Blackjack: Best stand on a no possible bust?
September 5th, 2011 at 1:53:47 PM
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Hey Wizard, I have been following your original site for years. Great site and forum!
In a typical Vegas game of blackjack, when dealt an initial hand total of 3-10 what are the best circumstances for standing and still beating the dealer? So even though there is no chance of busting, the player stands pat on his low total. ( Insane or just the sort of confidence a woman loves? haha)
At first I examined the strategy table, but it would seem the simple answer is that you want to stand pat in the circumstances that would most likely lead to a dealer bust. So the 'ballsy stand' would be anything 3-10 against a dealer 6? Is it that simple or more complicated? I made the assumption that even a ballsy player would still split aces or hit on an 11 total.
Bonus question would be, how would be, what is the house edge on the "Ballsy Stand Simple Strategy"?
In a typical Vegas game of blackjack, when dealt an initial hand total of 3-10 what are the best circumstances for standing and still beating the dealer? So even though there is no chance of busting, the player stands pat on his low total. ( Insane or just the sort of confidence a woman loves? haha)
At first I examined the strategy table, but it would seem the simple answer is that you want to stand pat in the circumstances that would most likely lead to a dealer bust. So the 'ballsy stand' would be anything 3-10 against a dealer 6? Is it that simple or more complicated? I made the assumption that even a ballsy player would still split aces or hit on an 11 total.
Bonus question would be, how would be, what is the house edge on the "Ballsy Stand Simple Strategy"?
September 5th, 2011 at 2:21:32 PM
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I agree with your name.
September 5th, 2011 at 6:44:50 PM
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Fair enough, if it makes you feel better, your response is what I would expect from one with your name.
In all seriousness, I am interested in an answer to my question. I understand the math behind perfect strategy and I am curious if my intuition is close to the real answer. You can program yourself by memorizing a strategy table, but to expand you mind you must apply what you learned to a new circumstance. Anyway, Im hoping the experts chime in.
In all seriousness, I am interested in an answer to my question. I understand the math behind perfect strategy and I am curious if my intuition is close to the real answer. You can program yourself by memorizing a strategy table, but to expand you mind you must apply what you learned to a new circumstance. Anyway, Im hoping the experts chime in.
September 5th, 2011 at 6:50:20 PM
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I am an expert.
September 5th, 2011 at 7:57:54 PM
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Quote: IdiotWheelFair enough, if it makes you feel better, your response is what I would expect from one with your name.
In all seriousness, I am interested in an answer to my question. I understand the math behind perfect strategy and I am curious if my intuition is close to the real answer. You can program yourself by memorizing a strategy table, but to expand you mind you must apply what you learned to a new circumstance. Anyway, Im hoping the experts chime in.
Anything less than 17 in BJ is Zero, so as you said, you would only win a dealer bust. Your total, whether it is 3 or 16, is meaningless if you are standing pat. So just look at the Dealer's Up Card Bust Percentage.
https://wizardofodds.com/blackjack/appendix2.html
So if you are wondering how you'd do, you'd get slaughtered even if the dealer had a 5 or 6 up every time. You'd only win about 40-42% of hands, depending on the number of decks. I don't quite understand the bonus question. Are you always standing on 3-11, or just when it's a 6? Also, you said Ballsy "simple strategy". What strategy are you talking about? A strategy to give the house some extra edge but to look cool?
September 6th, 2011 at 11:16:23 AM
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Quote: matildaI am an expert.
Lol this reminds me of "can i speak to your manager?" "I AM the manager." "sh!t."
September 6th, 2011 at 11:24:35 AM
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Thanks for the charts cclub79, that is very helpful.
So, like you said, on a multi-deck table the dealer will bust >42% of the time with a 6 showing. Looking at the charts it would only make sense to ever stand on a dealer 5 or 6. Lets narrow it down to just standing on dealer 6 for simplicity.
So with a dealer 6 showing, a player who always stands pat will win 42% of the time. Obviously, that is the best you can do by standing pat.
I guess the better question would be, WHAT are you giving up by NOT applying simple or perfect strategy when the dealer has 6? Obviously you would do better then 42%. How ever you would still be faced with the possibility of busting yourself, or losing to the dealer.
There must be at least one square on the perfect strategy chart where if you stood pat against a dealer 6 your odds are maximized (obviously never being as great as with perfect strategy ). I imagine it must be a dealer 6 versus a player, 4, 5, or 6.
I apologize again for the question, this is more of an "interesting probability/math" question as opposed to a "maximize your gambling returns" question.
So, like you said, on a multi-deck table the dealer will bust >42% of the time with a 6 showing. Looking at the charts it would only make sense to ever stand on a dealer 5 or 6. Lets narrow it down to just standing on dealer 6 for simplicity.
So with a dealer 6 showing, a player who always stands pat will win 42% of the time. Obviously, that is the best you can do by standing pat.
I guess the better question would be, WHAT are you giving up by NOT applying simple or perfect strategy when the dealer has 6? Obviously you would do better then 42%. How ever you would still be faced with the possibility of busting yourself, or losing to the dealer.
There must be at least one square on the perfect strategy chart where if you stood pat against a dealer 6 your odds are maximized (obviously never being as great as with perfect strategy ). I imagine it must be a dealer 6 versus a player, 4, 5, or 6.
I apologize again for the question, this is more of an "interesting probability/math" question as opposed to a "maximize your gambling returns" question.
September 6th, 2011 at 11:33:41 AM
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As requested, the extended Basic Strategy for Ballsiness:
Ballsy: Stand on a total of 3-10.
Ballsier: Split your 20 and double down in the dark.
Ballsiest: Announce to that lady beside you that the ducks are coming, and ask to 'hit me three times' on your 15.
Balls of fire and nuclear waste: Point at the pit boss yelling 'hey look, there's an ugly asshole standing behind you!' and when the dealer turns around to look, quickly take a peek at her hole card.
Let me know how it turns out, buy me a drink if you get laid.
Ballsy: Stand on a total of 3-10.
Ballsier: Split your 20 and double down in the dark.
Ballsiest: Announce to that lady beside you that the ducks are coming, and ask to 'hit me three times' on your 15.
Balls of fire and nuclear waste: Point at the pit boss yelling 'hey look, there's an ugly asshole standing behind you!' and when the dealer turns around to look, quickly take a peek at her hole card.
Let me know how it turns out, buy me a drink if you get laid.
September 6th, 2011 at 11:36:11 AM
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Quote: IdiotWheel'ballsy stand' would be anything 3-10
you always hit with 11 or less, why not? and if you have 8 or better you have a much better hand a very good percentage of the time. You should only fear hitting a 12 or better with at least one card
the next time Dame Fortune toys with your heart, your soul and your wallet, raise your glass and praise her thus: “Thanks for nothing, you cold-hearted, evil, damnable, nefarious, low-life, malicious monster from Hell!” She is, after all, stone deaf. ... Arnold Snyder
September 6th, 2011 at 1:46:24 PM
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These Blackjack appendices are filled with neat tables! I was perusing this one:
https://wizardofodds.com/blackjack/appendix5.html
And had another thought. If the goal was to find a best case scenario to stand on a 3-10, there are really two approaches. As discusses above, you could figure out the optimal situation choose to stand when the dealer is most likely to bust and lose.
Alternatively, you could choose a 3-10 player hand in which the player return is already very poor. In this case the ballsy (fine...stupid) stand would just make that poor hand that much worse. This would be the pessimist play.
Looking at the appendix 5 chart: It looks like for single digit player hands, the worst hand is a Player 6 Versus a Dealer 10. This has a player return of a poor -.3377 when simple strategy is applied. How much worse can that get if you stubbornly stand pat with that 6!?
thoughts?
https://wizardofodds.com/blackjack/appendix5.html
And had another thought. If the goal was to find a best case scenario to stand on a 3-10, there are really two approaches. As discusses above, you could figure out the optimal situation choose to stand when the dealer is most likely to bust and lose.
Alternatively, you could choose a 3-10 player hand in which the player return is already very poor. In this case the ballsy (fine...stupid) stand would just make that poor hand that much worse. This would be the pessimist play.
Looking at the appendix 5 chart: It looks like for single digit player hands, the worst hand is a Player 6 Versus a Dealer 10. This has a player return of a poor -.3377 when simple strategy is applied. How much worse can that get if you stubbornly stand pat with that 6!?
thoughts?
September 6th, 2011 at 2:41:30 PM
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Quote: IdiotWheel. This has a player return of a poor -.3377 when simple strategy is applied. How much worse can that get if you stubbornly stand pat with that 6!? thoughts?
-.5404
September 6th, 2011 at 3:57:55 PM
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I fail to see what's ballsy about doing something inane. Ballsy is hitting a hard 18 against a dealer ten. Or splitting ten versus a dealer 6. Both maybe dumb moves, but occasionally they pay off. Standing when you can't bust... you've changed nothing.
"Then you can admire the real gambler, who has neither eaten, slept, thought nor lived, he has so smarted under the scourge of his martingale, so suffered on the rack of his desire for a coup at trente-et-quarante" - Honore de Balzac, 1829
September 6th, 2011 at 4:04:43 PM
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Quote: IdiotWheelThese Blackjack appendices are filled with neat tables! I was perusing this one:
https://wizardofodds.com/blackjack/appendix5.html
And had another thought. If the goal was to find a best case scenario to stand on a 3-10, there are really two approaches. As discusses above, you could figure out the optimal situation choose to stand when the dealer is most likely to bust and lose.
Alternatively, you could choose a 3-10 player hand in which the player return is already very poor. In this case the ballsy (fine...stupid) stand would just make that poor hand that much worse. This would be the pessimist play.
Looking at the appendix 5 chart: It looks like for single digit player hands, the worst hand is a Player 6 Versus a Dealer 10. This has a player return of a poor -.3377 when simple strategy is applied. How much worse can that get if you stubbornly stand pat with that 6!?
thoughts?
You're looking at the wrong charts. Appendix 9 on WoO is what you want.
For the common 6DH17 game, hitting on player 6 (player holds 4, 2) vs. dealer 10 is about -0.339. Standing is -0.541. If you want to derive the "best case scenario" for standing on a 3-10, look at the Appendix 9 charts and find the row where standing leads to the smallest loss compared to the proper play.
"In my own case, when it seemed to me after a long illness that death was close at hand, I found no little solace in playing constantly at dice."
-- Girolamo Cardano, 1563
September 6th, 2011 at 4:41:47 PM
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Quote: MathExtremistYou're looking at the wrong charts. Appendix 9 on WoO is what you want.
For the common 6DH17 game, hitting on player 6 (player holds 4, 2) vs. dealer 10 is about -0.339. Standing is -0.541. If you want to derive the "best case scenario" for standing on a 3-10, look at the Appendix 9 charts and find the row where standing leads to the smallest loss compared to the proper play.
His -.3377 came from appx. 5---S17, infinite deck. Nevertheless we agree on -.54.
September 6th, 2011 at 4:54:21 PM
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Right, but the Wiz doesn't have an infinite-deck table for the EV of every action based on player's two vs. upcard (unless I missed it somewhere). If I'm reading properly, the OP wanted to find the "least bad" time to stand on 3-10 vs. dealer X. Not sure why you ever would, but those charts are how you'd answer the question.
"In my own case, when it seemed to me after a long illness that death was close at hand, I found no little solace in playing constantly at dice."
-- Girolamo Cardano, 1563
September 6th, 2011 at 5:30:48 PM
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Quote: IdiotWheel
I guess the better question would be, WHAT are you giving up by NOT applying simple or perfect strategy when the dealer has 6? Obviously you would do better then 42%. How ever you would still be faced with the possibility of busting yourself, or losing to the dealer.
Well, you are off on that one. You will never bust on a dealer 6 with basic strategy. When you have 3-11, you are taking a "free card". There is no way your hand can get worse (you already have "zero") and you can not bust. But several or many cards will make your hand much, much better. Still, even if you end up with 12, 13, or anything else, you are not going to take another card (following Basic Strategy) so you will never do worse than your 3-11.
September 6th, 2011 at 6:54:25 PM
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Great point cclub.
On Mathextremist's advice I perused the appendix 9 tables.
Working with the first table. I used excel to calculated the delta between the stand and hit expected returns for a dealer 5 and 6. Then I sorted from least to greatest. The first no bust player hand with the lowest delta expectation between hit and stand is: Dealer 6 vs. Player 4,2. Not surprisingly dealer 5 vs player, 4,2 is not too far behind. Im sure some one will chime in if I am interpreting this wrong.
sort excerpt:
DealerPlayer Stand Hit Double Probability Delta
5 10,2 -0.161126 -0.188759 -0.377518 0.00367661 0.027633
5 7,5 -0.157776 -0.190982 -0.381963 0.00088085 0.033206
5 8,4 -0.158944 -0.192389 -0.384778 0.00091915 0.033445
5 9,3 -0.160055 -0.19404 -0.38808 0.00091915 0.033985
6 7,A 0.222598 0.178453 0.356906 0.00091915 0.044145
5 7,A 0.198998 0.151132 0.302263 0.00091915 0.047866
6 10,2 -0.121479 -0.170569 -0.341138 0.00367661 0.04909
6 7,5 -0.118699 -0.173201 -0.346403 0.00091915 0.054502
6 8,4 -0.119502 -0.174273 -0.348546 0.00091915 0.054771
6 9,3 -0.120539 -0.175904 -0.351809 0.00091915 0.055365
5 10,3 -0.160699 -0.254211 -0.508423 0.00367661 0.093512
5 9,4 -0.159657 -0.253758 -0.507517 0.00091915 0.094101
5 7,6 -0.158476 -0.259536 -0.519071 0.00091915 0.10106
5 8,5 -0.158596 -0.259746 -0.519492 0.00088085 0.10115
6 10,3 -0.121086 -0.239032 -0.478064 0.00367661 0.117946
6 9,4 -0.120173 -0.238607 -0.477213 0.00091915 0.118434
6 7,6 -0.122651 -0.246688 -0.493376 0.00088085 0.124037
6 4,2 -0.114844 0.009881 -0.212121 0.00091915 0.124725
6 8,5 -0.119409 -0.244828 -0.489656 0.00091915 0.125419
5 4,2 -0.154631 -0.026761 -0.291219 0.00091915 0.12787
On Mathextremist's advice I perused the appendix 9 tables.
Working with the first table. I used excel to calculated the delta between the stand and hit expected returns for a dealer 5 and 6. Then I sorted from least to greatest. The first no bust player hand with the lowest delta expectation between hit and stand is: Dealer 6 vs. Player 4,2. Not surprisingly dealer 5 vs player, 4,2 is not too far behind. Im sure some one will chime in if I am interpreting this wrong.
sort excerpt:
DealerPlayer Stand Hit Double Probability Delta
5 10,2 -0.161126 -0.188759 -0.377518 0.00367661 0.027633
5 7,5 -0.157776 -0.190982 -0.381963 0.00088085 0.033206
5 8,4 -0.158944 -0.192389 -0.384778 0.00091915 0.033445
5 9,3 -0.160055 -0.19404 -0.38808 0.00091915 0.033985
6 7,A 0.222598 0.178453 0.356906 0.00091915 0.044145
5 7,A 0.198998 0.151132 0.302263 0.00091915 0.047866
6 10,2 -0.121479 -0.170569 -0.341138 0.00367661 0.04909
6 7,5 -0.118699 -0.173201 -0.346403 0.00091915 0.054502
6 8,4 -0.119502 -0.174273 -0.348546 0.00091915 0.054771
6 9,3 -0.120539 -0.175904 -0.351809 0.00091915 0.055365
5 10,3 -0.160699 -0.254211 -0.508423 0.00367661 0.093512
5 9,4 -0.159657 -0.253758 -0.507517 0.00091915 0.094101
5 7,6 -0.158476 -0.259536 -0.519071 0.00091915 0.10106
5 8,5 -0.158596 -0.259746 -0.519492 0.00088085 0.10115
6 10,3 -0.121086 -0.239032 -0.478064 0.00367661 0.117946
6 9,4 -0.120173 -0.238607 -0.477213 0.00091915 0.118434
6 7,6 -0.122651 -0.246688 -0.493376 0.00088085 0.124037
6 4,2 -0.114844 0.009881 -0.212121 0.00091915 0.124725
6 8,5 -0.119409 -0.244828 -0.489656 0.00091915 0.125419
5 4,2 -0.154631 -0.026761 -0.291219 0.00091915 0.12787
September 6th, 2011 at 9:47:06 PM
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Quote: cclub79Well, you are off on that one. You will never bust on a dealer 6 with basic strategy.
Well, to be precise, you should actually Hit 10,2 vs. 6 in Single Deck game and Stand Soft 17: https://wizardofodds.com/blackjack/appendix3.html. It is a "fine point in basic strategy" but it is still basic strategy.
September 8th, 2011 at 9:56:28 AM
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Thanks help and pointers guys! This settled a discussion I was having with my wife. If someone like Austin Powers was playing BJ, his unfounded confidence would allow him to stand on any no-bust hand. But what would be the smartest-dumbest play...
Anyway, I will be in Vegas this weekend and I might even try it. Im sure I will get icey glares from people who think that I didnt "take" my card and screwed up the entire cosmos. But now I will be able to explain to them that it really was the smartest play if you intend to stand on a no-bust hand. I am sure to make friends!
Anyway, I will be in Vegas this weekend and I might even try it. Im sure I will get icey glares from people who think that I didnt "take" my card and screwed up the entire cosmos. But now I will be able to explain to them that it really was the smartest play if you intend to stand on a no-bust hand. I am sure to make friends!
September 8th, 2011 at 10:20:38 AM
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Quote: IdiotWheelBut now I will be able to explain to them that it really was the smartest play if you intend to stand on a no-bust hand.
Yep, like shooting your foot with the smallest caliber gun is the smartest play if you've already decided to shoot your own foot...
"So as the clock ticked and the day passed, opportunity met preparation, and luck happened." - Maurice Clarett
September 17th, 2011 at 12:42:57 AM
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I have no data to back any of this up (too lazy to look, and it seems like someone has already posted a table), but I'll use some logic:
If you are simply trying to figure out what low hand (4-10 as you can't get a 3, it would be a 13) is the most likely to be a winner I would first say:
It doesn't matter one bit, if the dealer busts any standing hand wins, and if the deal does not bust, any one of these hands loses. So what your hand consists of does not matter. But then the card counter in me realized no, this isn't quite the case. If your hand consists of a pair of 5's, those 5's are unavailable to the dealer. 5's are generally helpful to the dealer as they take stiffs (12-16) and turn them into standing hands (17-21). A dealer can never bust by drawing a 5 or less. As a result, 5's have the highest "effect of removal" (EOR). A hand consisting of a pair of 5's versus a dealer's 6 would be the most likely to win.
Now, if you're trying to compare the EV of the hand standing versus the EV of the hand doing the correct basic strategy play, I would say that an 11 consisting of a 6 and a 5 versus a dealer's 6 would be the most costly hand to stand on versus correct BS. For the same effect of removal reasons and the huge opportunity cost of NOT doubling the best hand that is not a natural blackjack.
Hope that answers your question.
If you are simply trying to figure out what low hand (4-10 as you can't get a 3, it would be a 13) is the most likely to be a winner I would first say:
It doesn't matter one bit, if the dealer busts any standing hand wins, and if the deal does not bust, any one of these hands loses. So what your hand consists of does not matter. But then the card counter in me realized no, this isn't quite the case. If your hand consists of a pair of 5's, those 5's are unavailable to the dealer. 5's are generally helpful to the dealer as they take stiffs (12-16) and turn them into standing hands (17-21). A dealer can never bust by drawing a 5 or less. As a result, 5's have the highest "effect of removal" (EOR). A hand consisting of a pair of 5's versus a dealer's 6 would be the most likely to win.
Now, if you're trying to compare the EV of the hand standing versus the EV of the hand doing the correct basic strategy play, I would say that an 11 consisting of a 6 and a 5 versus a dealer's 6 would be the most costly hand to stand on versus correct BS. For the same effect of removal reasons and the huge opportunity cost of NOT doubling the best hand that is not a natural blackjack.
Hope that answers your question.
September 17th, 2011 at 12:44:47 AM
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Quote: thecesspitI fail to see what's ballsy about doing something inane. Ballsy is hitting a hard 18 against a dealer ten. Or splitting ten versus a dealer 6. Both maybe dumb moves, but occasionally they pay off. Standing when you can't bust... you've changed nothing.
Splitting 10's vs a 6 isn't terribly costly to the player. In fact, at a true hi-lo count of +3 it becomes the optimal strategy.
September 17th, 2011 at 8:39:33 AM
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Hitting 20 against a 6, now that's ballsy. And STUPID !!!!!!
September 17th, 2011 at 8:47:46 AM
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OOPS Even ballsier, Double down on that BJ.
September 17th, 2011 at 10:54:40 AM
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Quote: buzzpaffOOPS Even ballsier, Double down on that BJ.
No, the hitting 20 would be more reckless. Let's assume that it's at least at TT, not A9, as that would remove one instance of THE ONLY CARD THAT CAN IMPROVE YOUR HAND. For 6-Decks Hit 17, here are selected data from the wizard's blackjack appendix 9:
Dealer You Stand Hit Double
10 10,10 0.559145 -0.847142 -1.694283
A 10,A 1.500000 0.104246 0.10859
The formatting should resolve itself if you paste it into excel. As we see, hitting a 20 against a dealer 10 (the least bad time to do it), costs us 1.40 units, whereas doubling the blackjack versus an ace (the worst time to do it) "only" costs us 1.39 units. So no matter what the dealer has, it would always be better to double a natural than to hit a 20.
I don't know why I spent the last 10 minutes analyzing this--it was a waste of my life.
September 17th, 2011 at 7:58:22 PM
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Welcome to the forum. You are now a fully accredited member. LOL
September 27th, 2011 at 6:36:40 PM
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Pirate in Training sez I. Arrr.
N&B
N&B
To err is human.
To air is Jordan.
To arrr is pirate.
September 28th, 2011 at 9:01:03 AM
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Quote: thecesspitI fail to see what's ballsy about doing something inane. Ballsy is hitting a hard 18 against a dealer ten. Or splitting ten versus a dealer 6. Both maybe dumb moves, but occasionally they pay off. Standing when you can't bust... you've changed nothing.
Say what????? You've minimized your chance of winning!
