Try our new blackjack hand calculator.

One project that has been on my "to do" list for at least a decade is a good blackjack hand analyzer. Something that would give the exact expected values of any given play for any common set of rules, including with more than two cards in the player's hand. Such a calculator would be perfect for playing blackjack online. As a reminder, the basic strategy gives only the best average advice for a given hand. There are exceptions based on the composition of the hand itself. I knew it would be a difficult job and beyond my abilities. JB was always capable of doing it, but at any given time I always had something of higher priority for him to do, or the site wasn't healthy enough financially to pay him to do it.

The good news is that the wait is over! The new boss had JB create one and it is ready for beta testing. So, please try out our new Blackjack Hand Calculator.

As our faithful guinea pigs, please provide your feedback, comments, suggestions, and especially corrections.

The question for the poll is what do you give the calculator on a 0 to 4 scale?

All due credit and praise to JB for what I think is an outstanding job.

A+ , gold star

Very nice calculator.

Next project a PG Tiles number of hands against banking breakeven chart please? :)

I had programmed one of these at home myself about 10 years ago but with slightly less flexibility on the rules (and none of the sexy GUIs that your has.) I know which hands are the most troublesome to calculate so I tried those on your calculator and your calculator crashed repeatedly on this hand:

Dealer: 2
Player: 2-2

8 Decks
Dealer hits Soft 17
All other options at default.

Your calculator repeatedly gave me an error message on this hand. I also got an error message on the 1-Deck version of this hand once before it was successfully calculated on the next attempt

I have a version of this that also calculates one deck BJ hands after seeing another hand played out first (i.e., cards missing from the deck).

EDIT: The calculators I have programmed previously only calculated for the initial two cards, not for multiple cards -so your calculator is a bit more ambitious. Hats off to you for what you are attempting to do -and have achieved so far!

Quote: gordonm888

Your calculator repeatedly gave me an error message on this hand.

Odd. That hand worked fine for me.

Okay, I also was able to get your calculator to calculate this hand successfully on a re-try, but only after considerable lag. I used an online stopwatch to time your calculator on this hand and recorded a calculation time of 11.16 seconds -but the actual calc time was slightly longer than that since I could not start the calculator and timer simultaneously.

Could it be conceivable that the lengthy calculation time is a more of a problem for remote users and that they might possibly "time out" on some intermediate server? I.e., that some intermediate server is judging your site as unresponsive because it hasn't responded after, say, 10 seconds? This is not a subject area where I have much competency.

I'm just trying to be helpful. It would be interesting to hear from other forum-ites whether they experience any problem with this particular hand. It might also be useful if you could use a stopwatch to time the calculator on this hand from your site and see if you experience the same 11-12 second latency that I am reporting.

Very Cool !

I had never given this any deep thought, but it looks like player 10-10 vs dealer upcard 8 is better than player 10-10 vs dealer upcard 6 !

Now, one observation:

If you just want to compare a couple of hands to each other, you have to hit the calculate button over again. Any reason not to automatically calculate and update the table if you change one of the dealer's cards ?

Quote: gordonm888

...It would be interesting to hear from other forum-ites whether they experience any problem with this particular hand...

The first time I tried that hand with those rules I didn't receive an error... but the calculation did take noticeably longer than any of the other hands I looked at.

The second time I tried it, when I was planning on timing it, I "timed out" and saw that "ERROR" box on the screen. Note that I do have a very fast internet connection.

Quote: EdCollins

Ed, how did you do at chess? (Maybe reply in the chess thread).

Quote: gordonm888

I had programmed one of these at home myself about 10 years ago but with slightly less flexibility on the rules (and none of the sexy GUIs that your has.) I know which hands are the most troublesome to calculate so I tried those on your calculator and your calculator crashed repeatedly on this hand:

Dealer: 2
Player: 2-2

8 Decks
Dealer hits Soft 17
All other options at default.

Your calculator repeatedly gave me an error message on this hand. I also got an error message on the 1-Deck version of this hand once before it was successfully calculated on the next attempt

nice work JB
i gave it a try in google chrome and 1st attempts were all successful

but my video capture program caught the error at abouts 1:58
edit
Sally

Okay, I am about to offer some minor technical criticisms of this calculator. I do this with a genuine sense of dread because I know that the Wizard is a very careful and thoughtful calculator of gaming odds and that he is virtually perfect at stating the limitations of his calculations in a way that is fair and accurate. I have enormous respect for him and his very impressive body of work.

But peer review is healthy, and the Wizard has asked for comments. I will make some comments realizing that there is some chance that the Wizard is correct and I am wrong (because Dadgum it, the Wizard is almost always correct).

1. The first issue with the calculator is simple - it cannot be used to help with online BJ in the way that he claims for certain kinds of hands. If you have a hand where the first two cards are a small pair, and the right strategy is to split the cards -then you can no longer simulate your BJ hand after you have split the pair. The calculator always assumes that whatever player's cards are defined beyond the first two cards are to be used in hitting the UNSPLIT first two cards.

So, if the game is 1Deck BJ and the players hand is 3-3 vs a dealer's 3, the calculator tells us to split the pair of 3s. So far, so good. But what happens after I do that and the next card is the case 3? Is it best to continue to split the 3s? Or is is better to hit the 3-3 as a 6? The calculator cannot help us with this because it does not allow us to simulate that situation.

2. Playing a small hand like an A-2, or a small pair like a 2-2 or a 3-3, has a complexity to it beyond the initial decision. You must decide what to do if and when you make a soft 17 or a soft 18 during the course of playing your hand. And the numbers calculated for splitting and hitting hands like A-2 and 2-2 should (in my opinion) be calculated based on making the right decisions in scenarios where the play of the hands includes decisions on soft 18 and soft 17.

Let me give an example to show what I am talking about. Use the Wizard's calculator to calculate these 4 hands, all ONE DECK, DEALER HITS SOFT 17 and all versus a dealer's 10: A-7 vs 10, A-5-2 vs 10, A-3-3-A vs 10 and A-2-2-2-A vs 10.

You will see see, using the Wiz's own calc, that the Basic strategy of HITTING a soft 18 against a 10 is optimal for the first two hands but that STANDING on soft 18 is optimal for the last two hands. The problem, as I perceive it is that the the calculator correctly calculates A-2-2-2-A vs 10, but when calculating "A-2 vs 10" it assumes that any emergent soft 18 will be HIT, when calculating the EV for the HIT scenario.

The result is that the value for the return on hitting hands like A-2 vs 10 appear to be lower than "Perfect Play" EV by roughly 0.004, because of non-optimal composition-dependent Soft 18 decisions (also non-optimal 16 vs 10 decisions, see footnote below.) Is this a big deal? No, in my judgment. It has no effect on the strategy decision regarding how to play this hand, and it is a relatively small "error." But the calculated EV's or "returns" are given to six digits of accuracy! And if you undertake to publish a calculator on the web I suggest that it should either (1) calculate the correct numbers, or (2) the website should explicitly state the limitations of the calculator even when the limitations only compromise a small number of combinations of hands and game rules (like single deck). Currently, I question whether this website calculator meets either of those criteria.

Consider for a moment what the calculator does when calculating the return on splitting 2's against a 10 (Single Deck, etc. as before). Imagine that whilst HITTING the split pair of twos, all four 2s and all four 3's have come out and the 2nd hand is 2-3-2-A. Would any decent BJ player HIT the soft 18 in the second hand given that there is zero chance of getting a 2 or a 3 and making a 20 or 21 with the next card? No, they would not. And there would be a very substantial -EV for making that decision. Yet the Wiz's calculator appears to fold that large negative EV decision into its calculation of SPLIT 2's vs a 10. That just bothers me, because I feel that the calculated EV's are compromised by this methodology choice.

So that's it. The calculator does not simulate multi-card hands when a pair has been split. And certain calculations of EV for HITTING and Splitting are suspected to be unreliable by a small amount, particularly for single deck hands in which the first two cards are small and the dealer's up-card is a 10, A, 9, 8 or 7.

Footnote: Another type of non-optimal composition-dependent decision that is compromising your calculation of 6-digit EVs is the 16 vs 10 decision (and similar decisions such as 15 vs 10, 16 vs 9 and Ace, etc.) When starting out with split 2s or A-2 and hitting those -by the time you have a hard 16 or 15, you are quite likely to have a used a disproportionate number of cards in the range A-5 and your use of a Basic Strategy decision such as hitting a hard 16 vs 10 is going to involve a substantially negative EV -which causes your 6 digit EV to be wrong (or misleading) in the 3rd digit , or perhaps even in the second digit. I know its difficult to do these calculations right (because I've struggled with this myself in developing my own personal calculators) but I wanted to raise this topic with you.

Working with calculator further I got this prompt error message in a tiny fraction of a second.

http://i58.tinypic.com/amqiyv.jpg

Quote: Wizard

<snip>a good blackjack hand analyzer.
Something that would give the exact expected values <snip>

i like what JB did, i say it is good
but really

how good and exact is it
in your opinion and compared to other programs similar?
(i mean after the bugs are worked out)


example:
6deck
H17
Dealer : K
Player: 10,9

STAND: +0.069444
Hit: -0.726389
Double: -1.452778

Blackjack Combinatorial Analyzer v1.60
STAND: -0.01361963456
Hit: -0.7476404232
Double: -1.4176109



ok
well
just checking
math
lots of it
i no no
Sally

What, IMO, would be a fabulous use for this tool, would be to incorporate this calculator into real game training scenario. Many training simulators only tell you if you made a good or bad play, and don't have the math to back it up.

Quote: mustangsally

example:
6deck
H17
Dealer : K
Player: 10,9

STAND: +0.069444
Hit: -0.726389
Double: -1.452778

Blackjack Combinatorial Analyzer v1.60
STAND: -0.01361963456
Hit: -0.7476404232
Double: -1.4176109

I stand by my calculator's results for that hand. They match the figures calculated by Wizard here as well as another online blackjack calculator here.

Quote: JB

I stand by my calculator's results for that hand.

well, of course i knew you would

Blackjack Combinatorial Analyzer v1.60 that i showed
i think by looking at the double value could not be correct
i mean lose -1 unit after a double?

but their online page looks like it matches your value(s) - for that hand - and others like 8,8
so that should make you both happier
http://www.bjstrat.net/cgi-bin/cdca.cgi

but as the Wizard says
"Something that would give the exact expected values"

how about close enough
thank you
Sally

When I have the ENHC option selected it still shows splits (but not doubles) against a 10 or A being correct (which would be right under American rules) that shouldn't.

Review Comments

1. I have checked the calculator for over 40 single-deck hands in which the player has a non-paired hand in the range of hard 8 to 20. For those hands I checked, I found no issues with the calculated values of EV for any of the player options. (I didn't check any European No-peek cases - I don't normally calculate those.) Way to go JB! Error-free calcs are not trivially easy to achieve.

2. The first time I used this calculator, I was confused when I set it to single-deck mode and I was evaluating hands such as Dealer: 2s, Player: 2s-2s where 's' signifies 'spades'. Of course, I understand that the suits are immaterial to the calculation, I am just saying it feels odd to see multiple identical cards when analyzing a single deck hand. I realize it would be needlessly cumbersome to give the user the option of picking cards of the same rank but different suits -I am not advocating that at all. Here are some possible workarounds:
- don't show suits at all, just show ranks
- at least make the dealer's cards of a different suit, such as Hearts - that would improve the situation a little bit, and it might also provide a more aesthetically-pleasing screen.

3. I tried to break the calculator in a couple of different ways and it performed well. My only comment based on this exercise was that the calculator allows me to define a single-deck player hand composed of 5 or more cards of the same rank without telling me that I've exceeded any limit. When I press the CALCULATE button for such a hand, an error message (ERR) appears, but the reason for the error is not stated. That's okay, I guess, but I prefer the way that your calculator handles the situation when a player's hand is defined to be K-Q-T.
- similarly, I am permitted to define a player's hand of 9 Aces for a 2 deck case and then calculate on it. I get the ERR message.
-LOL, I did learn that one should stand on a 16 vs. a dealer 7 in a four deck game when the 16 is made up of 16 Aces. What fun!

4. When I define a player hand of K-J, the calculator provides me a calculated EV for splitting the hand. Of course, the rules of BJ do not permit a player to split such a hand.

Quote: Kellynbnf

When I have the ENHC option selected it still shows splits (but not doubles) against a 10 or A being correct (which would be right under American rules) that shouldn't.

My apologies. The calculator doesn't actually compute splitting values; it uses a lookup table with Wizard's figures. ENHC figures aren't included in the lookup table and I completely overlooked that, so I have disabled ENHC for now.

Quote: gordonm888

the calculator allows me to define a single-deck player hand composed of 5 or more cards of the same rank without telling me that I've exceeded any limit. ... similarly, I am permitted to define a player's hand of 9 Aces for a 2 deck case and then calculate on it. I get the ERR message.

I chose to let it error on the back-end intentionally. For example, suppose you select 8 decks, enter 10 aces, and then change it to 1 deck. It's simpler to let the back-end catch this.

Quote: gordonm888

4. When I define a player hand of K-J, the calculator provides me a calculated EV for splitting the hand. Of course, the rules of BJ do not permit a player to split such a hand.

Most casinos do allow splitting of "unlike" 10-value cards (of course it's never right under BS to split tens whether or not they "match").

I have found a hand for which the calculator recommends the wrong strategy because of the programming short-cuts that have been taken.

The hand is Single Deck, American; 5-5-4-A vs. 10. The calculator results are Stand = - 0.550185 and HIT = - 0.554080. The recommended strategy, implied by the use of bold type font and the calculated EVs, is to STAND on 5-5-4-A vs 10

The best strategy with Single Deck 5-5-4-A vs. 10 is to "HIT until you make a Hard 16." In other words, HIT the 5-5-4-A and if you get an Ace, making a 16, then STAND. One does this because, as your calculator itself reveals:



thus choosing to HIT the 5-5-4-A-A vs 10 is a decision with a negative EV of approximately -0.079. There are dozens of basic strategy decisions that have less of an EV swing than 0.079.

Returning to the original hand: 5-5-4-A vs. 10

Stand	Hit (until 17)	Hit Until 16
- 0.550185	- 0.554080	- 0.549110

So, the best strategy, is to HIT until 16, not Stand. And if "HIT until 16 when you have 5-5-4 vs a 10", falls outside of single deck BJ Basic Strategy, I'm sorry. That's a failure of BJ Basic Strategy. But Hit until 16 is fundamentally and mathematically correct.

Now please brace yourself for a harsh statement: We do not need any more calculators on the internet that recommend non-optimal strategies and that have programming short-cuts that produce misleading or wrong results. Especially when said "misleading or wrong results" are displayed to 6 significant digits of accuracy under the banner of "The last word on gaming odds."

Quote: gordonm888

I have found a hand for which the calculator recommends the wrong strategy because of the programming short-cuts that have been taken.

The hand is Single Deck, American; 5-5-4-A vs. 10. The calculator results are Stand = - 0.550185 and HIT = - 0.554080. The recommended strategy, implied by the use of bold type font and the calculated EVs, is to STAND on 5-5-4-A vs 10

The best strategy with Single Deck 5-5-4-A vs. 10 is to "HIT until you make a Hard 16." In other words, HIT the 5-5-4-A and if you get an Ace, making a 16, then STAND. One does this because, as your calculator itself reveals:

5-5-4-A-A (=16) vs 10 is STAND = - 0.547553 and HIT = - 0.627072

thus choosing to HIT the 5-5-4-A-A vs 10 is a decision with a negative EV of approximately -0.079. There are dozens of basic strategy decisions that have less of an EV swing than 0.079.

Returning to the original hand: 5-5-4-A vs. 10

Stand	Hit (until 17)	Hit Until 16
- 0.550185	- 0.554080	- 0.549110

So, the best strategy, is to HIT until 16, not Stand. And if "HIT until 16 when you have 5-5-4 vs a 10", falls outside of single deck BJ Basic Strategy, I'm sorry. That's a failure of BJ Basic Strategy. But Hit until 16 is fundamentally and mathematically correct.

Now please brace yourself for a harsh statement: We do not need any more calculators on the internet that recommend non-optimal strategies and that have programming short-cuts that produce misleading or wrong results. Especially when said "misleading or wrong results" are displayed to 6 significant digits of accuracy under the banner of "The last word on gaming odds."

5-5-4-A vs. 10 is stand in single deck. Both online calculators linked to earlier in this thread agree. bj appendix 3a on WoO has composition dependent strategy for single deck.

The bottom of the page has video poker stuff. Was that intentional? I would think more BJ links would be better.

Quote:

5-5-4-A vs. 10 is stand in single deck. Both online calculators linked to earlier in this thread agree. bj appendix 3a on WoO has composition dependent strategy for single deck.

Wow, I cannot believe you misunderstood so completely the point that I was making.

When you define a (hard 15) 5-5-4-A vs 10 BJ hand as having only 2 options: STAND or HIT -and by "HIT" you mean "HIT until 17" - then everyone agrees that "STAND" is the best option. But those two options are not the complete universe of options. When the word HIT is used to mean "HIT until 17" - as all those appendices and calculators do - they are missing the even better option of "HIT until 16" for 5-5-4-A vs 10.

There is nothing fundamental about Hitting until 17. Math is math, and the cold equations say that hitting until 16 or higher (and then standing) is better with certain hands. There are other game strategy websites -for non-cash BJ variants that are played on-line for fun- that have published optimal BJ strategies with "HIT until 16" and "HIT until 15." It is surprising to me that game strategists for online just-for-fun games are so ahead of the casino BJ crowd on this.

I have publicly disagreed with

• J.B.'s calculator
• the Wizard's Appendix 3a, published on the internet
• Two other on-line BJ calculators
• another forum participant

regarding the optimum strategy for Single Deck 5-5-4-A vs 10.

I am asking the Wizard to please break his silence and provide a response on this topic. We all respect the Wiz for his 1st-class mind and understanding of gambling mathematics and I think his thoughts on this highly-pregnant topic are needed.

Quote: gordonm888

Quote:

5-5-4-A vs. 10 is stand in single deck. Both online calculators linked to earlier in this thread agree. bj appendix 3a on WoO has composition dependent strategy for single deck.

Wow, I cannot believe you misunderstood so completely the point that I was making.

When you define a (hard 15) 5-5-4-A vs 10 BJ hand as having only 2 options: STAND or HIT -and by "HIT" you mean "HIT until 17" - then everyone agrees that "STAND" is the best option. But those two options are not the complete universe of options. When the word HIT is used to mean "HIT until 17" - as all those appendices and calculators do - they are missing the even better option of "HIT until 16" for 5-5-4-A vs 10.

There is nothing fundamental about Hitting until 17. Math is math, and the cold equations say that hitting until 16 or higher (and then standing) is better with certain hands. There are other game strategy websites -for non-cash BJ variants that are played on-line for fun- that have published optimal BJ strategies with "HIT until 16" and "HIT until 15." It is surprising to me that game strategists for online just-for-fun games are so ahead of the casino BJ crowd on this.

Your logic is correct, but the situation you described in your post is impossible in real casino play. Imagine you got dealt a 5,5 vs a dealer up card 10 during the first round of a single deck game, you hit for a 4, then you hit again for an Ace. Now you have 5,5,4,A vs dealer 10, and it's still your turn to play. Now, you ONLY have two options, you either stand, or you hit, that's it. Then standing would be the correct choice in this case.

For your 3 option scenario, again image you have a 5,5,4,A vs a dealer 10, the dealer would have to ask you: (option 1)would you like to stand? or (option 2)would you like to hit and I will give you any card from the rest of the deck other than an Ace? OR (option 3)would you like to hit and I will give you an Ace? Then yeah, follow your logic, option 3 is the best play.

Quote: gordonm888

I have publicly disagreed with

• J.B.'s calculator
• the Wizard's Appendix 3a, published on the internet
• Two other on-line BJ calculators
• another forum participant

regarding the optimum strategy for Single Deck 5-5-4-A vs 10.

I am asking the Wizard to please break his silence and provide a response on this topic. We all respect the Wiz for his 1st-class mind and understanding of gambling mathematics and I think his thoughts on this highly-pregnant topic are needed.

I stand by my calculator's results. The blackjack calculators at these independent sources (source 1, source 2) also agree with my calculator.

What figures did you calculate?

Quote: Numpkin

Your logic is correct, but the situation you described in your post is impossible in real casino play. Imagine you got dealt a 5,5 vs a dealer up card 10 during the first round of a single deck game, you hit for a 4, then you hit again for an Ace. Now you have 5,5,4,A vs dealer 10, and it's still your turn to play. Now, you ONLY have two options, you either stand, or you hit, that's it. Then standing would be the correct choice in this case.

For your 3 option scenario, again image you have a 5,5,4,A vs a dealer 10, the dealer would have to ask you: (option 1)would you like to stand? or (option 2)would you like to hit and I will give you any card from the rest of the deck other than an Ace? OR (option 3)would you like to hit and I will give you an Ace? Then yeah, follow your logic, option 3 is the best play.

What I am saying is

when you have a 5-5-4-A you have an initial decision: you can either hit it or stand. Let us call this Decision A.

If you hit it,one of these things will happen:

you get a 7,8,9 or ten-value card and you bust.

or, you get a 6 and make a 21 and either stand or hit again (Decision B)

or, you get a 5 and make a 20 and either stand or hit again (Decision C)

or, you get a 4 and make a 19 and either stand or hit again (Decision D)

or, you get a 3 and make an 18 and either stand or hit again (Decision E)

or, you get a 2 and make a 17 andeither stand or hit again (Decision F)

or, you get an Ace and make a 16 and either stand or hit again (Decision G)

Now clearly, whenever the normal player makes a 17-21 in BJ they decide to stand -that is so second-nature that we don't even think of it as a decision. So Decisions B through F are always STAND

But what about Decision G? What would you do if you hit 5-5-4-A vs 10 and received an Ace? Would you stand on your 16 (5-5-4-A-A)? Or would you hit it? I claim that which way you go on Decision G will be be the determining factor in determining what is optimum for decision A.

Basic Strategy says that a player should hit a hand 12-16 versus 10 and to keep hitting it until you make a 17 or higher. That is "Hit Until 17." Because JP assumes Basic Strategy in his calculator, he calculates the EV or return for HITTING a 5-5-4-A vs 10 with the assumption that when receiving an Ace and making a 16 (5-5-4-A-A) the player will follow Basic Strategy for Decision G and HIT the hand a 2nd time.

JB's calculator follows the same methodology for a simple hand such as 10-2 vs 10. The calculated return for HITTING a 12 vs 10 assumes that the player will continue to HIT until 17 or HIGHER. So JB's calculated EV's for hitting the 12 vs 10 assume that if the player gets a 2 and makes a 14 that he will HIT again and keep hitting until reaching 17 or higher. That is standard methodology and is used in the other 2 on-line calculators and in the calculations underlying Appendix C.

Quote:

Now you have 5,5,4,A vs dealer 10, and it's still your turn to play. Now, you ONLY have two options, you either stand, or you hit, that's it. Then standing would be the correct choice in this case.

Obviously, I don't agree with this. By your way of thinking, if you have a Hard 5, a 2-3, vs. a Dealer 10 then you have ONLY two options- "you either stand, or you hit, that's it. " By my way of thinking, the best option is usually "Hit Until 13" for a hard 5 vs. 3.

The Wizard has already stated that J.B. is using the assumption that Basic Strategy rules are assumed to be followed in calculating the return on various kinds of strategy options. And my original point was that this methodology ground-rule causes a problem on this particular hand 5-5-4-A vs 10 because it is better to HIT the 5-5-4-A (Vs STAND) only if the assumption is that the player will stand on their 16 in the scenario in which he/she receives an Ace.

Quote: JB

I stand by my calculator's results. The blackjack calculators at these independent sources (source 1, source 2) also agree with my calculator.

What figures did you calculate?

First, the numbers I have calculated were presented in this thread about 5-7 posts ago.

Second, I have spent a great deal of time (in the above posts) explaining the specific methodology groundrule in your calculator that I disagree with. I quote specific results from your calculator and discuss concepts and ideas. So, I'm a bit frustrated that you did not even read the preceding posts and simply insist that you "stand by your calculator."

Third. The same methodology ground rule that I am challenging is used in the other two calculators. I really am trying to bring up something new that you may not have thought about before, it is a detail in methodology. Again, it is necessary for you and Mr Shackleford to read the preceding posts. I would really prefer that Mr Shackleford himself review this issue and respond, because I am raising a mathematical methodology issue that I think he would be interested in.

For 1 deck, H17, DOA, MGP's BJ CA gives the following for the hand A455,

Stand EV = -0.5501846064283
Hit EV = -0.5540797403871

It follows that it is correct to stand.

Reminds me of 7,7 vs. T.

Because it may be useful if you want to do this by hand, for the hand AA455 (draw an Ace to the previous),

Stand EV = -0.5818621384778
Hit EV = -0.6320326846602

I am certain that MGP's program is recursive, meaning that it computes the current hand's EV based on the EVs for the exact hand compositions in all future decisions from a given starting hand. That's pretty much how you do it anyway.

Quote: gordonm888

First, the numbers I have calculated were presented in this thread about 5-7 posts ago.

Second, I have spent a great deal of time (in the above posts) explaining the specific methodology groundrule in your calculator that I disagree with. I quote specific results from your calculator and discuss concepts and ideas. So, I'm a bit frustrated that you did not even read the preceding posts and simply insist that you "stand by your calculator."

Third. The same methodology ground rule that I am challenging is used in the other two calculators. I really am trying to bring up something new that you may not have thought about before, it is a detail in methodology. Again, it is necessary for you and Mr Shackleford to read the preceding posts. I would really prefer that Mr Shackleford himself review this issue and respond, because I am raising a mathematical methodology issue that I think he would be interested in.

I think I understand -- you don't like how the return for hitting is based on recursively optimal strategy because it assumes the player has optimal strategy memorized for every possible situation, which of course cannot be the case.

When I first started writing the blackjack calculator, I considered tackling hitting by using a "hit until soft X or hard Y" (or "hit until X" if no soft total is possible) approach, because it seemed simpler and more informative.

I also have always assumed that all calculators and return tables have the underlying assumption that for every move in every situation, be it the optimal move or not, all subsequent move(s) are optimal.

Quote: teliot

For 1 deck, H17, DOA, MGP's BJ CA gives the following for the hand A455,

Stand EV = -0.5501846064283
Hit EV = -0.5540797403871

It follows that it is correct to stand.

Reminds me of 7,7 vs. T.

Because it may be useful if you want to do this by hand, for the hand AA455 (draw an Ace to the previous),

Stand EV = -0.5818621384778
Hit EV = -0.6320326846602

I am certain that MGP's program is recursive, meaning that it computes the current hand's EV based on the EVs for the exact hand compositions in all future decisions from a given starting hand. That's pretty much how you do it anyway.

By the way, JB's calculator doesn't agree with that second set of numbers that you quoted. For One deck, H17 and 554AA vs 10, JB's calculator gets STAND = - 0.547553 and HIT = - 0.627072.

I agree with Teliot and Redjack that one needs to do the calculation in a way that anticipates and optimizes the decisions in possible multicard hands that result from the current hand. That is how I have always done it on my personal "calculators" over the years and is precisely the point I have been trying to make.

But my impression (apparently misstaken) was that this calculator wasn't using composition-dependent optimal strategy in the recursion when calculating the return on HITTING. See my post, immediately following, to JB.

Quote: JB

I think I understand -- you don't like how the return for hitting is based on recursively optimal strategy because it assumes the player has optimal strategy memorized for every possible situation, which of course cannot be the case.

When I first started writing the blackjack calculator, I considered tackling hitting by using a "hit until soft X or hard Y" (or "hit until X" if no soft total is possible) approach, because it seemed simpler and more informative.

JB - I just noticed this post of yours. Sorry I didn't see it sooner.

If your calculator's determination of the return on HIT is indeed based on "recursively optimized strategy" then I absolutely agree with what you have done. I agree with you, RedJack and Teliot that the calculator should indeed show the maximum theoretical return based on "perfectly optimized play." IMO, the issue of whether or not a player can memorize the detail strategy rules is not relevant -we all memorize a tremendous amount of stuff in our lives (The Star Spangled Banner, names and stats of professional athletes, etc) and we have the option to memorize strategy rules in BJ to whatever level of detail we want.

I somehow developed the impression from the Wizard's initial post in this thread that your calculator was using Basic Strategy rules (i.e., HIT on 16 vs 10) rather than composition-dependent rules (i.e., STAND on 5-5-4-A-A vs 10) in its recursively-optimized logic. If you are indeed using composition-dependent optimal decisions in calculations on the return for HITTING, then I drop my objections and apologize for raising such a dust storm. You have done a very nice job with the calculator.

As I understand it, the last frontier in BJ mathematics would be to work out a method for handling split pairs analytically (rather than Monte Carlo.) This is clearly a very hard problem and I think your use of a look-up table to utilize the Wizard's former work is a "best-available" work-around and a prudent decision.

Quote: gordonm888

What I am saying is

when you have a 5-5-4-A you have an initial decision: you can either hit it or stand. Let us call this Decision A.

If you hit it,one of these things will happen:

you get a 7,8,9 or ten-value card and you bust.

or, you get a 6 and make a 21 and either stand or hit again (Decision B)

or, you get a 5 and make a 20 and either stand or hit again (Decision C)

or, you get a 4 and make a 19 and either stand or hit again (Decision D)

or, you get a 3 and make an 18 and either stand or hit again (Decision E)

or, you get a 2 and make a 17 andeither stand or hit again (Decision F)

or, you get an Ace and make a 16 and either stand or hit again (Decision G)

Now clearly, whenever the normal player makes a 17-21 in BJ they decide to stand -that is so second-nature that we don't even think of it as a decision. So Decisions B through F are always STAND

But what about Decision G? What would you do if you hit 5-5-4-A vs 10 and received an Ace? Would you stand on your 16 (5-5-4-A-A)? Or would you hit it? I claim that which way you go on Decision G will be be the determining factor in determining what is optimum for decision A.

Basic Strategy says that a player should hit a hand 12-16 versus 10 and to keep hitting it until you make a 17 or higher. That is "Hit Until 17." Because JP assumes Basic Strategy in his calculator, he calculates the EV or return for HITTING a 5-5-4-A vs 10 with the assumption that when receiving an Ace and making a 16 (5-5-4-A-A) the player will follow Basic Strategy for Decision G and HIT the hand a 2nd time.

JB's calculator follows the same methodology for a simple hand such as 10-2 vs 10. The calculated return for HITTING a 12 vs 10 assumes that the player will continue to HIT until 17 or HIGHER. So JB's calculated EV's for hitting the 12 vs 10 assume that if the player gets a 2 and makes a 14 that he will HIT again and keep hitting until reaching 17 or higher. That is standard methodology and is used in the other 2 on-line calculators and in the calculations underlying Appendix C.



Obviously, I don't agree with this. By your way of thinking, if you have a Hard 5, a 2-3, vs. a Dealer 10 then you have ONLY two options- "you either stand, or you hit, that's it. " By my way of thinking, the best option is usually "Hit Until 13" for a hard 5 vs. 3.

The Wizard has already stated that J.B. is using the assumption that Basic Strategy rules are assumed to be followed in calculating the return on various kinds of strategy options. And my original point was that this methodology ground-rule causes a problem on this particular hand 5-5-4-A vs 10 because it is better to HIT the 5-5-4-A (Vs STAND) only if the assumption is that the player will stand on their 16 in the scenario in which he/she receives an Ace.

I disagree with your logic on multiple decisions.

The "decisions" you listed A-G, those are not decisions, those are possible outcomes resulting from your decision on either hitting or standing on your hand of 5,5,4,A. When given the decision on your hand, you only have the choice to hit or stand, and the outcome of your decision is unknown (as you listed A-G).

Basic strategy does not tell you to hit until 17, it gives you the correct decision based on your hand verse the dealers hand. It tells you to stand on 17 and above simply because the EV on standing is greater than the EV on hitting. Say you have a 13, the BS tells you to hit, if you get a 2 and make a 15, the BS tells you to hit again and so on. The BS does not tell you to hit until 17 on a 13, it tells you it is correct decision to hit a 13, and based on the outcome of that decision, it tells you to either hit or stand.

Similar logic can be applied to your 2,3 vs 3 example, the BS tells me to hit that hand. Based on the outcome of that decision, BS tells me to hit again or to stand. Again my choices on a 2,3 is either to hit or stand (assuming you don't double), that's the only 2 decisions you can make at that moment. "Hitting until 13" is a desired outcome of the particular hand, it may take multiple decisions to achieve.

Wizard,

Do the calculator values take into account dealer checking for BJ?

10,10 vs Ace shows an EV of +65% but that can't be possible if the dealer is getting blackjack 30.7% of the time.

EV = -1*.307+1*.693 = 40% EV, which is also too high since I'm not accounting for pushes with a 9 and 3/4/5 card 20s/21s.

I'm getting an EV of 35% for this hand in my calculator assuming the dealer stands on soft 7.

Am I mathing wrongly?

Something I noticed playing with the calculator..

If you select J and A, against a dealer J - standing has a +1 EV.
But the interesting thing is hitting apparently has a + 0.1 EV. How would hitting have a positive EV?

Quote: TwelveOr21

Something I noticed playing with the calculator..

If you select J and A, against a dealer J - standing has a +1 EV.
But the interesting thing is hitting apparently has a + 0.1 EV. How would hitting have a positive EV?

TwelveOr21,

Well, if you hit, you're hitting on a hard 11 vs. the J, so why wouldn't the EV be positive?

Dog Hand

Blackjack Hand Calculator https://wizardofodds.com/games/blackjack/hand-calculator/

My first random attempt to use the calculator was a Dealer 5 vs. Player 7 & 9 for 16.
Surrender is -0.500000
Stand is -0.164136
Hit is -0.450710
Double Down is -0.901420

So if I have a $120 bet out there, a surrender would lose me half my bet (-$60), a Stand would lose me on average $20, a Hit would lose me on average $54, and a double down would lose me on average $108.

My next attempt is a Dealer 6 against a 7 & 4, hard 11.
Surrender is -0.500000
Stand is -0.119352
Hit is +0.336525
Double Down is +0.673051

So if I have a $120 bet out there, a surrender would lose me half my bet (-$60), a Stand would lose me on average $14.32, a Hit would win me on average $40, and a double down would win me on average $80.

Awesome Mike!