances at a 14 or a soft 15 and we divide it by 13.

Let's multiply all this by two because now, the player asked to double his bet.

We can simply copy that down through the 11.

With the 12, it gets a little bit different because now the ace is going to count as-- it must count as a one.

So, we just adjust the formula a little bit like that.

There are all your expected values for doubling for hard totals.

Now, let's do it for the soft totals, start out by with the two because again, the player's doubling his bet.

If the player starts with a soft 12, his next card could give him anywhere from a soft 13 through 21, and four chances at a soft 22, which, again, is the same thing as a hard 12 and divided by 13.

A soft 22 is again the same thing as a hard 12, so there's all your expected values for doubling.

Now, let's make a sheet.

We'll call it "HSD" for Hit Stand Double, which is going to represent the expected value of the best choice between hitting, standing, and doubling.

So, this is going to be the maximum of hitting, standing, and doubling.

Let's adjust this little sheet here, "the basic strategy," to show the best choice between hitting, standing, and doubling.

Voila, and let's color all this in-- color in all the doubling squares blue because everyone seems to use blue for doubling.

Here's our basic strategy for doubling.

Again, take it from me, you'll see this same chart in any legitimate blackjack book, and here it is for the soft totals.

Now, here are the couple differences between four to eight decks and infinite decks.

These are two very borderline situations.

With four to eight decks, you're also going to double a soft 15 against a four and you're going to double a soft 13 against a five.

Again, the only reason these are different is because of the infinite decks.

There, we have doubling.

Next, let's talk about surrendering.

Surrendering is really easy.

Let's call this "SUR" for surrender.

The expected value of surrendering-- sorry, let me make this bigger for you again.

The expected value of surrendering is negative 0.

Let's make another sheet.

We'll call this one "HSDR," that's going to represent the maximum expected value between hitting, standing, doubling, and surrendering.

Why do we use an R for surrender?

Because S was already taken for standing.

Why does this zoom keep changing?

So, the expected value between all those four choices is the maximum of hitting, standing, doubling, and-- oops.

You can see right here, it's only optimal to surrender if the player has a 16 and the dealer is showing a 9, 10, or ace, or a 15 against the dealer 10.

Let's update our chart here.

I hope my wife gets that.

I guess she's not.

I hope it wasn't too important.

There you see the four surrenders that I just set.

Finally, let's talk about splitting.

The player could have a pair of anything from a two through 10s or two aces.

Okay, what's the expected value if the player splits a pair of twos against a two?

Well, first, let's put a two because the player has a double as a bet, and after splitting that, each hand could be anything.

After he hits each one, it could be anywhere from a four through an 11, four chances at the 12, and one chance at a soft 13.

By the way, I am assuming that the player may only split once, no re-splitting, just to keep visit web page simple.

We copy and paste that.

Things are different with aces.

With aces, we're going to go to the stand sheet because the way blackjack is played is you only get one card after splitting aces.

So, after splitting an ace with each ace, you could have it anywhere from a 12 through 20 and four chances of the 21.

Here's your expected values for splitting.

Well, let's see when those are better than the best alternative.

Down here, let's look at the better value between, for example, with a pair of twos against the two, the higher of the splitting expected value or a hard four.

With a three, it's going to be greater of the expected value of splitting the threes or a hard six, so, we're going to have to alternate the rows in the standing sheet.

For the pair of twos, we looked at cell B2 in the sheet for hitting, standing, or doubling.

For a pair of threes, we're going to look at cell B4; for the fours, D6; for the fives, B8; and so on.

With aces, it's going to be the greater of splitting the aces or playing it out as a soft 12.

Copy and paste it for the other dealer up cards.

Now, let's make a little chart to show when it's best to split.

So, if the best expected value equals the splitting expected value, we'll put a Y for "Yes, you should split," otherwise put a, "No.

If it's equal to a Y for "Yes, we should split," let's use green.

Here, we have the splitting basic strategy.

Take it from me, look in any blackjack book and it's going to tell you that you should split in these situations with four or more decks or 48 decks and the dealer standing on a soft 17.

So, there's your basic strategy.

Here's this basic strategy for splitting.

Here's a basic strategy for all your hard totals and your soft totals.

Again, all that starting from just a blank spreadsheet.

It wasn't all that complicated.

I hope you understood this.

I'm going to put this spreadsheet in Google Documents so you can look at it more closely on your own if you want to.

In my next video, I'm going to expand on this one to show you how we go from all these expected values to the actual house advantage of the game.

Thank you and I hope that wasn't too boring.

Michael Shackleford: Hi, this is Mike with the Wizard of Odds.

The purpose of this video is to create the blackjack basic strategy from scratch in Excel starting with just a blank spreadsheet.

Why am I doing this?

Because I'm getting a little tired of hearing dealers say that the basic strategy is a myth, that it was created by Ed Thorp, Beat the Dealer fame back in 1962 on an old UNIVAC computer or whatever and he must've made a mistake somewhere and this mistake has been repeated for decades by other gambling writers who never once thought to confirm his work and we've all just been repeating his work like parrots.

Number one I'd like to correct something is actually, Ed Thorp was not the first person to publish the basic strategy.

There were four guys in the army in the 50s who did it before him and published it in the American Statistical Journal.

However, Ed Thorp was the first one to write a book about it including addressing card counting and broke all kinds of new ground in the game.

I might also add that blackjack analysis has been repeated over and over by lots of gambling writers, including myself, and we all-- all the legitimate writers basically agree with each other.

Nevertheless, dealers will continue to say, "Well, I've seen players play by the book and lose lots of times.

But, as I always say, the more ridiculous a belief is, the more tenaciously it tends to be held, but let's quit talking and actually show you the basic strategy starting from nothing.

I'm going to use an assumption of an infinite number of decks of cards for the sake of simplicity.

The mathematics of the game are not tremendously different between eight decks and an infinite number of decks.

The basic strategy will be different in a couple borderline plays as we'll see later.

But let's jump in, shall we?

Let's call the first sheet real money reddit online blackjack the spreadsheet, "the dealer sheet.

So, one of these things are going to happen to the dealer; he could bust, he could end up with 17, 18, 19, 20, or 21, and we're going to do this by American rules where the dealer peeks for blackjack and he exposes it, if he doesn't-- if he has it otherwise, the player is not drawing dead to a handy can't be.

We will factor in the us online blackjack real money later on in another video where I show you how to calculate the house advantage.

There's 10 possible up cards the dealer can have, which we'll put across the first row.

This table up here will represent the possible probabilities under the American rules.

Again, it's a little tricky because in the-- again, because of this peeking rule.

So, let's do it underneath here according to the European rule where the dealer doesn't peek for a blackjack and let's consider all the possible totals all the way up to 31 which will make-- doing the spreadsheet a little bit easier and we also will look at the soft totals and we'll start there from a 12, also up to a 31.

What's a soft 31, you might ask?

That's the same thing as a hard 21.

For a soft 22 or more, just subtract 10 and it's the same thing as a hard total.

All right, if the dealer has a-- that's the 17.

There's a 100% chance he will end up with a 17 because he's going to stop and same thing with an 18 through a 21.

The dealer ends up with a 22 or more.

There's a 100% chance he's going to bust.

With the soft hands, let's assume the rule that the dealer stands on a soft 17.

We can do the same thing there.

With a soft 22, that's going to be the same thing as a hard 12.

Okay, let's start with looking at what is the probability of the dealer getting a 17 if he starts with a two?

Well, the next card could bring him up to a four all the way up to an 11, each with equal chance.

There's 4 chances he could end up with a 12 because there's four ranks in the deck that are 10 points, and one chance he could get to a soft 13.

We divide by 13 because there's 13 ranks.

This same formula is going to work all the way up to 16 for all the other possible totals.

Now, let's work on the soft hands.

The dealer starts with-- hit's a soft 12.

He could end up with a 13 up to a 21 each with equal chance, and four chances at a 22, copying paste that down.

Let's take the total to make sure it adds up to one.

Let's make sure it does for all the other outcomes.

Looks good so far.

All right, now, let's think about the American rules.

Blackjack is the same, all other things being equal in the US and Europe if the dealer's showing a two through nine because there's no chance a dealer can have a blackjack, so we can just refer to the European numbers for two through nine.

Let me add another row here for the total.

For the 10 and the ace, there's no chance the dealer has a blackjack because he already peeked for it and again, we'll adjust for that later on when we figure out the house edge.

But if the dealer has a 10 showing and when he hits that, that could leave him with a 12 up through a 19, each with one chance and four chances of the 20, and we divide it by 12 because there's 12 ranks, not counting the ace.

Similar kind of logic with the ace, but there you can end up with a soft 12 up to a soft 20 and divide by 9, because there's only nine ranks that won't give them a blackjack.

There are all your dealer probabilities.

Let's save this before I forget.

We'll just call this "basic strategy.

Let's make our next sheet called "stand.

Let's do everything by the 10-possible dealer up cards.

Let's do all the player sheets according to having anywhere from a hard four all the way to 31 and a soft 12 all the way to 31.

Let me make the screen a little bigger for you.

I hope that helps so you can see what I'm doing.

What if the dealer stands on a four against a two?

The only way he's going to win is if the dealer busts.

His expected value is the probability of the dealer busting minus the probability of anything else happening.

So, he can expect to lose by standing on a four against a two of about 29.

That's the same number for standing on everything all the way through a 16 because a 16 is no better than a four or a zero.

Things start to get better with a 17 because now, a 17 is going to turn from a loss to a push, so the expected value there is the probability of the dealer busting minus the probability of an 18 through learn more here 21.

We can ignore the dealer getting a 17 because that's going to result in a push with a player.

Eighteen, expected value is the probability of the bust or 17 minus the probability of a 19 to21.

With a 19, expected value is the probability of a dealer having a bust 17 or 18 minus odds strategy wizard blackjack 20 or 21.

With a 20, it's a bust through a 19 minus a 21 and with a 21, it's anything except another 21 which would be a push.

So, the expected value of a 17 against a two is a expected loss of about 15.

cheat sheet blackjack simple the dealer gets to 22 or more, these loss's expected value is negative one.

So, let's copy and paste that all over through to an ace.

Now, with the soft totals, it doesn't help the player if it's soft if he's just going to stand on it.

We can just refer to the hard totals.

Soft 22 is the same thing as a soft 12 and expected value for standing.

There's our expected values of if the player stands.

Let's talk about hitting next.

We'll make a sheet called "hit" and let's also make one called "HS" which will represent the expected value of the better choice between hitting and standing because the player should make the choice with the higher expected value at every stage of the game.

Let's zoom this so you can see it better.

For the hit stand sheet, at any given stage of the game, the expected value is going to be the higher of the expected value for that state between hitting and standing.

We're going to need to reference that sheet when we talk about hitting because after the player hits, he can still keep hitting.

So, if the player hits a hard four against the two for example, he might be left with anywhere from a six through a 13, each with equal chance, four chances at a 14 and one chance at a soft 15 and divide it by 13 and just copy and paste.

The player hits a 21, he's going to bust, so his expected value is negative one, or if the player hits a soft 12, well, then he can have anywhere from a soft 13 to 21, four chances at the soft 22 which is the same thing as a 12, and again, divide by 13.

Copy and paste that down through 21.

As usual, a soft 22 is the same thing as a 12, so we can refer to the hard totals there.

So, there's our expected values for hitting.

Now, let's see what the basic strategy looks like if the player is only limited to hitting and standing which is the case with three or more cards.

If this greater expected value is the same as standing, let's put an S, otherwise an H for hitting.

Now, let's color that in.

Blackjack writers seem to always use red for hitting, I think it comes from Lawrence Revere, and yellow for standing.

Here's what it looks like.

Take it from me, this is correct.

Any legitimate blackjack book will show you this is the correct strategy for hitting and standing for any possible situation.

Let's talk about doubling next.

Let's make a new sheet called "double.

The doubling sheet is going to be based on the stand sheet, because when you double, you get one card only.

There's no option to hit after that.

So, if the player doubles on a four against the two, he could end up with a six through a 13 or four chances at a 14 or a soft 15 and we divide it by 13.

Let's multiply all this by two because now, the player asked to double his bet.

We can simply copy that down through the 11.

With the 12, it gets a little bit different because now the ace is going to count as-- it must count as a one.

So, we just adjust the formula a little bit like that.

There are all your expected values for doubling for hard totals.

Now, let's do it for the soft totals, start out by with the two because again, the player's doubling his bet.

If the player starts with a soft 12, his next card could give him anywhere from a soft 13 through 21, and four chances at a soft 22, which, again, is the same thing as a hard 12 and divided by 13.

A soft 22 is again the same thing as a hard 12, so there's all your expected values for doubling.

Now, let's make a sheet.

We'll call it "HSD" for Hit Stand Double, which is going to represent the expected value of the best choice between hitting, standing, and doubling.

So, this is going to be the maximum of hitting, standing, and doubling.

Let's adjust this little sheet here, "the basic strategy," to show the best choice between hitting, standing, and doubling.

Voila, and let's color all this in-- color in all the doubling squares blue because everyone seems to use blue for doubling.

Here's our basic strategy for doubling.

Again, take it from me, you'll see this same chart in any legitimate blackjack book, and here it is for the soft totals.

Now, here are the couple differences between four to eight decks and infinite decks.

These are two very borderline situations.

With four to eight decks, you're also going to double a soft 15 against a four and you're going to double a soft 13 against a five.

Again, the only reason these are different is because of the infinite decks.

There, we have doubling.

Next, let's talk about surrendering.

Surrendering is really easy.

Let's call this "SUR" for surrender.

The expected value of surrendering-- sorry, let me make this bigger for you again.

The expected value of surrendering is negative 0.

Let's make another sheet.

We'll call this one "HSDR," that's going to represent the maximum expected value between hitting, standing, doubling, and surrendering.

Why do we use an R for surrender?

Because S was already taken for standing.

Why does this zoom keep changing?

So, the expected value between all those four choices is the maximum of hitting, standing, doubling, and-- oops.

You can see right here, it's only optimal to surrender if the player has a 16 and the dealer is showing a 9, 10, or ace, or a 15 against the dealer 10.

Let's update our chart here.

I hope my wife gets that.

I guess she's not.

I hope it wasn't too important.

There you see the four surrenders that I just set.

Finally, let's talk about splitting.

The player could have a pair of anything from a two through 10s or two aces.

Okay, what's the expected value if the player splits a pair of twos against a two?

Well, first, let's put a two because the player has a double as a bet, and after splitting that, each hand could be anything.

After he hits each one, it could be anywhere from a four through an 11, four chances at the 12, and one chance at a soft 13.

By the way, I am assuming that the player may only split once, no re-splitting, just to keep things simple.

We copy and paste that.

Things are different with aces.

With aces, we're going to go to the stand sheet because the way blackjack is played link you only get one card after splitting aces.

So, after splitting an ace with each ace, you blackjack cards 21 have click here anywhere from a 12 through 20 and four chances of the 21.

Here's your expected values for splitting.

Well, let's see when those are better than the best alternative.

Down here, let's look at the better value between, for example, with a pair of twos against the two, the higher of the splitting expected value or a hard four.

With a three, it's going to be greater of the expected value of splitting the threes or a hard six, so, we're going to have to alternate the rows in the standing sheet.

For the pair of twos, we looked at cell B2 in the sheet for hitting, standing, or doubling.

For a pair of threes, we're going to look at cell B4; for the fours, D6; for the fives, B8; and so on.

With aces, it's going to be the greater of splitting the aces or playing it out as a soft 12.

Copy and paste it for the other dealer up cards.

Now, let's make a little chart to show when it's best to split.

So, if the best expected value equals the splitting expected value, we'll put a Y for "Yes, you should split," otherwise put a, "No.

If it's equal to a Y for "Yes, we link split," let's use green.

Here, we have the splitting basic strategy.

Take it from me, look in any blackjack book and it's going to tell you that you should split in these situations with four or more decks or 48 decks and the dealer standing on a soft 17.

So, there's your basic strategy.

Here's this basic strategy for splitting.

Here's a basic strategy for all your hard totals and your soft totals.

Again, all that starting from just a blank spreadsheet.

It wasn't all that complicated.

I hope you understood this.

I'm going to put this spreadsheet in Google Documents so you can look at it more closely on your own if you want to.

In my next video, I'm going to expand on this one to show you how we go from all these expected values to the actual house advantage of the game.

Thank you and I hope that wasn't too boring.

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It is a simple game, and the rules are not very difficult to understand.

It is one of the few games where the players do not compete against one another but compete against the dealer for each hand.

However, when it comes to playing the game successfully, there is a need to understand something more about Wizard of Odds blackjack, and that is what we will be learning about the next few lines.

Wizard of Odds: Blackjack Before getting to know more about Wizard of Odds blackjack strategy, it would be better to have a basic understanding of the rules pertaining to blackjack.

read article can be played either with either a single pack or cards or multiple packs of cards.

There are many blackjack tables where around eight stacks of cards are used.

The game is all about the players trying to reach 21 points without crossing it or overshooting it.

The values for the cards vary and cards starting from 2 to 10 have the same points as their face value.

The picture cards, i.

A, Jack, Queen, and King are referred to as aces, and their points could vary from 1 to 11.

The Importance of Wizard of Odds If the players overshoot continue reading points, then the hand belongs to the dealer, and, therefore, the players must find out various ways by which this can be done.

It is about keeping in mind the cards that are dealt and finding out ways and means by which the cards can be counted.

When there are seven or eight stacks of 52 cards being dealt, counting could become a major problem.

In such situations, it might be therefore necessary to make use of other help and aids in the form of Wizard of Odds blackjack trainer and other such ways and means.

We will what these wizards of odds are all about and how do they work on the ground.

Variations to Blackjack Rules There wizard of odds blackjack basic strategy calculator no denying the fact that variations to rules will certainly have a negative impact on the expected returns of the players.

For example, it has been found that opting for Blackjack pay 2 to 1 could impact the outcome of the game and the variation percentage could be as high as 2.

Hence, before getting into the blackjack table, there is a need to understand the subtle changes to the rules.

Though they might look insignificant, there is every possibility that it could lead to making the difference between winning and losing.

How to Handle Such Changes?

There is a need to understand the theory or probabilities to some extent if you are keen on handling such changes to rules and style of playing.

The best way to learn more about it would be to make use of the time-tested Wizard of Odds blackjack chart.

This will certainly help you to get a decent idea as to how the changes in rules will impact the winning and losing chances.

The chart might look a bit confusing in the beginning but if you are ready to put some time and effort in understanding it, over a period of time you will be able to understand how it actually works.

However, this would depend on where the dealer stands wizard of odds blackjack basic strategy calculator terms of the finite deck or an infinite deck.

Handling of Splits Will Also Impact The way the players decide to handle splits will also impact the outcomes of the game.

The number of hands to be played by the participants will also have an impact.

However, one simple strategy should always be https://clearadultskin.com/blackjack/21-3-extreme-blackjack.html in mind.

Before getting into the playing arena, it would be ideal to have a look at the table.

The one which offers the greatest returns is perhaps the best play.

What the players stand to gain by standing and hitting should also be understood to get the best possible returns.

How to Use Math to Beat Odds?

There is also something known as Wizard of Odds blackjack calculator which also should be understood properly.

The calculator is quite complex, and it is wizard of odds blackjack basic strategy calculator likely that new players will be able to understand much about this calculator.

However, on a closer look and by regular practice things will become much clearer.

It is all about understanding the shoe composition vis-Γ -vis the number of decks that are in play.

Then, there is a need to know more about other important points like hold card, soft 17 where the dealer hits or standsdrawing to split aces, doubling after split and surrender.

There are other attributes too above blackjack percentage table believe must be understood and only then would it be possible to move forward and master and understand the way in which odds work.

The Crux Lies In Mastering Counting Though there could be doubts about the legality and validity of counting, there is no doubt that it is perfectly legal though the efficacy and benefit of the same are till shrouded in doubts and mystery.

There are some classic set of players who are masters when it comes to card counting.

Their main objective is to try and find wizard of odds blackjack basic strategy calculator ways and means by which they can reduce the advantage of the dealers.

They try and keep a tab of all the high and low-value cards which are visible to the player.

Mastering this - is an important part of Wizard of Odds.

There are reasons to believe that to bet more with lesser risk.

It also helps in minimizing losses whenever the count is unfavorable.

It could also play a big role in making mid-course corrections to playing decisions based on the composition of the cards which have still not been dealt.

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The first rule, and the one that you see a lot is really obvious.

Now, let me explain what is a low and high up card.

And this is going to be true throughout my whole strategy.

A low dealer up card is a two through a six.

A high dealer up card is a seven through an ace.

If the dealer showing a two through six, you double.

And this one covers a lot of hands and are frequently misplayed.

These are the stiff hands.

If you remember just one thing from this whole video it should be that because these situations happen all the click and their frequently misplays.

Next rule is pretty obvious.

If you have a total of hard 17 or more, you stand.

And we will get to the soft doubles and splits later.

Okay, Angela, what should I do?

Angela: You should stand.

Angela: Because you have a 20 against a dealer's tag.

visit web page I have a hard 17 or more, I stand which I obviously do.

Mike: Okay, Angela, what should I do?

And before all the perfectionists out there write to me I want to remind you this is a simple strategy.

Angela: 12 on a two.

Dan: Tag one please.

Now, I make it.

If you have a soft hand of 13 to 15, then you always hit.

This is pretty obvious but another rule is if you have a soft 19 or more, you always stand.

Dan: All right, insurance closed.

Mike: Okay, what should I do?

We count the ace as 11 points.

Dan: 19, two winners.

What are you going to do?

Angela: 10 on four, I will double.

Mike: Because you outrank the dealer.

Dan: One card, 20.

Five, 13, 15, busted.

Mike: So, what should you do?

Angela: I should hit.

If you have a click the following article 13 to 15, you always hit.

And now what do you do?

Angela: Card 13 so I hit.

So, this is obvious.

If this were a two card 11, I will double.

So, with a hard nine, 10 or 11, composed of three or more cards, you always just hit.

Dan: And you lockout.

Angela: Double, 11 on everything except- Dan: An ace.

Angela: - an ace.

Mike: Wow, look at this.

Two hands where the player can split.

Those being twos, threes, sixes, sevens and nines.

Dan: And you get one card only.

Those are two 21s.

But those are good hands and you needed every bit of it, and you got it.

I have got a nine, and then it depends on the dealers off card.

If the dealer was showing a low card two through six, I would split these.

Angela: I double the 10 on the eight.

Angela: One more, double and double for that.

Mike: This hand gives me an opportunity to explain another rule about soft hands.

I explained before that if the player has a soft 13 to a fifteen, you hit no matter what.

Angela: I have a 16, oops on 17.

Now I have got 15, dealer has a low card so I stand.

What do you do Angela?

Angela: Oh I have got a soft 17 against dealer low card.

If you have a soft 16 through an eighteen and then dealer has a low card then you double.

The only time you surrender is 16 against a ten.

Mike: What kind of hand does what you say apply to?

Angela: Twos, threes, sixes, sevens, and nines.

Mike: Right, so you need to remember that, two, three, six, seven and nine.

Mike: You wizard of odds blackjack basic strategy calculator into that range but the dealer has a high card, so what do you do?

Angela: Revert to hit or stand.

Mike: Yes, this is the closest play there is in black jack, it happens all the time.

As I just explained if this wizard of odds blackjack basic strategy calculator two cards 16 against a ten you would surrender.

But you can only surrender on your initial hand.

Dan: Go down swing and sometimes you had no choice, you had a bad hand.

If you click the strategy like I said earlier you will get to 99.

Well thank you very much for being my student Angela.

Mike: And for you Dan to the dealer and good luck to all of you.

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Fermat and Pascal developed the concept of probability theory from correspondence started when the Chevalier de Mere asked them to settle a gambling problem.

Today, the authority on casino games is Michael Shackleford, the Wizard of Odds.

His website,provides data, advice, calculators, and simulators for players in hundreds of variations of casino games.

When the media needs an answer, they ask Mr.

He also follows his own advice; he is a successful professional gambler.

The casinos respect his knowledge to hire him to consult on game design, payouts, and discerning patterns in their operating results.

Hash Tag in Vegas Mike was nice enough to have breakfast with me recently in Las Vegas.

Shackleford is generally accessible to the media, I am lucky to get this block of his time.

He told an interviewer for LiveScience.

To be safe, I arrived fifteen minutes early.

He has salt-and-pepper hair, a sun-creased face, and is tall and fit.

He looks like a grown-up California kid he turns 50 in May who spends a lot of time outdoors on hobbies like hiking and bicycling.

What he does not look like is a man who earned his living in casinos or hunched over a computer.

He also loves travelling and has been a devotee of unicycling and juggling.

He also collects license plates and math problems.

He has a website displaying the math problems.

Blackjack and Baby Names Michael Shackleford was born in Pasadena, California, on May 23, 1965.

He grew up in Orange County, where he lived until 1992.

He received his B.

please click for source childhood Mike was interested in games, math, and odds.

Not surprisingly, when he turned twenty-one, he started playing 21.

Over the next several years, he took a series of wizard of odds blackjack basic strategy calculator examinations.

In 1992, he moved to Baltimore to work as an actuary at the headquarters of the Social Security Administration.

Note who has more chips.

This is how Michael killed time on camping trips.

Photo: Michael Shackleford The move East put his blackjack hobby on hold.

In 1997, while still at SSA, Mike demonstrated how his dexterity with complex data and sense of fun were never far apart.

With his wife expecting their first child, he wrote a program to sort Social Security card applicants by year of birth, gender, and first name.

Years later he wrote on Nameberry.

It was too good to keep to myself; I thought the whole country would want to see this.

The baby name information became a media sensation.

In early 2000, the site began accepting advertising, and soon after, he left SSA to work full time on the website and casino consulting.

His 2002 scoop on Las Vegas slot machine returns demonstrated his ability and instincts.

Shackleford could obtain and explain complex material.

He also had the imagination to anticipate and feed public appetites.

Unlike combinations of dice or cards, casinos can program returns on individual slot machines by changing the reel stripping.

Shackleford got access to casino par sheets, went to the casinos, and played the machines long enough to determine the reel-stripping settings.

No one had seen this information before.

Once available, everyone wanted to know it and quickly understood it.

It was like the baby-name list, for slot players.

Over a decade later, those rotten airport slots still get plenty of action.

The casino at the top of his nickel-slot survey, the Palms, splashed his conclusion read more billboards for years.

The infamous billboard Photo: WizardOfOdds.

In the years since, Mr.

Shackleford has earned the right to be considered a gambling authority.

His accessibility and adroitness with the media has multiplied exposure for his site, especially when a casino issue β or simply a question of long odds β enters the news cycle.

The website now has detailed rules and optimal strategy pages for approximately 200 games.

For blackjack players, the site covers 40 variations.

An additional series of game calculators allows players to calculate odds, returns, and strategy for any casino variations later introduced.

The page notes Faro was played in Reno as recently as 1985, but its height of popularity was in the Old West, when you could run into Wyatt Earp or Doc Holliday dealing the game.

All this advice is not static.

The game uses a 64-card deck a standard deck plus read article 11s, 12s, and 13s.

Following optimal strategy on a multicolored chartthe house edge is 1.

If you are at a Grosvenor property or on Royal Caribbean, should you make the Protection side bet, paying 5-to-1 with a multiplier increasing the payout to wizard of odds blackjack basic strategy calculator much as 200-to-1 for busting on your first two cards?

If you do, you are ceding the house an edge of 8.

The Player How does the Wizard of Odds find time to play games on his own account?

What https://clearadultskin.com/blackjack/blackjack-multiplayer-online-gratis-espaol.html he play?

As a further complication, Mike is ridiculously efficient about spending his time.

But I would go there if it was just making a right turn.

And I will plan my whole day so that I make a right turn instead of a left turn.

Still, he has played relatively little blackjack since moving to Las Vegas in 2001.

By then I was making good money from my web site and consulting, especially in comparison to what I could make at the tables.

One of his https://clearadultskin.com/blackjack/html5-blackjack.html games to analyze and play in a casino has been Pai Wizard of odds blackjack basic strategy calculator Tiles.

It is a complicated game with rules like Pai Gow with a touch of Baccarat and game equipment like Mah Jong or Dominoes.

Shackleford for several reasons.

First, it has rarely been analyzed, so it provided him a new and challenging puzzle for developing optimal strategy.

Based on his analysis, a player plays nearly even with the house and occasionally remarkable dollar blackjack in vegas join a small edge.

Second, he gets a kick out of being one of the relatively few non-Asians at the table.

Third, the game is fun when played at a casino with friends, giving him a break from his mostly solitary pursuits in gambling.

As a bettor, Shackleford has focused over the last several years on sports betting, specifically NFL games.

Photo: Michael Shackleford He will bet other sports if he finds the right opportunity.

The profusion of online sports books must be a giant amusement park to Michael Shackleford.

He told me about one situation where he was so successful that the site β and every other Internet casino β stopped offering the bet.

However, if you sell too many, then it becomes a good value for the player.

They should be increasing the price on an exponential basis, but most places incorrectly do it on a geometric basis.

I calculated at the time that a fair price to buy 5 extra points was 233.

So, I was getting a 3.

It may not sound like much, but I was betting every game, and both sides on most of them.

He rarely had a losing day.

This was not a feat of inside information or experience scouting and handicapping the NBA.

It came from recognizing and exploiting the opportunity the site provided.

He made no attempt to disguise his strategy or identity.

Almost immediately, all the sites stopped taking that kind of bet.

The Advisor Mike started his gaming consulting business even before he moved to Las Vegas.

The number wizard of odds blackjack basic strategy calculator game designers has multiplied over the last few decades.

The number of casinos, especially online, has also exploded.

Only a small amount of his consulting has been for land-based casinos.

A main area of his consulting has concerned game design and testing.

They always want to see more math.

When that happens, they hire Mr.

Shackleford to figure it out and explain it to them.

Usually, the result is less obvious and requires analyzing mountains of data.

He described one casino that had a bad month in table games and asked him if, based on the results, they were doing something wrong.

He reviewed results from every shift, then every pit, then every table, and then from every player.

One player got lucky in blackjack.

Mike said it should be doing the opposite, because encouraging him to play more was its best chance to win back that money.

Perhaps I should have expected this from a famously methodical analyst of games.

Beating casinos or joining them is riskier business than even Michael Shackleford can make it appear.

In May wizard of odds blackjack basic strategy calculator, despite nearly fifteen years as a successful operator of WizardOfOdds.

Never mind that WizardOfOdds.

Instead of having advertisers pay an account at, say, Bank of America, he had to accept the money initially at a Cyprus bank.

He had to eat the loss and continue transacting with another Cypriot bank, which apparently decided it could simply ignore his requests to withdraw money.

In September 2014, he sold WizardOfOdds.

Based on his initial experience with the new owners, he has declared that he hopes to stay on even wizard of odds blackjack basic strategy calculator />He also finds himself in the crossfire continue reading the continuing war between casinos and players.

Because he advises casinos, some players consider him a defector.

I look at it like the wolf and the sheepdog in the Looney Tunes cartoons.

We can be friends but once we punch our time cards and the whistle blows, we work against each other.

When it blows again and we punch out, we go back to being friends.

As an extra tool at Mr.

Michael Craig is an author, journalist, and lawyer.

He has written four books, including The Professor, the Banker, and the Suicide King: Inside the Richest Poker Game of All Time.

Follow him on MikeCraigIsAmok and.

This article is part of his collaboration with and on the lives and games of smart, interesting risk takers.