Confused: Basic Strategy
February 22nd, 2025 at 10:13:40 AM
permalink
My math skills are limited. But I seem to have found some flaws in the basic strategy for Blackjack, maybe? To simplify, take the hand A,2 with a 6 up. The analyzer on the Wizard's simulator recommends doubling down and provides the following analysis: a double down provides a return, per dollar bet, of 0.230210. As compared to a lessor return per dollar bet when hitting: 0.168495. But because the option of hitting allows more wins overall, due to the options of additional hits, all of which are risk-free, for example an A,2 can draw an Ace, a 2, 3, 4, or even a 5, and still take another hit without any risk of busting. So, if this hand is played in accordance with Basic Strategy, a player will never bust and win much more often when hitting rather than when doubling down (of course doubling down only allows a draw of one card). So, on a per dollar bet basis, how might the return when doubling down be higher than when hitting?
February 22nd, 2025 at 11:07:01 AM
permalink
I will have to look at this some more, but I have a feeling the answer is, "per dollar bet" refers to only the original bet - not the additional bet when you double.
In other words, if you bet $100 and are dealt A,2 against a dealer's 6:
If you hit, you are expected to make a profit of $16.85.
If you double, you are expected to make a profit of $23.02.
In other words, if you bet $100 and are dealt A,2 against a dealer's 6:
If you hit, you are expected to make a profit of $16.85.
If you double, you are expected to make a profit of $23.02.
February 22nd, 2025 at 11:14:27 AM
permalink
As far as basic strategy:
Over time, if you double when you should, you should win more money.
Just as, if you split 8s against 10, over time, you should lose less.
Over time, if you double when you should, you should win more money.
Just as, if you split 8s against 10, over time, you should lose less.
I tell you it’s wonderful to be here, man. I don’t give a damn who wins or loses. It’s just wonderful to be here with you people.
https://wizardofvegas.com/forum/gambling/betting-systems/33908-the-adventures-of-mdawg/
February 22nd, 2025 at 11:26:15 AM
permalink
Perhaps that is correct, it makes sense. But the simulator's recommendations would be more telling if the comparison between hitting or doubling were giving the actual difference in money gained or lost per choice. Naturally, there are other hands which have this same issue, mostly the other soft hands such as A,3 - A,4 - and so on, but then too there is the hard 8 and 9 which will win more hands when hit as opposed to doubled (assuming here again that the Basic Strategy is adhered to).
Thanks for the response, just trying to better understand the game.
Thanks for the response, just trying to better understand the game.
Last edited by: RLL123 on Feb 22, 2025
February 22nd, 2025 at 11:27:04 AM
permalink
Essentially, in general, by doubling you are sacrificing the opportunity to win when you would want to draw another card (e.g. A22) compared with winning twice as much when you do win. So typically you will win less often by doubling, but because you win two units rather than one unit, it's more profitable.
(Usually you double where your chances of winning is greater than 50%, but technically there are several exceptions for some Blackjack variants like FreeBet or where the initial/doubled bet pays more than evens.)
(Usually you double where your chances of winning is greater than 50%, but technically there are several exceptions for some Blackjack variants like FreeBet or where the initial/doubled bet pays more than evens.)
February 22nd, 2025 at 11:35:49 AM
permalink
Thanks for the response. And yes, doubling a bet will double the winnings but it will also double the losses. So, on a per dollar bet basis, how can winning 53 hands out of a hundred with a $10 bet (doubling down), have a better return per dollar bet if by hitting with a $5 bet wins more than 53 hands out of a hundred? Half as much was bet, but more was won per dollar bet.
February 22nd, 2025 at 11:49:11 AM
permalink
(Assume for simplicity that there aren't ties, or if you want to be more specific that if you double you win 6% more often than losing, etc.)
Case (a) You double and have $10 out winning 53% and losing 47%. Net profit is 6% * $10.
Case (b) You hit and have $5 out winning 55% and losing 45%. Net profit is 10% & $5.
As you can see 6*10 is greater than 10*5.
If you look at doubling 10 vs 9 ( https://wizardofodds.com/games/blackjack/expected-return-infinite-deck/ ) you get 14c or 11c, which suggests the numbers are 7% (dbl) and 11% (hit).
Case (a) You double and have $10 out winning 53% and losing 47%. Net profit is 6% * $10.
Case (b) You hit and have $5 out winning 55% and losing 45%. Net profit is 10% & $5.
As you can see 6*10 is greater than 10*5.
If you look at doubling 10 vs 9 ( https://wizardofodds.com/games/blackjack/expected-return-infinite-deck/ ) you get 14c or 11c, which suggests the numbers are 7% (dbl) and 11% (hit).
February 22nd, 2025 at 12:02:37 PM
permalink
Quote: RLL123Thanks for the response. And yes, doubling a bet will double the winnings but it will also double the losses. So, on a per dollar bet basis, how can winning 53 hands out of a hundred with a $10 bet (doubling down), have a better return per dollar bet if by hitting with a $5 bet wins more than 53 hands out of a hundred? Half as much was bet, but more was won per dollar bet.
link to original post
You want more money on the table when you have your best opportunities for a win. A/2 vs 6 is a strong hand, and it is worth giving up a small winning percentage to double your win. That assumes you have a proper bankroll available.
The older I get, the better I recall things that never happened
February 22nd, 2025 at 12:11:38 PM
permalink
Still, that time I doubled on beyond table limit on an ace 6 against 3 up, and lost, does stand out. In that particular hand I drew a 5, and dealer turned over an 8 under the 3 and drew a 9. I will hit hard 12 against 3 up one time absent some other knowledge of what might be coming, so that makes the recollection sharper.
But there are plenty of hands where I doubled with massive amounts down and won. More than I have lost, for sure.
Jack King said, "Few players recall big pots they have won, strange as it seems, but every player can remember with remarkable accuracy the outstanding tough beats of his career."
But there are plenty of hands where I doubled with massive amounts down and won. More than I have lost, for sure.
Jack King said, "Few players recall big pots they have won, strange as it seems, but every player can remember with remarkable accuracy the outstanding tough beats of his career."
I tell you it’s wonderful to be here, man. I don’t give a damn who wins or loses. It’s just wonderful to be here with you people.
https://wizardofvegas.com/forum/gambling/betting-systems/33908-the-adventures-of-mdawg/
February 22nd, 2025 at 12:41:23 PM
permalink
Yes, Charliepatrick, I understand that "you are sacrificing the opportunity to win when you would want to draw another card (e.g. A22) compared with winning twice as much when you do win. So typically you will win less often by doubling, but because you win two units rather than one unit, it's more profitable."
But it is not more profitable 'per dollar bet'. This is however somewhat confusing, but if a player were to win 58 times out of 100 hands at $1 per hand, and lose 42 times, when hitting, that player's profit would be $16, or 0.16 per dollar bet. In comparison, a player doubling down and betting $2 per hand a hundred times and winning the same number of times, 58, would win twice as much, naturally, but the same on a per dollar bet basis. Twice as much bet, and twice as much won, yet via the analyzer on 'simulator 2', and in the appendix here on this site, the analysis has the double down option winning more per dollar bet (Double Down @ 0.230210 - Hit @ 0.168495).
Thanks for the interest.
But it is not more profitable 'per dollar bet'. This is however somewhat confusing, but if a player were to win 58 times out of 100 hands at $1 per hand, and lose 42 times, when hitting, that player's profit would be $16, or 0.16 per dollar bet. In comparison, a player doubling down and betting $2 per hand a hundred times and winning the same number of times, 58, would win twice as much, naturally, but the same on a per dollar bet basis. Twice as much bet, and twice as much won, yet via the analyzer on 'simulator 2', and in the appendix here on this site, the analysis has the double down option winning more per dollar bet (Double Down @ 0.230210 - Hit @ 0.168495).
Thanks for the interest.
February 22nd, 2025 at 12:51:42 PM
permalink
A good point billryan, but still not explaining how an A,2 could possibly return more 'per dollar bet' when doubled on when the hit play will win more hands overall. Maybe there is something I'm unaware of, but isn't the Basic Strategy based on a 'per dollar bet' analysis, combinatorial or otherwise?
February 22nd, 2025 at 12:58:00 PM
permalink
Quote: RLL123A good point billryan, but still not explaining how an A,2 could possibly return more 'per dollar bet' when doubled on when the hit play will win more hands overall. Maybe there is something I'm unaware of, but isn't the Basic Strategy based on a 'per dollar bet' analysis, combinatorial or otherwise?
link to original post
It’s on an EV basis per dollar of base bet. (So doesn’t include the added money for doubling or splitting.)
The race is not always to the swift, nor the battle to the strong; but that is the way to bet.
February 22nd, 2025 at 1:26:52 PM
permalink
Thanks, unJon, your explanation supports what 'ThatDonGuy' suggested in the first response. It seems odd though considering how meticulous math-nurds are about such things that so many have ignored what is clearly misleading. The choice is 'to hit, or not to hit'... or to risk more due to the presented opportunity... and double down, or not? So, in trying to make an informed decision, it would be better to know which option is the better play... per dollar bet.
Besides that, the listed probabilities are presented as evaluations of wins and losses 'per dollar bet'.
And of course, more profit is predictable with twice the bet on a hand with a win rate of better than 50%, so the numerical comparison offered is not as useful as an actual comparison of a 'return on investment' calculation.
Besides that, the listed probabilities are presented as evaluations of wins and losses 'per dollar bet'.
And of course, more profit is predictable with twice the bet on a hand with a win rate of better than 50%, so the numerical comparison offered is not as useful as an actual comparison of a 'return on investment' calculation.
February 22nd, 2025 at 3:48:10 PM
permalink
As a player, you will play a finite amount of hands. Having bigger bets on strong hands will result in more money when you stop playing. Isn't that what you want?
The older I get, the better I recall things that never happened
February 22nd, 2025 at 4:02:33 PM
permalink
So are you unconfused now?
I tell you it’s wonderful to be here, man. I don’t give a damn who wins or loses. It’s just wonderful to be here with you people.
https://wizardofvegas.com/forum/gambling/betting-systems/33908-the-adventures-of-mdawg/
February 22nd, 2025 at 4:04:39 PM
permalink
Quote: RLL123Thanks, unJon, your explanation supports what 'ThatDonGuy' suggested in the first response. It seems odd though considering how meticulous math-nurds are about such things that so many have ignored what is clearly misleading. The choice is 'to hit, or not to hit'... or to risk more due to the presented opportunity... and double down, or not? So, in trying to make an informed decision, it would be better to know which option is the better play... per dollar bet.
Besides that, the listed probabilities are presented as evaluations of wins and losses 'per dollar bet'.
And of course, more profit is predictable with twice the bet on a hand with a win rate of better than 50%, so the numerical comparison offered is not as useful as an actual comparison of a 'return on investment' calculation.
link to original post
APs use metrics like you are describing all the time. We use risk-averse indices, because a play like A2 vs. 6 is going to be more or less profitable depending on the count. That's a Basic Strategy play so it is profitable right off the top of the deck.
What you're saying is technically correct, but practically not useful. If you're a counter you are betting a tiny fraction of your bankroll on any hand, so whether or not you double isn't going to break the bank, and making your indices risk averse doesn't change them much. The increased win rate you get for doubling is going to be well above the expected win rate for putting out that bet at that count in the first place; if you expected 1% when you placed the bet getting 1% on the doubled bet is all you're looking for, and that's going to be the case for all doubled hands except in rare circumstances.
February 22nd, 2025 at 5:02:39 PM
permalink
As others have said, the expected value is relative to the initial bet. Yes, the probability of winning is more by hitting, but by doubling you get more action on a good hand.
What would you rather have?
A) 80% chance of winning $1, otherwise lose $1
B) 70% chance of winning $2 otherwise lose $2.
What would you rather have?
A) 80% chance of winning $1, otherwise lose $1
B) 70% chance of winning $2 otherwise lose $2.
"For with much wisdom comes much sorrow." -- Ecclesiastes 1:18 (NIV)
February 23rd, 2025 at 10:20:03 AM
permalink
Quote: Wizard" As others have said, the expected value is relative to the initial bet. Yes, the probability of winning is more by hitting, but by doubling you get more action on a good hand."
"What would you rather have?"
"A) 80% chance of winning $1, otherwise lose $1
B) 70% chance of winning $2 otherwise lose $2."
A good and fair question but my original comment above is not meant to suggest that the EV on any particular bet is incorrect, and I fully understand the 'opportunity' aspect involved. What confuses me here is that if the EVs are based on a 'per dollar bet' basis... then the probabilities provided by the Wizard simulator, and those listed in the appendix, for double downs and splits, are simply misleading and not based on a per dollar bet calculation. Granted the Wizard's simulator is the best one I'm aware of, and from now on I'll know that with a little math I can derive a clear comparative by simply multiplying the hit calculation by 2. For example, on the A,2 vs the 6 up, the return for hitting compares evenly with the double down as 0.168495 x 2 for a return of about 33 cents 'if' the double down return remains as 0.230210 or about 23 cents. Or... the return number for the double down option could be divided by 2, which comes to about 11 cents, and then that is commensurate with the 16-ish cents given for the hit option. My point being that if the comparisons were on equal terms insofar as the amount of the bet is concerned... that information would be more useful than what is currently provided.
A great site though.
Last edited by: unnamed administrator on Feb 23, 2025
February 23rd, 2025 at 10:27:34 AM
permalink
Quote: RLL123Quote: Wizard" As others have said, the expected value is relative to the initial bet. Yes, the probability of winning is more by hitting, but by doubling you get more action on a good hand."
"What would you rather have?"
"A) 80% chance of winning $1, otherwise lose $1
B) 70% chance of winning $2 otherwise lose $2."
A good and fair question but my original comment above is not meant to suggest that the EV on any particular bet is incorrect, and I fully understand the 'opportunity' aspect involved. What confuses me here is that if the EVs are based on a 'per dollar bet' basis... then the probabilities provided by the Wizard simulator, and those listed in the appendix, for double downs and splits, are simply misleading and not based on a per dollar bet calculation. Granted the Wizard's simulator is the best one I'm aware of, and from now on I'll know that with a little math I can derive a clear comparative by simply multiplying the hit calculation by 2. For example, on the A,2 vs the 6 up, the return for hitting compares evenly with the double down as 0.168495 x 2 for a return of about 33 cents 'if' the double down return remains as 0.230210 or about 23 cents. Or... the return number for the double down option could be divided by 2, which comes to about 11 cents, and then that is commensurate with the 16-ish cents given for the hit option. My point being that if the comparisons were on equal terms insofar as the amount of the bet is concerned... that information would be more useful than what is currently provided.
A great site though.
link to original post
I don’t understand what you are saying. You shouldn’t divide the double EV by 2 and then compare to the hit calculation. That might mislead you into thinking a hit is a better option.
Last edited by: unnamed administrator on Feb 23, 2025
The race is not always to the swift, nor the battle to the strong; but that is the way to bet.
February 23rd, 2025 at 11:57:28 AM
permalink
As you say, the double down and split calculations are based on the "initial bet". So, that is only half of what is actually at risk.
February 23rd, 2025 at 12:19:18 PM
permalink
Quote: RLL123As you say, the double down and split calculations are based on the "initial bet". So, that is only half of what is actually at risk.
link to original post
That’s right. That makes them apples to apples. You get more EV by doubling if you started with a $1 bet than hitting.
The race is not always to the swift, nor the battle to the strong; but that is the way to bet.
February 23rd, 2025 at 12:42:20 PM
permalink
Quote: RLL123Quote: Wizard" As others have said, the expected value is relative to the initial bet. Yes, the probability of winning is more by hitting, but by doubling you get more action on a good hand."
"What would you rather have?"
"A) 80% chance of winning $1, otherwise lose $1
B) 70% chance of winning $2 otherwise lose $2."
A good and fair question but my original comment above is not meant to suggest that the EV on any particular bet is incorrect, and I fully understand the 'opportunity' aspect involved. What confuses me here is that if the EVs are based on a 'per dollar bet' basis... then the probabilities provided by the Wizard simulator, and those listed in the appendix, for double downs and splits, are simply misleading and not based on a per dollar bet calculation. Granted the Wizard's simulator is the best one I'm aware of, and from now on I'll know that with a little math I can derive a clear comparative by simply multiplying the hit calculation by 2. For example, on the A,2 vs the 6 up, the return for hitting compares evenly with the double down as 0.168495 x 2 for a return of about 33 cents 'if' the double down return remains as 0.230210 or about 23 cents. Or... the return number for the double down option could be divided by 2, which comes to about 11 cents, and then that is commensurate with the 16-ish cents given for the hit option. My point being that if the comparisons were on equal terms insofar as the amount of the bet is concerned... that information would be more useful than what is currently provided.
A great site though.
link to original post
Missing /q tag. Enjoy the day.
May the cards fall in your favor.
February 23rd, 2025 at 1:15:59 PM
permalink
Yes, of course, there is more "EV by doubling" but there is also more short-term risk in many cases. And that is maybe best explained using a different scenario:
Player's bankroll is down to $2k and he or she has bet half of that and received a pair of 8s with a 10 up. Basic strategy recommends splitting and so the player puts down his or her last dollar and loses both hands. But had the player surrendered that player would still have $1,500, had the player stood, or hit and lost, now the bankroll would be at $1k. So, the risk is all too often a matter of managing the bankroll, but the Basic Strategy assumes an endless bankroll.
So, in the case of double downs and splits it is folly to assume that the EV is the only consideration. This becoming the most interesting when doubling or splitting. Another germane example is the hard 9 vs 4 -6 up, there is of course a 7-ish % chance of the player receiving a 2, and of course hitting elevens will allow for many more wins than an 11. So, doubling down is considerably riskier than hitting the 9, and so a wise gambler should consider the risk to his or her bankroll being depleted in such cases.
Anyway, if double down and split hands are evaluated based on the initial bet instead of the total bet, then the calculation on a per dollar bet basis is inaccurate. As it stands, if double down and split bets are being calculated on the initial bet... that amounts to a 'per half dollar bet'. But as currently presented on the simulator and in the appendix -- as compared to hits, stands, and surrenders, on 'per dollar bet' calculation, the return per dollar 'seems' better than those bets actually are. And the circumstances are rarely as simple as what the EV suggests.
Player's bankroll is down to $2k and he or she has bet half of that and received a pair of 8s with a 10 up. Basic strategy recommends splitting and so the player puts down his or her last dollar and loses both hands. But had the player surrendered that player would still have $1,500, had the player stood, or hit and lost, now the bankroll would be at $1k. So, the risk is all too often a matter of managing the bankroll, but the Basic Strategy assumes an endless bankroll.
So, in the case of double downs and splits it is folly to assume that the EV is the only consideration. This becoming the most interesting when doubling or splitting. Another germane example is the hard 9 vs 4 -6 up, there is of course a 7-ish % chance of the player receiving a 2, and of course hitting elevens will allow for many more wins than an 11. So, doubling down is considerably riskier than hitting the 9, and so a wise gambler should consider the risk to his or her bankroll being depleted in such cases.
Anyway, if double down and split hands are evaluated based on the initial bet instead of the total bet, then the calculation on a per dollar bet basis is inaccurate. As it stands, if double down and split bets are being calculated on the initial bet... that amounts to a 'per half dollar bet'. But as currently presented on the simulator and in the appendix -- as compared to hits, stands, and surrenders, on 'per dollar bet' calculation, the return per dollar 'seems' better than those bets actually are. And the circumstances are rarely as simple as what the EV suggests.
February 23rd, 2025 at 2:04:40 PM
permalink
If you are worried about the short term risk, perhaps you are gambling at too-high stakes.
You are welcome to play your hand non-optimally. It's your money on the line, you play your cards how you like.
Trying to rationalize the decisions you made in fear just doesn't make sense.
Best of luck!
You are welcome to play your hand non-optimally. It's your money on the line, you play your cards how you like.
Trying to rationalize the decisions you made in fear just doesn't make sense.
Best of luck!
May the cards fall in your favor.
February 23rd, 2025 at 2:26:02 PM
permalink
Quote: RLL123Yes, of course, there is more "EV by doubling" but there is also more short-term risk in many cases. And that is maybe best explained using a different scenario:
Player's bankroll is down to $2k and he or she has bet half of that and received a pair of 8s with a 10 up. Basic strategy recommends splitting and so the player puts down his or her last dollar and loses both hands. But had the player surrendered that player would still have $1,500, had the player stood, or hit and lost, now the bankroll would be at $1k. So, the risk is all too often a matter of managing the bankroll, but the Basic Strategy assumes an endless bankroll.
So, in the case of double downs and splits it is folly to assume that the EV is the only consideration. This becoming the most interesting when doubling or splitting. Another germane example is the hard 9 vs 4 -6 up, there is of course a 7-ish % chance of the player receiving a 2, and of course hitting elevens will allow for many more wins than an 11. So, doubling down is considerably riskier than hitting the 9, and so a wise gambler should consider the risk to his or her bankroll being depleted in such cases.
Anyway, if double down and split hands are evaluated based on the initial bet instead of the total bet, then the calculation on a per dollar bet basis is inaccurate. As it stands, if double down and split bets are being calculated on the initial bet... that amounts to a 'per half dollar bet'. But as currently presented on the simulator and in the appendix -- as compared to hits, stands, and surrenders, on 'per dollar bet' calculation, the return per dollar 'seems' better than those bets actually are. And the circumstances are rarely as simple as what the EV suggests.
link to original post
You are arguing from a corner case when bankroll approaches initial bet. If your bankroll is $2k, the problem isn’t basic strategy, it’s playing at a $1,000 minimum table.
You should play at a level where you are comfortable playing correct basic strategy, or recognize that you are depleting your bankroll more quickly (on average) by deviating.
The race is not always to the swift, nor the battle to the strong; but that is the way to bet.
February 23rd, 2025 at 2:48:27 PM
permalink
If losing a couple of double-downs is going to affect your play, either drop down a level or just follow your guts and ignore BS. Play how you want, as if no one else was at the table. It's your money. We can tell you how to make more money, but we can't make you do it.
BS assumes you have the proper BR for the level of your bet.
BS assumes you have the proper BR for the level of your bet.
The older I get, the better I recall things that never happened
February 23rd, 2025 at 2:51:18 PM
permalink
No, I'm not" arguing from a corner case when bankroll approaches initial bet. If your bankroll is $2k, the problem isn’t basic strategy, it’s playing at a $1,000 minimum table."
The same logic applies if the player were playing at a $1 minimum table and he or she bet $10 and drew a pair of 8s. Then he or she bet all of what was left of a $5k bankroll (The Player has had a very bad run of luck for the sake of this example!). Then our player splits and adheres to the Basic Strategy only to lose both hands. Had our player surrendered, hit, or stood, the bankroll would still be sufficient to battle on. But instead, another player takes our player's seat at an otherwise empty table only to enjoy the winning streak of a lifetime.
Our player goes home sad and beaten, but maybe more aware that the Basic Strategy doesn't cover the nuances that every good gambler must know.
The same logic applies if the player were playing at a $1 minimum table and he or she bet $10 and drew a pair of 8s. Then he or she bet all of what was left of a $5k bankroll (The Player has had a very bad run of luck for the sake of this example!). Then our player splits and adheres to the Basic Strategy only to lose both hands. Had our player surrendered, hit, or stood, the bankroll would still be sufficient to battle on. But instead, another player takes our player's seat at an otherwise empty table only to enjoy the winning streak of a lifetime.
Our player goes home sad and beaten, but maybe more aware that the Basic Strategy doesn't cover the nuances that every good gambler must know.
February 23rd, 2025 at 3:10:21 PM
permalink
Quote: RLL123No, I'm not" arguing from a corner case when bankroll approaches initial bet. If your bankroll is $2k, the problem isn’t basic strategy, it’s playing at a $1,000 minimum table."
The same logic applies if the player were playing at a $1 minimum table and he or she bet $10 and drew a pair of 8s. Then he or she bet all of what was left of a $5k bankroll (The Player has had a very bad run of luck for the sake of this example!). Then our player splits and adheres to the Basic Strategy only to lose both hands. Had our player surrendered, hit, or stood, the bankroll would still be sufficient to battle on. But instead, another player takes our player's seat at an otherwise empty table only to enjoy the winning streak of a lifetime.
Our player goes home sad and beaten, but maybe more aware that the Basic Strategy doesn't cover the nuances that every good gambler must know.
link to original post
Fortune Favors The Bold.
You can't succeed in cards if you constantly dwell on worst-case scenarios.
The older I get, the better I recall things that never happened
February 23rd, 2025 at 8:46:37 PM
permalink
Quote: RLL123Our player goes home sad and beaten, but maybe more aware that the Basic Strategy doesn't cover the nuances that every good gambler must know.
link to original post
I think you would be happier reading a John Patrick book than spending time at site that respects math like this one.
"For with much wisdom comes much sorrow." -- Ecclesiastes 1:18 (NIV)
February 24th, 2025 at 10:28:20 AM
permalink
LOL, math wizards all, and so respectful too.
February 24th, 2025 at 10:53:48 AM
permalink
Quote: RLL123LOL, math wizards all, and so respectful too.
link to original post
Imagine if instead of a double down, it was a 100x down. So you could bet 100 times your initial bet and draw just one card.
Your analysis would divide the EV by 100 so leave it as hit looking like the better option.
That would miss the point that this BJ game is massively a player advantage solely due to this amazing role, and that of course the 100 down should be used.
The race is not always to the swift, nor the battle to the strong; but that is the way to bet.
February 24th, 2025 at 11:51:06 AM
permalink
Quote: RLL123LOL, math wizards all, and so respectful too.
link to original post
The problem is as billryan said you're focusing on worst case scenarios in hypothetical situations.
Say you're down to your last $20 and you have a $10 bet out. Dealt A2 against dealer 6. You just hit and get a 3. Whew good thing you didn't double right? Take another hit and it's a 4! Woohoo 20!!
Except the dealer had a 5 under and the next card out of the chute was a Q. You'd be sitting with $40 if you doubled and now you're down to $10.
It's a negative expectation game unless you're counting. Playing more conservative to preserve a bankroll isn't a strategy that will lead to more winning. But I mean it's your choice when all is said and done.
February 24th, 2025 at 1:55:32 PM
permalink
I simply used a hypothetical to make a point, I in no way have proposed a "strategy", (ironically, your last response uses a hypothetical to the same end but with an added degree of hypocrisy).
Anyway, I came here in good faith and brought up what is clearly a misleading aspect of how Basic Strategy comparatives are presented. Oddly though, what could have been an interesting conversation turned out to be mostly a waste of time. I did learn however that the returns per dollar bet on double downs and splits are twice what those actually are. Then too, I was provided with advice such as "Fortune favors the bold"(as if courage can alter the math, lol, combine that with your "respect" for the math claim and maybe you can see how sophomoric this conversation has been, mostly).
So, getting back to what this conversation should have been about, using only the cost of the initial bet to determine the return per dollar bet, when that is only half of the actual cost, is plainly misleading. But the well-informed gambler can simply divide the EV for the applicable hands by 2, and, lo and behold, the truth emerges. So, no big deal, except that the question of why remains. Is there an element of propaganda involved in the Basic Strategy? Is that maybe why those on the 'dark side' are so often providing charts on sites such as this one? As if losing less should encourage anyone other than the occasional fool.
And since everyone seems to provide parting advice with each comment, the most successful gambler I've ever been privy to once said this: "It is easier to teach a monkey to count cards than it is to teach a card counter how to gamble"
Anyway, I came here in good faith and brought up what is clearly a misleading aspect of how Basic Strategy comparatives are presented. Oddly though, what could have been an interesting conversation turned out to be mostly a waste of time. I did learn however that the returns per dollar bet on double downs and splits are twice what those actually are. Then too, I was provided with advice such as "Fortune favors the bold"(as if courage can alter the math, lol, combine that with your "respect" for the math claim and maybe you can see how sophomoric this conversation has been, mostly).
So, getting back to what this conversation should have been about, using only the cost of the initial bet to determine the return per dollar bet, when that is only half of the actual cost, is plainly misleading. But the well-informed gambler can simply divide the EV for the applicable hands by 2, and, lo and behold, the truth emerges. So, no big deal, except that the question of why remains. Is there an element of propaganda involved in the Basic Strategy? Is that maybe why those on the 'dark side' are so often providing charts on sites such as this one? As if losing less should encourage anyone other than the occasional fool.
And since everyone seems to provide parting advice with each comment, the most successful gambler I've ever been privy to once said this: "It is easier to teach a monkey to count cards than it is to teach a card counter how to gamble"
February 24th, 2025 at 3:31:44 PM
permalink
If you are playing on a $1 table and average two cocktails an hour, the drinks make the game EV positive. When you hit the $10 level, the advantage is mostly lost.
Is the player better off on the $1 table?
Is the player better off on the $1 table?
The older I get, the better I recall things that never happened
February 24th, 2025 at 4:42:04 PM
permalink
The player is most likely turning down the drinks. But I say that after just having 2 drinks.
February 24th, 2025 at 5:08:58 PM
permalink
Quote: billryanIf you are playing on a $1 table and average two cocktails an hour, the drinks make the game EV positive. When you hit the $10 level, the advantage is mostly lost.
Is the player better off on the $1 table?
link to original post
Yes, but if I am there for three hours and have 10 drinks the EV is reduced by the fine for the DUI.
You can't know everything, but you can know anything.
February 24th, 2025 at 5:20:57 PM
permalink
Quote: RLL123I simply used a hypothetical to make a point, I in no way have proposed a "strategy", (ironically, your last response uses a hypothetical to the same end but with an added degree of hypocrisy).
Anyway, I came here in good faith and brought up what is clearly a misleading aspect of how Basic Strategy comparatives are presented. Oddly though, what could have been an interesting conversation turned out to be mostly a waste of time. I did learn however that the returns per dollar bet on double downs and splits are twice what those actually are. Then too, I was provided with advice such as "Fortune favors the bold"(as if courage can alter the math, lol, combine that with your "respect" for the math claim and maybe you can see how sophomoric this conversation has been, mostly).
So, getting back to what this conversation should have been about, using only the cost of the initial bet to determine the return per dollar bet, when that is only half of the actual cost, is plainly misleading. But the well-informed gambler can simply divide the EV for the applicable hands by 2, and, lo and behold, the truth emerges. So, no big deal, except that the question of why remains. Is there an element of propaganda involved in the Basic Strategy? Is that maybe why those on the 'dark side' are so often providing charts on sites such as this one? As if losing less should encourage anyone other than the occasional fool.
And since everyone seems to provide parting advice with each comment, the most successful gambler I've ever been privy to once said this: "It is easier to teach a monkey to count cards than it is to teach a card counter how to gamble"
link to original post
Again you can’t divide the EV of the double by 2. That’s no longer the EV. This is really the crux of the point you aren’t seeing. The EV is the EV based on the initial bet. It incorporates the fact that a double means sometimes losing double and sometimes winning double.
The race is not always to the swift, nor the battle to the strong; but that is the way to bet.
February 25th, 2025 at 10:56:11 AM
permalink
Yes unJon, you bring up a good point. The double down losses should play a role here, but the DD hands are those which the player has a better than 50% chance of winning and so the EV is thereby skewed. Strangely though, in trying to understand this better I went to Appendix #9 and picked a scenario in which the BS recommends a DD, but, if the player were to hit (player out of money maybe), the BS would not recommend more than one hit, IOW, I chose a simple hand, and I found the following:
Player has 6,5 vs 6-up. A hit results in an EV of 0.380696. The double down EV is 0.761392. The number, 0.761392 divided by 2 = 0.380696, or exactly half which is the value given for the hit option. Not all DD hands have this symmetry though. And as I have already explained... there are many potential DD hands that will win more often when hit, than when doubled on, and those have EV outcomes which put the per dollar bet value higher for the DD option when that option will most certainly result in more losses (a mathematical impossibility). So, dividing the DD option in half provides a fairly accurate comparison in all of the instances I have done the math on. The main point being here that the EV numbers are misleading when it comes to DDs and splits. Even more so with splits because of course those can be repeated in some cases.
So, as for the DD losses to offset the DD wins as a way to explain how the initial bet is all that is needed to provide an accurate comparative for the EV outcomes, nope.
Player has 6,5 vs 6-up. A hit results in an EV of 0.380696. The double down EV is 0.761392. The number, 0.761392 divided by 2 = 0.380696, or exactly half which is the value given for the hit option. Not all DD hands have this symmetry though. And as I have already explained... there are many potential DD hands that will win more often when hit, than when doubled on, and those have EV outcomes which put the per dollar bet value higher for the DD option when that option will most certainly result in more losses (a mathematical impossibility). So, dividing the DD option in half provides a fairly accurate comparison in all of the instances I have done the math on. The main point being here that the EV numbers are misleading when it comes to DDs and splits. Even more so with splits because of course those can be repeated in some cases.
So, as for the DD losses to offset the DD wins as a way to explain how the initial bet is all that is needed to provide an accurate comparative for the EV outcomes, nope.
February 25th, 2025 at 11:26:44 AM
permalink
I’m sorry I’m not following. Can you explain what is misleading about the EVs in the example you give above? I just don’t see why it’s misleading and am trying to understand what you mean.
EV is the amount you expect to win or lose from making some bet. That is determined by the amounts you win or lose and the probability of winning and losing.
EV is the amount you expect to win or lose from making some bet. That is determined by the amounts you win or lose and the probability of winning and losing.
The race is not always to the swift, nor the battle to the strong; but that is the way to bet.
February 25th, 2025 at 12:11:22 PM
permalink
Quote: WizardAs others have said, the expected value is relative to the initial bet. Yes, the probability of winning is more by hitting, but by doubling you get more action on a good hand.
What would you rather have?
A) 80% chance of winning $1, otherwise lose $1
B) 70% chance of winning $2 otherwise lose $2.
A has a value of +60¢ or +60%.
B has a value of +80¢ or +40%
in this example I would rather have B. There are lots of real-world examples I would take the higher % instead of the higher $.
how about:
-risk $1 million to win $1 million on the under total points in the Super Bowl with a 50.1% chance of winning
-risk $2000 to win $2000 on no safety
in this case I would much rather have the lower expected value.
February 25th, 2025 at 12:41:03 PM
permalink
Yes, I can explain what is misleading about the EVs. The first example I provided on this thread makes this the most easily understood but simply because it is so obvious that hitting the A,2 vs 6 will result in more wins than doubling down and yet the EVs on the DD are higher for the DD than for the hit option. Using Appendix 9 again, there is roughly a $0.16 return per dollar bet for the hit option, while the DD option is shown as a plus $0.23 per dollar bet. But of course, this cannot be for the reason that the hit option will win more hands with half as much bet. This example is simplified by the fact that if the BS is followed to the letter, A,2 can be hit multiple times with no risk of busting, for example the A,2 player draws a 2, and then another A, the hand is still of course soft, and then a 5 for a 21. This as opposed to: had the player doubled down and was only allowed the first hit which of course amounts to a 15. So, obviously the player will win more hands by hitting since there is no risk of busting. So, on a per dollar bet basis, the hit option must have a higher return than the DD option.
As for the example above, the 6,5 vs 6-up, if the BS recommendations are followed, this hand plays exactly the same when hit or doubled down on. So, the return per dollar bet is the same for either play but the DD is listed on this site as having twice the EV as the hit option. The act of doubling down though requires a doubling of the bet and thus the DD wins twice what the hit wins, but at twice the cost. Each option then has an EV of 0.380696 insofar as the numbers provided are concerned. (Naturally, the DD option is the better play by far in this case, but again, this is a simple hand which would never be hit in accordance with the Basic Strategy. But the misleading EVs are apparent in all of the Double down EV comparatives that I have checked so far.).
As for the example above, the 6,5 vs 6-up, if the BS recommendations are followed, this hand plays exactly the same when hit or doubled down on. So, the return per dollar bet is the same for either play but the DD is listed on this site as having twice the EV as the hit option. The act of doubling down though requires a doubling of the bet and thus the DD wins twice what the hit wins, but at twice the cost. Each option then has an EV of 0.380696 insofar as the numbers provided are concerned. (Naturally, the DD option is the better play by far in this case, but again, this is a simple hand which would never be hit in accordance with the Basic Strategy. But the misleading EVs are apparent in all of the Double down EV comparatives that I have checked so far.).
February 25th, 2025 at 12:56:15 PM
permalink
Sorry that didn’t help me understand. If you would permit me to ask a few clarifying questions?
Are you saying that hitting A,2 against a dealer 6 is a “better” play than doubling?
If so, is it “better” in all circumstances or just when your bankroll is very low?
How do you propose “better” be measured if not by EV? By EV divided by amount risked? Or some other measure?
It sounds like you are saying it is doubling is always “better” than hitting eleven be a dealer 6. Yes? True even if it’s the very end of your bankroll?
Are you saying that hitting A,2 against a dealer 6 is a “better” play than doubling?
If so, is it “better” in all circumstances or just when your bankroll is very low?
How do you propose “better” be measured if not by EV? By EV divided by amount risked? Or some other measure?
It sounds like you are saying it is doubling is always “better” than hitting eleven be a dealer 6. Yes? True even if it’s the very end of your bankroll?
The race is not always to the swift, nor the battle to the strong; but that is the way to bet.
February 25th, 2025 at 1:37:02 PM
permalink
I see these card counters whip out cash for an extra buy-in to cover a split or double down on a large bet in the middle of a hand. Of course they have a lot of cash and they are expected to get kicked out of the casino in 30 minutes or less. But their strategy is to bet more when the deck favors them, even if only for 0.5% or more.
February 25th, 2025 at 1:38:06 PM
permalink
I'm simply saying that the EVs on double downs and splits are incorrect as compared to the EVs on other options. Maybe you did not read all of my comments on this thread, but I have already answered all of your most recent questions.
February 25th, 2025 at 2:14:10 PM
permalink
Quote: RLL123I'm simply saying that the EVs on double downs and splits are incorrect as compared to the EVs on other options. Maybe you did not read all of my comments on this thread, but I have already answered all of your most recent questions.
link to original post
We usually describe out advantage as IBA or TBA, relative to the initial bet or the total bet.
IBA, initial bet, is important. That determines how much money we are going to bet on a hand before we see a card. TBA, not so important, because in a real-world game that does not significantly affect any decision we make. If I'm going to bet $100 on a hand with a predicted advantage, based on count, of 1%, doubling my bet on a hand that pays 12% doubled is preferable to simply hitting a hand that pays 20% hitting. Because 12% of $200 is $24 and 20% of $100 is $20. And I like $24 more than $20.
But it appears you've caught us. It's all a big plot! Evvvvverybody is trying to screw you and make you lose money by giving you false information about the EV of doubled hands!
February 25th, 2025 at 2:20:54 PM
permalink
Quote: RLL123I'm simply saying that the EVs on double downs and splits are incorrect as compared to the EVs on other options. Maybe you did not read all of my comments on this thread, but I have already answered all of your most recent questions.
link to original post
It’s ok we don’t have to converse about it if you don’t want to.
To be clear though, the EVs are correct. That’s the point of disagreement I am trying to get to the bottom to with you.
I’ll give you an example:
I bet $10 at blackjack and are dealt A, 2 vs a deal 6.
If I hit, my expected win is $1.68 (rounded), which comes from sometimes winning $10 and slightly less often losing $10 (and sometimes pushing).
If I double, my expected win is $2.30 (rounded), which comes from sometimes winning $20 and slightly less often losing $20 (and sometimes pushing).
And nothing in what you posted shows the math on those EVs are wrong. They are correct. And they are what the wizard shows in his BJ calculator.
You’ve argued, as far as I can tell, that despite hitting having a lower EV, it can be (or maybe is?) the better option because you are risking less.
The race is not always to the swift, nor the battle to the strong; but that is the way to bet.
February 25th, 2025 at 2:22:26 PM
permalink
Well put, but the winning percentage in question here, for the A,2 vs the 6-up is a more complicated issue. The winning % is only 52.6%, with the losing % at 43% and a push % of 4.4%. So, double the monetary risk for what is a weak double down opportunity, and when hitting provides a considerably better chance of winning the hand. On a similar hand, the A,2 vs 4-up the winning percentage drops below 50% (49.4%) and so the 'opportunity' factor here is very low for a doubling of the bet when the odds of winning with a hit are better.
So, it seems rather obvious to me... that misleading EVs on double downs and splits should 'taken with a grain of salt', and this is especially true on some split hands when more than one split is allowed. The EVs on splits are made even less reliable due to frequency factors which seem of little interest to APs. The split EVs do however include some very rare hands which allow for multiple wins per hand ( 8,8,8,8 split to 8,3, 8,2, 8,3 and yet another 8,3 and then nothing but wins (I've had this hand and won all). And while this and other similar situations only occur very rarely, these hands skew the EVs enough to cause misinterpretations in the short-term.
Econ professors commonly use an old 'joke' to make a point that loosely fits here:
Bill Gates goes into a bar where 3 bums, a construction worker, and an 'unemployed' economist are sitting. The economist then declares "we have an average income of over billion dollars each" (short version). The longer version includes explaining how the construction worker's income is the median income. (econ jokes are not all that funny, typically.)
So, it seems rather obvious to me... that misleading EVs on double downs and splits should 'taken with a grain of salt', and this is especially true on some split hands when more than one split is allowed. The EVs on splits are made even less reliable due to frequency factors which seem of little interest to APs. The split EVs do however include some very rare hands which allow for multiple wins per hand ( 8,8,8,8 split to 8,3, 8,2, 8,3 and yet another 8,3 and then nothing but wins (I've had this hand and won all). And while this and other similar situations only occur very rarely, these hands skew the EVs enough to cause misinterpretations in the short-term.
Econ professors commonly use an old 'joke' to make a point that loosely fits here:
Bill Gates goes into a bar where 3 bums, a construction worker, and an 'unemployed' economist are sitting. The economist then declares "we have an average income of over billion dollars each" (short version). The longer version includes explaining how the construction worker's income is the median income. (econ jokes are not all that funny, typically.)
February 25th, 2025 at 2:25:18 PM
permalink
In case you missed my post after AutoMonkeys, as you were posting simultaneously, I’m just noting it here. I address your A,2 vs 6 example.
And I again don’t see what’s misleading about the EV on the double.
And I again don’t see what’s misleading about the EV on the double.
The race is not always to the swift, nor the battle to the strong; but that is the way to bet.
February 25th, 2025 at 4:02:19 PM
permalink
To save my typing muscles allow me to quote myself, using the following example:
" the 6,5 vs 6-up, if the BS recommendations are followed, this hand plays exactly the same when hit or doubled down on. So, the return per dollar bet is the same for either play but the DD is listed on this site as having twice the EV as the hit option. The act of doubling down though requires a doubling of the bet and thus the DD wins twice what the hit wins, but at twice the cost. Each option then has an EV of 0.380696 insofar as the numbers provided are concerned. (Naturally, the DD option is the better play by far in this case, but again, this is a simple hand which would never be hit in accordance with the Basic Strategy. But the misleading EVs are apparent in all of the Double down EV comparatives that I have checked so far.)."
That example should have included that the EV for the DD is in fact listed as twice that for the hit option: a hit has an EV of 0.380696 as opposed the EV being listed for the DD as 0.761392... which is exactly twice of 0.380696. But the 2 hands play exactly the same insofar as hits taken via the BS. And the EVS are based on dollars won or lost per dollar bet. The hit requires half as much bet, so how could twice the bet not be the same EV on a per dollar bet computation.
Take 10 bets of $1 on the hit option with 6 wins and 4 losses, for a EV of $2. Then compare that to 10 bets of $2 with 6 wins and 4 losses for an EV of $4. For each dollar bet the return is $2. But the EV, here at least, in the Appendices, and on the simulator's analyzer, puts the EV for the DD at exactly twice that of the hit option. This particular hand being just one example which I chose in response to you claiming that the initial bet is adequate for this equation and canceled out by the losses also being factored in. But, for that to be true, the win/loss ratio would need to be equal, and the win/loss ratio is not equal.
" the 6,5 vs 6-up, if the BS recommendations are followed, this hand plays exactly the same when hit or doubled down on. So, the return per dollar bet is the same for either play but the DD is listed on this site as having twice the EV as the hit option. The act of doubling down though requires a doubling of the bet and thus the DD wins twice what the hit wins, but at twice the cost. Each option then has an EV of 0.380696 insofar as the numbers provided are concerned. (Naturally, the DD option is the better play by far in this case, but again, this is a simple hand which would never be hit in accordance with the Basic Strategy. But the misleading EVs are apparent in all of the Double down EV comparatives that I have checked so far.)."
That example should have included that the EV for the DD is in fact listed as twice that for the hit option: a hit has an EV of 0.380696 as opposed the EV being listed for the DD as 0.761392... which is exactly twice of 0.380696. But the 2 hands play exactly the same insofar as hits taken via the BS. And the EVS are based on dollars won or lost per dollar bet. The hit requires half as much bet, so how could twice the bet not be the same EV on a per dollar bet computation.
Take 10 bets of $1 on the hit option with 6 wins and 4 losses, for a EV of $2. Then compare that to 10 bets of $2 with 6 wins and 4 losses for an EV of $4. For each dollar bet the return is $2. But the EV, here at least, in the Appendices, and on the simulator's analyzer, puts the EV for the DD at exactly twice that of the hit option. This particular hand being just one example which I chose in response to you claiming that the initial bet is adequate for this equation and canceled out by the losses also being factored in. But, for that to be true, the win/loss ratio would need to be equal, and the win/loss ratio is not equal.
February 25th, 2025 at 4:17:05 PM
permalink
It’s not EV per dollar bet. It’s EV per dollar of initial bet.
It’s a conceptual error you’re making. But I can’t get you to engage with the example, instead you go back to your original post.
Let me try something else.
Do you play UTH table game? There’s the ability to raise 3x or 4x preflop. Basic strategy says never bet 3x because if your hand is good enough to raise, raise the max to maximize EV. But if you think about it as “EV per dollar bet” you would conclude that betting 3x has the same EV for less risk. And that would be “irrational” (in the economic sense of not acting as if you are maximizing expected utility).
Alternately, do you know roulette? Imagine a $5 double zero table sitting next to a $10 single zero table . . .
It’s a conceptual error you’re making. But I can’t get you to engage with the example, instead you go back to your original post.
Let me try something else.
Do you play UTH table game? There’s the ability to raise 3x or 4x preflop. Basic strategy says never bet 3x because if your hand is good enough to raise, raise the max to maximize EV. But if you think about it as “EV per dollar bet” you would conclude that betting 3x has the same EV for less risk. And that would be “irrational” (in the economic sense of not acting as if you are maximizing expected utility).
Alternately, do you know roulette? Imagine a $5 double zero table sitting next to a $10 single zero table . . .
The race is not always to the swift, nor the battle to the strong; but that is the way to bet.
