BlackJack: 9,9 better than 10,10?
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This wizardofodds webite gives all the expected payouts for everyplay:
/games/blackjack/appendix/1/
(cant post the full link as I do not yet have 20 posts!)
1) In the "Player Expected Returns By Splitting" section it seems to say that against ANY dealer upcard, splitting 9's ALWAYS has a higher expected payout than splitting 10's. How is this possible? Surely having a 10 is always better than a 9 - especially as you can hit blackjack with your 10's.
Hope this makes sense!
Edit
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We are onto page 4 of the discussion. I don't expect people to read through 4 pages before posting so I thought I'd paste the best & most common answers here and my thoughts on them. I have also deleted my second question as it has been lost in the discussion, I will post it again in a seperate thread.
You shouldn't split TT
Correct. However this is not the question, and definitely not the answer.
No, but seriously, you should be comparing Splitting TT to Standing TT, not Splitting TT to Splitting 99
Well, I am comparing splitting TT to spitting 99... Sorry?
Good Answer 1
Quote: mustangsallyi think the double down rule makes the difference
see what the evs are for no double after split
and that might be where it is at
A 9 can double on an A and a 2
not the 10
Sally
This answer looks promising! Certainly better Doubling Down chances on a 9 could make the difference.. I will look into it more, would be interested to hear other people's thoughts.
Good Answer 2
Quote: sabre
It's a good question, my guess is it's because the expected return for the split is calculated assuming you continue to resplit if possible. In the case of 99v6 for example, the resplit is the optimal play. In the case of TTv6, the resplit drags down the overall EV of the play.
In other words, I suspect that splitting TTv6 has a higher ev than splitting 99v6 IF you don't resplit on the TTv6 when dealt another T. The number in the table you cite however, most likely assumes that you continue to resplit up to the maximum 3 times.
In other other words, if you assumed no resplits, then the EV for splitting TTv6 would be higher than splitting 99v6. Obviously, the EV for standing on TTv6 is higher than both. This is my assumption, I haven't actually run any numbers.
Again, a thought provoking answer. I completely understand what you are saying about re-splitting, however I'm guessing this isn't the answer (it might be, though!). The "infinite deck" means that no matter how many times you split Ts, you are not removing Ts from the deck. If you can only split 3 times you are just as likely to hit more TTs.
RS expanded upon this, suggesting if you keep resplitting TT then you never end on 20 (except t-2-8 etc). Again, thought provoking, but still doesn't feel like the right answer. The optimal play AFTER splitting TT would be to stick on TT. So, surely it would be calculated as taking the optimal play after the split rather than "you did this stupid thing last time, you will prob do it again"
Example of "not my question"
Quote:Infinite deck my a$$.
I have never played against an infinite deck ( I don't play online ).
Straight Basic Strategy ( for a relative beginner ), which sounds like the OP question;
I have assumed (for hundreds of thousands of played hands ) that the difference in splitting 9,9 and 10,10 is the remaining cards in the shoe, not tracking the cards gone by, just the average over the long haul. I would love for you to prove me wrong, but I'd have to go over to GF to fully express myself when you do.
Respectfully, 2F
This is actually a nice example of why it isnt my question. I'm not interested in ACTUAL GAME PLAY, or any kind of optimal strategy. I'm also not interested in playing vs Infinite Decks. The point is, this is a math questions in the Math sub-forum.
I'm not asking if I should, simply why I would get a less return splitting 10's vs 9's? Surely this suggests that you are better being dealt your first card as a 9, than being dealt a 10.
Quote: WizardChrisespecially as you can hit blackjack with your 10's.
In the rule variants that I've encountered, if you split 10s and get dealt an ace, that is not always paid out as a 3:2 blackjack, but as an even money 21.
Also,
A pair of tens=20, almost certainly a winning hand. Split it and you could end up with a couple of rubbish hands. But a pair of 9s is only a moderately good hand so there is more to be gained by splitting it.
Double on hitting 2 on a 9: surely this is the same as hitting a 1 on a 10? You could double, especially if it doesnt pay 3:2 after split
Edit: OnceDear
Im not comparing splitting 10s to standing on them. Simply splitting 10s to splitting 9s 🙂
Quote: WizardChrisI'm not comparing splitting 10s to standing on them. Simply splitting 10s to splitting 9s 🙂
Hmmm. I think I get what you are saying, but you do need to consider the damage you do to your hand by splitting tens which is more than the damage of not splitting 9s. Remember that splitting nines you could end up with two darned good 19s compared to one moderately good 18. Split two tens, you have a weak chance of getting one or more 21s but a strong chance of getting one or more rubbish hands.
That's part of your error. 20 is usually a winner. 18 is often a loser.Quote: WizardChris
Im not comparing splitting 10s to standing on them.
For that reason, you split 9s but not 10s.
Sigh, dear Wizard Chris,Quote: WizardChrisFor a bit more info: Im not really interested in the best play, Im trying to understand the maths. It's really just because I don't understand why/how you can get a better payout from essentially holding 2 hands starting with a 9 in each than 10 in each. Even without blackjacks etc having a 10 should always be better.
This question reminds me of the the very first one I asked here on the Forums.
They beat the crap out of me, so we have apparently become kinder and gentler over time.
Or you asked the question more politely ( very true ).
The maths have been done, repeatedly. The decisions are often close, so close as to become negligible without considering other factors at play in the shoe, but they have been checked and double checked by the best of the best.
Your post shows you are thinking, thinking is a very good thing.
Welcome to the Forums.
+1Quote: TwoFeathersATLThe maths have been done, repeatedly. The decisions are often close, so close as to become negligible without considering other factors at play in the shoe, but they have been checked and double checked by the best of the best.
Your post shows you are thinking, thinking is a very good thing.
Welcome to the Forums.
Quote: TwoFeathersATLSigh, dear Wizard Chris,
This question reminds me of the the very first one I asked here on the Forums.
They beat the crap out of me, so we have apparently become kinder and gentler over time.
Or you asked the question more politely ( very true ).
The maths have been done, repeatedly. The decisions are often close, so close as to become negligible without considering other factors at play in the shoe, but they have been checked and double checked by the best of the best.
Your post shows you are thinking, thinking is a very good thing.
Welcome to the Forums.
Thanks for your reply! I don't doubt that their maths is correct, I just don't understand! My only goal is to understand it.
Also everyone seems to be missing my second question 🙁
Im sure 90% of people will keep telling me not to split 10s, not realising that this is not my question, and that I dont disagree. Im just hoping someone comes along who can explain why split 9s win more often than split 10s 🙂
Quote: WizardChrisIm just hoping someone comes along who can explain why split 9s win more often than split 10s 🙂
I haven't read the WoO article that you are referring to, so I'm just speculating here:
Are you certain that it says that split 9s win more often than split 10s, or could it be saying that act of splitting 9s increases your EV more than the act of splitting 10s does?
Quote: DocI haven't read the WoO article that you are referring to, so I'm just speculating here:
Are you certain that it says that split 9s win more often than split 10s, or could it be saying that act of splitting 9s increases your EV more than the act of splitting 10s does?
Yes, pretty sure! Eg. Expected return vs dealer 7:
Splitting 9,9: +0.36
Splitting 10,10: +0.29
Odd, right??
Edit: FYI the return on standing:
9,9: +0.40
10,10: +0.77
Hence why you should split 9s and not 10s - but doesnt explain why split 9s perform better than split 10s
Ken Smith explains it better. Hope you get the answer you looking for.
if you split the 9's your trading in a 18 which only beats one dealer hand (17) lots of upside to this split you could get two doubles with a deuce or 19's with tens, 20's with an ace, also if you pull crap you can still hit.
Simply put there is just more potential good that can happen splitting the 9's.
not oddQuote: WizardChrisYes, pretty sure! Eg. Expected return vs dealer 7:
Splitting 9,9: +0.36
Splitting 10,10: +0.29
Odd, right??
i think the double down rule makes the difference
see what the evs are for no double after split
and that might be where it is at
A 9 can double on an A and a 2
not the 10
this site may help
http://www.bjstrat.net/cgi-bin/cdca.cgi
splits and double downs also increases a player's session risk of ruin (Shhhhhh)
just thinking out loud
vacations get long with too much sun and food
Sally
But, big but, only considering standard Basic Strategy.
Removing two 10 point cards from the shoe is not the same as removing two 9 point cards from the shoe,
And you haven't specified the various rules of the game you are playing, not specifically ;-)
Cheers! 2F
no U B wrong here 100%.Quote: TwoFeathersATLIt's the difference between the remaining cards in the shoe, it's that simple.
U due knot understand the
OP
question
it is really a simple question
not at all unusual for humans to not understand a written question.
start over
the Wizard table is infinite deck
there are no 10s missing
something not offered but math folks use it for and easy answer(s)
Quote: WizardChrisFor a bit more info: Im not really interested in the best play, Im trying to understand the maths. It's really just because I don't understand why/how you can get a better payout from essentially holding 2 hands starting with a 9 in each than 10 in each. Even without blackjacks etc having a 10 should always be better.
It's a good question, my guess is it's because the expected return for the split is calculated assuming you continue to resplit if possible. In the case of 99v6 for example, the resplit is the optimal play. In the case of TTv6, the resplit drags down the overall EV of the play.
In other words, I suspect that splitting TTv6 has a higher ev than splitting 99v6 IF you don't resplit on the TTv6 when dealt another T. The number in the table you cite however, most likely assumes that you continue to resplit up to the maximum 3 times.
In other other words, if you assumed no resplits, then the EV for splitting TTv6 would be higher than splitting 99v6. Obviously, the EV for standing on TTv6 is higher than both. This is my assumption, I haven't actually run any numbers.
Quote: TwoFeathersATLIt's the difference between the remaining cards in the shoe, it's that simple.
But, big but, only considering standard Basic Strategy.
Removing two 10 point cards from the shoe is not the same as removing two 9 point cards from the shoe,
And you haven't specified the various rules of the game you are playing, not specifically ;-)
Cheers! 2F
The tables the OP quoted are assuming an infinite deck.
Quote: FranciscoGo to blackjackinfo.com---" why splitting 10 is a bad move"
Ken Smith explains it better. Hope you get the answer you looking for.
This has nothing to do with the OP's question.
You are comparing Apple ( 9,9) from orange (10,10) . You have to compare standing on 9,9 and splitting 9,9 .and then standing on 10,10 compare to splitting on 10,10 .
9,9 v 7. Standing ev 0.4 splitting ev 0.36
10,10 v7. Standing ev 0.77 splitting ev 0.29
You are comparing Apple ( 9,9) from orange (10,10) . You have to compare standing on 9,9 and splitting 9,9 .and then standing on 10,10 compare to splitting on 10,10 .
9,9 v 7. Standing ev 0.4 splitting ev 0.36
10,10 v7. Standing ev 0.77 splitting ev 0.29
Quote: FranciscoNow, I diagnosed your confusion.
You are comparing Apple ( 9,9) from orange (10,10) . You have to compare standing on 9,9 and splitting 9,9 .and then standing on 10,10 compare to splitting on 10,10 .
9,9 v 7. Standing ev 0.4 splitting ev 0.36
10,10 v7. Standing ev 0.77 splitting ev 0.29
This is further away from what the OP was asking.
I have never played against an infinite deck ( I don't play online ).
Straight Basic Strategy ( for a relative beginner ), which sounds like the OP question;
I have assumed (for hundreds of thousands of played hands ) that the difference in splitting 9,9 and 10,10 is the remaining cards in the shoe, not tracking the cards gone by, just the average over the long haul. I would love for you to prove me wrong, but I'd have to go over to GF to fully express myself when you do.
Respectfully, 2F
Quote: TwoFeathersATLInfinite deck my a$$.
I have never played against an infinite deck ( I don't play online ).
Straight Basic Strategy ( for a relative beginner ), which sounds like the OP question;
I have assumed (for hundreds of thousands of played hands ) that the difference in splitting 9,9 and 10,10 is the remaining cards in the shoe, not tracking the cards gone by, just the average over the long haul. I would love for you to prove me wrong, but I'd have to go over to GF to fully express myself when you do.
Respectfully, 2F
From the page the OP quoted.
"The following tables display expected returns for any play in blackjack based on the following rules: dealer stands on a soft 17, an infinite deck, the player may double after a split, split up to three times except for aces, and draw only one card to split aces. Based on these rules, the player's expected value is -0.511734%."
The numbers he is questioning were calculated assuming an infinite deck. You cannot answer his question by talking about card removal effects.
Quote: sabreFrom the page the OP quoted.
"The following tables display expected returns for any play in blackjack based on the following rules: dealer stands on a soft 17, an infinite deck, the player may double after a split, split up to three times except for aces, and draw only one card to split aces. Based on these rules, the player's expected value is -0.511734%."
The numbers he is questioning were calculated assuming an infinite deck. You cannot answer his question by talking about card removal effects.
My bad. I apologize to all concerned.
I have yet to see a discussion of an infinite anything produce a discourse that I should be involved in. I missed the 'infinite' notation. If I were infinitely aware, most of my posts, of all my posts here, would not have been.
Since you understand the OP's question better than I did, perhaps you could answer it for him, if you have the spare time. I would like to hear your take on it, I'm being serious now, I know that is a rare thing.
It's a good question, my guess is it's because the expected return for the split is calculated assuming you continue to resplit if possible. In the case of 99v6 for example, the resplit is the optimal play. In the case of TTv6, the resplit drags down the overall EV of the play.
In other words, I suspect that splitting TTv6 has a higher ev than splitting 99v6 IF you don't resplit on the TTv6 when dealt another T.
In other other words, if you assumed no resplits, then the EV for splitting TTv6 would be higher than splitting 99v6. Obviously, the EV for standing on TTv6 is higher than both. This is my assumption, I haven't actually run any numbers.
From the wizard blackjack appendex 1: expected value for every play review. 9,9 split v every 2-7 banker up cards are better than 10,10 split v 2-7 banker up cards.
But you have compare standing on 9,9 v spltting on 9,9 against 2-7 banker up cards. And then compare 10,10 standing v 10,10 splitting against 2-7 banker up cards. A big difference in EV.
That's why I said you are comparing Apple to orange .
Mr. WizardChris, does it makes sense to you? Is this the question you try to find the answer ?
Quote: FranciscoI think my guess is correct .
From the wizard blackjack appendex 1: expected value for every play review. 9,9 split v every 2-7 banker up cards are better than 10,10 split v 2-7 banker up cards.
But you have compare standing on 9,9 v spltting on 9,9 against 2-7 banker up cards. And then compare 10,10 standing v 10,10 splitting against 2-7 banker up cards. A big difference in EV.
That's why I said you are comparing Apple to orange .
Mr. WizardChris, does it makes sense to you? Is this the question you try to find the answer ?
I have said this and so has the OP -- there is no "standing" that it must be compared to. Look at the EV's yourself. They are what they are. They are NOT the difference in EV from BS to 'this' play. BS is simply playing whichever decision has the greatest EV for a hand matchup -- however, that has nothing to do with the question asked.
As far as why splitting TT vs splitting 99 is lower EV....I really don't know, but can only guess -- drawing a 2 would give you huge +EV for a double down when splitting 9's....but splitting T's never allows for that scenario.
If the chart was generated with a "keep re-splitting TT" [which I really doubt], then that could actually make sense why the EV is lower than splitting 99. You got almost a 1/3 shot of getting dealt another T, per T dealt. And, if you always resplit TT, then you cannot end a hand with TT -- therefore, you're going to have a significantly lower chance of having a 20, one of the best hands in BJ, for this matchup, giving that TT is impossible to end with. The only 20's you'd end with would be stuff like T-2-8, T-3-7, T-6-2, T-2-A-7, T-2-2-6, etc.
But, I have a feeling the chart was generated with a "make decision X, then follow basic strategy after that", for instance, splitting 88vs6 or 99vs6, the EV would include the probability of getting dealt another 9 and re-splitting, while it would not include the probability of getting dealt another T and resplitting the TT, because splitting TT is not proper basic strategy.
Quote: RSI have said this and so has the OP -- there is no "standing" that it must be compared to. Look at the EV's yourself. They are what they are. They are NOT the difference in EV from BS to 'this' play. BS is simply playing whichever decision has the greatest EV for a hand matchup -- however, that has nothing to do with the question asked.
You got it! Thanks for taking the time Francisco, but comparing splitting to not splitting simply isnt the question.
There have been quite a few answers since my last visit (in the UK - timezones!) so I will go through them one by one. As we are onto page 4 I will also be editing this reply into the original post as I doubt people will read through 4 pages before joining the discussion :)
Quote: mustangsallyi think the double down rule makes the difference
see what the evs are for no double after split
and that might be where it is at
A 9 can double on an A and a 2
not the 10
this site may help
link removed
splits and double downs also increases a player's session risk of ruin (Shhhhhh)
just thinking out loud
vacations get long with too much sun and food
Sally
This answer looks promising! Certainly better Doubling Down chances on a 9 could make the difference.. I will look into it more, would be interested to hear other people's thoughts.
Quote: sabre
It's a good question, my guess is it's because the expected return for the split is calculated assuming you continue to resplit if possible. In the case of 99v6 for example, the resplit is the optimal play. In the case of TTv6, the resplit drags down the overall EV of the play.
In other words, I suspect that splitting TTv6 has a higher ev than splitting 99v6 IF you don't resplit on the TTv6 when dealt another T. The number in the table you cite however, most likely assumes that you continue to resplit up to the maximum 3 times.
In other other words, if you assumed no resplits, then the EV for splitting TTv6 would be higher than splitting 99v6. Obviously, the EV for standing on TTv6 is higher than both. This is my assumption, I haven't actually run any numbers.
Again, a thought provoking answer. I completely understand what you are saying about re-splitting, however I'm guessing this isn't the answer (it might be, though!). The "infinite deck" means that no matter how many times you split Ts, you are not removing Ts from the deck. If you can only split 3 times you are just as likely to hit more TTs.
RS expanded upon this, suggesting if you keep resplitting TT then you never end on 20 (except t-2-8 etc). Again, thought provoking, but still doesn't feel like the right answer. The optimal play AFTER splitting TT would be to stick on TT. So, surely it would be calculated as taking the optimal play after the split rather than "you did this stupid thing last time, you will prob do it again"
Quote: TwoFeathersATL
Infinite deck my a$$.
I have never played against an infinite deck ( I don't play online ).
Straight Basic Strategy ( for a relative beginner ), which sounds like the OP question;
I have assumed (for hundreds of thousands of played hands ) that the difference in splitting 9,9 and 10,10 is the remaining cards in the shoe, not tracking the cards gone by, just the average over the long haul. I would love for you to prove me wrong, but I'd have to go over to GF to fully express myself when you do.
Respectfully, 2F
Quite a few times it has been pointed out that this is not the question, but this is actually a nice example of why it isnt. I'm not interested in ACTUAL GAME PLAY, or any kind of optimal strategy. I'm also not interested in playing vs Infinite Decks. The point is, this is a math questions in the Math sub-forum.
The problem is that you base your question on the data from Wizard' blackjack appendex 1 .so, you have to ask Wizard himself the question. The Math sub- forum, indeed.
Based simply upon previous Wizard posts, 'He's watching You'. Now that doesn't mean he's watching every minute, he really does have a real life outside the Forums. Hopefully he's off camel wrangling in Tangiers, or tiger stalking in Asia. But the Wiz, I believe, checks in here occasionally. You asked a question, you might get answered by the Wiz, you might not. Let's face it, your question does not represent a hoop he has to jump thru. Bah! You might get lucky, he still cares about the ravings and goings-on here ;-)Quote: WizardChrisHow can I ask him directly? On WoO website ot says to put questions on the forums!
If one assumes you continue to make the wrong play then there is a 4/13 chance on each 10 to get another, thus re-splitting the second time costs (standing 20 - splitting 10's). This gets closer to wizard's numbers and might explain, because you have such a good chance of throwing money away by re-splitting, why "splitting 10's" is a worse position to be than "splitting 9's".
Assuming you don't re-split 10's these are the approximate numbers I got (a) UK rules so A's 10's not the same as wizard's (b) I assumed you didn't re-split if it wasn't correct.
| Upcard | Split 9's | Split 10's | Stand 20 |
|---|---|---|---|
| A | -.377 061 | -.502 608 | .146 095 |
| 2 | .195 110 | .365 000 | .639 987 |
| 3 | .257 780 | .412 176 | .650 272 |
| 4 | .322 445 | .460 940 | .661 050 |
| 5 | .390 646 | .512 517 | .670 360 |
| 6 | .470 030 | .575 590 | .703 959 |
| 7 | .399 554 | .513 817 | .773 227 |
| 8 | .233 552 | .395 907 | .791 815 |
| 9 | -.078 742 | .233 059 | .758 357 |
| 10 | -.241 509 | -.107 123 | .434 958 |
Sorry for the incorrect use of the apostrophe!
Quote: charliepatrickI'm not sure about the wizard's figures as splitting 10's should be better than doubling a hard total of 10. In the former you have two bets running (one on each 10), in the latter you have two bets running (on a 10). Thus, infinite deck, doubling 10 should be identical to splitting 10's if you subsequently stood (assuming no re-split). The reason splitting should be better than doubling is after splitting 10's you can hit any 10 2 whereas if you double you have to stand.
I had to read this a couple of times, but it completely makes sense to me! Really interesting observations, would love to hear Wizards take on it.
Quote: WizardChrisThanks for replies on how to contact Mr Wizard - for now I'll just hang tight and see if he swings by :)
I had to read this a couple of times, but it completely makes sense to me! Really interesting observations, would love to hear Wizards take on it.
The Wizard prefers not to provide details publicly about his schedule or movements. However, he is not available at the moment. Please be patient, and I will ensure he sees this thread. That in itself does not ensure a response, but I suspect that it will; this is the kind of question he particularly enjoys.
Agreed especially as it's counter-intuitive - I had also written to him summarising the question and the links. But as you say he is very busy.Quote: beachbumbabsThe Wizard ...this is the kind of question he particularly enjoys.
Shame someone has down-rated the thread - it was doing so well!
Probably because the Wizard hasn't weighed in yet! ;)Quote: WizardChrisShame someone has down-rated the thread - it was doing so well!
I wouldn't worry about the star-rating. 99.54% of the posters here don't use it. I do think you have come up with an interesting question, and I would also be interested in the answer.
Quote: wizardYes, I assume that if the player splits once then he will keep doing it as long as he can resplit. ...., you're welcome to quote me.
Charlie asked me about this while I was gone and he quoted me correctly. In that appendix, I assume that if the player splits once, then he wants to split that situation and will keep doing it as long as he can. So, if he splits tens, he will keep doing it as long as he can, which can be a lot of hands when it comes to tens, depressing the expected value.
In that appendex, the rule says you can only split 3 times. Same with 10,10 .
I have one question: after split, you follow basic strategy for all the decisions on hit, stand, double, etc ?Example. First 10, you are deal with a 2, then you hit when the dealer's up card is 2,3 , and stand when up cards are 4,5,6 ? Thank you.
