Blackjack basic strategy -- Is it wrong?

I've been comparing my returns for Extra Draw Keno to those by IGT and sometimes don't agree. Let's look at the pick 4 game with this pay table as an example:

Catch 0: 0
Catch 1: 0
Catch 2: 1
Catch 3: 12
Catch 4: 31

If the player catches 3, his expected gross win by buying the extra ball is 12.95. After subtracting 1 for the cost of the extra ball, the net win is 11.95.

The way I've always analyzed every game of skill is to make the decision that results in the greatest net win, or smallest loss, for that situation. In other words, my goal is to advice the player how to play if he had a gun to your head and forced to play the game for x initial bets. My advice seeks to advise that player how to lose the least amount of money.

Getting back to that keno example, if you followed my advice, which would be to decline the extra ball after three catches, then the player can expect to get back 85.07% of an initial bet, per initial bet. This accounts for the cost of buying the extra ball after two catches. If the player buys the extra ball after three catches, then this ratio drops to 84.86%.

However, let's consider the ratio of the total return to total amount bet. I'll call this the "Element of Return." If the player declines the extra ball three catches his Element of Return is 87.69%. If he accepts it, then it increases to 87.94%.

The question of which strategy and return figure to use comes down to asking questions of why the player is playing in the first place. We mathematicians generally don't think about such things and just look at numbers, trying to make the most, or lose the least, at every decision point.

"Who cares about Extra Draw keno?", you might ask? Anybody who cared enough to study strategy probably wouldn't be playing keno in the first place.

The same issue applies to blackjack. Consider a soft 17 against a dealer 2 in a six-deck game where the dealer hits a soft 17.

Expected value of hitting = -0.000274
Expected value of doubling = -0.004882 (source)

It is easy to say the correct play is hitting, because the expected value is greater. But is it?

The house edge under those rules is 0.62%. The cost of that error is 0.46%. Again, it comes down to the player's reason for playing. If the player had a gun to his head and was forced to play x initial bets, and he wanted to lose the least money, then he should hit. If he was forced to bet x total units, including money bet doubling and splitting, then he should double.

Again, my strategies for every game seek to maximize the player's bankroll at every decision point. So my basic strategy says to hit in that situation. If I were to change it to double, then everybody and his brother would write to me asking why I differ from every other legitimate blackjack expert. I would also become a pariah in the blackjack community for going against the way the game has always been analyzed.

After all the set up, what do you think should be considered the right play for a soft 17 against a 2 under a hit-soft-17, 6-deck game?

Double at a TC of +1, otherwise hit is what I'd do.

Let's try this logic. It's a losing proposition no matter what you do. By hitting, you get multiple draws if you'd like. Following BS, you'd only do this by drawing a 5 for hard twelve. By doubling, your adding more money into an already losing proposition AND you're limited to that one single hit card. On the flip side of that coin, though, is that you cannot bust by doubling whereas hitting you can.

The answer depends on how you define your strategy goal. If your strategic goal is to maximize the EV of the wager you made at the beginning of the hand, without consideration to any wagers you might make in the future, then you should hit. That's the typical definition of "optimal strategy" -- you only look at the past. In that light, the only time you make an additional wager is if the conditional EV of that extra wager is greater than zero.

If you start looking at the future, then any strategic decision involving an additional wager is not evaluated against zero, it's evaluated against the EV of the alternative use of that same money for a subsequent bet. In that light, you might make an additional wager during a hand where the EV is negative, but less negative than using that same money for the next hand. Doubling down in blackjack where the cost of the double is less than the cost of a brand new hand (as in your example) is one such case.

Over any given time period, you'll always do better (from an EV standpoint) if you play optimal strategy. If you play the conditional-future strategy, you will do better from an EV percentage standpoint. Your loss will be greater in dollars, but smaller as a percentage of total wager volume.

But you can't buy dinner with percentages. I don't think it's useful to suggest that a strategy that loses more than optimal but has a smaller loss percentage is "better" in any meaningful way, because you can always play games with a denominator to alter percentages. If a $5 craps table offers 3/4/5x odds, and a $100 craps table offers 10x odds, it is not "better" for most to play at the $100 craps table just so they can achieve a lower percentage loss. The actual cost is too high for many.

The counterargument that I've heard before is "well, if you're going to bet the money anyway, you might as well get the best value for it." That's the same argument I hear for playing odds instead of making a new line bet. However, that ignores the fact that almost nobody plays for a fixed amount of total wagering action. Gamblers almost invariably play for a period of time, and if the goal is to maximize the EV in dollars over that timeframe, there is only one way to do that. If you're a $5 craps player, taking odds is irrelevant to maximizing that EV, but it often makes the game more fun. Making bets other than the line bet is counter to maximizing that EV, and so is doubling in blackjack when the double itself is negative, even if it's less negative than the cost of the next hand. If you're going to bet the next hand anyway, throwing in a -EV double does not help. To use your phrase, nobody has a gun to their head forcing them to bet x total units. If they do, tell the masked gunman to take his hostage to the craps table at Casino Royale and make 100x odds bets.

Also, I submit that anyone who has the capacity to evaluate whether the marginal cost of a double is less than the cost of a new hand should be counting cards anyway, and therefore should be evaluating both the cost of the double and new hand in terms of instantaneous EV rather than top-of-the-deck EV. If you want to do some research, that's where you should focus. For example, are there any scenarios where the instantaneous EV of a double compared to the EV of the next hand would change your doubling strategy based on your knowledge of the count? More broadly, can you alter play strategy in a card counting scenario to take advantage not only of what the current EV is, but what the future EV (for the next hand) is likely to be based on a distribution of cards that could come out during play of the current hand, and adjust the strategy accordingly? Perhaps the changes are too small to matter, but I don't know if anyone has ever looked.

I think another factor which you don't see talked about much, is the frequency of the play at hand. How often do we see A, 6 vs 2 on a H17 game. If the play is somewhat rare, then I'd say it's not going to make to much of a difference in a short period of time.

It's reasons like this that a lot of counters will ALWAYS stand on 16 vs 10 even in a negative count when the correct play is to hit. This is a very common match up and counters are trying to hide the fact they're counting so they won't deviate no matter the situation. If 16 vs 10 were a rare play, then you'd see the counters play it correct every time.

Good comments, thank you. I don't disagree with any of them.

One thing I'm seeing more of is that most gamblers play to a bet amount they are comfortable with and don't really care much about what they are playing or how they play it. The success of triple-zero roulette is a case in point.

I don't plan to change the foundation of the way I've analyzed games for 20 years. However, extremists of the philosophy of losing as little as possible criticize me for advocating taking odds in craps. I'm not indifferent about it -- I actively advocate doing so, unless the player is already at the minimum pass bet and betting the odds would be more than he is comfortable with. However, if you extend that logic to its end, I should advocate betting less per hand in blackjack and doubling soft 17 against a 2. The player will get a better return on all his money bet doing so. There does seem to be an inconsistency here.

Quote: Wizard

...However, if you extend that logic to its end...

If you extend it further, you'd tell people to stay the hell out of casinos!

Just let the math be the math without concern for bankrolls, time limits, table minimums, or how comfortable the player is with their bet sizes.

After all, people are coming to WoO for academic reasons. Not to learn that a different strategy would cost them 41¢ per $100.00 over a lifetime....

Quote: DJTeddyBear

After all, people are coming to WoO for academic reasons. Not to learn that a different strategy would cost them 41¢ per $100.00 over a lifetime....

I think people come for both reasons.

Quote: Wizard

However, if you extend that logic to its end, I should advocate betting less per hand in blackjack and doubling soft 17 against a 2. The player will get a better return on all his money bet doing so. There does seem to be an inconsistency here.

Not really, because if you bet less per hand in blackjack and play properly, you have an even lower EV in dollars, and that's what matters. The logic you presented implies that a $5 craps player making all sorts of center bets is better off than a $100 player on the line. It's not about minimizing EV overall (or you'd never play craps period), it's about minimizing EV for your play. If someone's play is $100 craps, telling them to play $5 craps and a bunch of hardways isn't relevant advice. Similarly, if their play is $25 blackjack, telling them to play $5 blackjack and make bad strategy decisions isn't relevant advice. That's like telling someone they can save money on their mortgage by buying a cheaper house, even if the interest rate is a bit higher. Well, obviously...

Quote: MathExtremist

Not really, because if you bet less per hand in blackjack and play properly, you have an even lower EV in dollars, and that's what matters. The logic you presented implies that a $5 craps player making all sorts of center bets is better off than a $100 player on the line. It's not about minimizing EV overall (or you'd never play craps period), it's about minimizing EV for your play. If someone's play is $100 craps, telling them to play $5 craps and a bunch of hardways isn't relevant advice. Similarly, if their play is $25 blackjack, telling them to play $5 blackjack and make bad strategy decisions isn't relevant advice. That's like telling someone they can save money on their mortgage by buying a cheaper house, even if the interest rate is a bit higher. Well, obviously...

But if it is about EV for your play, then the player should double soft 17 vs. 2. While he is losing a little more, he is also getting more "play" with the double down. Overall, his ratio of loss to total amount bet decreases. It isn't just about a "lower EV in dollars." If it were, I would be telling everybody to play penny video poker, one penny per hand.

Again, to discuss this in depth, the question needs to be asked about why negative EV gamblers gamble in the first place. I say it is for the fun/excitement. Most are not going to get their fix on penny video poker. Whatever it takes to get your fix, I suggest betting to that level, and then try to minimize your losses with correct strategy.

Funny thing about EV/math in regards to blackjack... There's ALWAYS 1 right answer =). Past that you could play differently for tons of situational reasons (such as cover), but mathematically speaking, there is only one right play here! If you're going to take the "eh it's small and I'm not trying to lose as little as possible I'm trying to gamble!" then why not double your hard 7 vs dealer 6? After all, we're here to gamble!

Here is what it comes down to. If the player doubles instead of hits soft 17 vs 2 the house edge goes up by 0.00127%. However, the Element of Risk goes down by 0.00051%.

Quote: Wizard

Here is what it comes down to. If the player doubles instead of hits soft 17 vs 2 the house edge goes up by 0.00127%. However, the Element of Risk goes down by 0.00051%.

That should put it in perspective, no?

When someone who's already playing at a $25 table with a $500 bankroll asks "I have soft 17 vs. a dealer 2, what's the right play?" isn't the answer the one that minimizes their losses given their initial wager? Do you think that player would ever care about minimizing their element of risk as you've quantified it above? I can't imagine anyone caring that their element of risk was 0.00051% smaller if it meant they were losing more money. Edited to clarify: making that suboptimal play means they're not only losing more theoretical money on that hand, but they'll also lose more EV over the course of their play session by doubling rather than hitting if it comes up again.

I mean, you can make all sorts of justifications for the "better" strategy to be increasing the loss while increasing the total wager proportionately more, and thereby decreasing the element of risk. But in the final analysis the loss is still higher regardless of the denominator. If someone brings $500 to a casino and wants to play $25 blackjack for some arbitrary timeframe, there is only one way to maximize their EV (without counting) and that's to play optimal strategy. Anything else has them either making fewer bets or costing them more in theoretical loss.

This is like the same thing as craps players taking odds. HE is to be determined by your initial wager and how to maximize wins or minimize losses. Putting out more money doesn't help you, even if you're getting fair odds (craps odds bet) or slightly better odds (doubling A6 vs 2) than what you may otherwise use that money for.


Now, there might be cases where coming up with a strategy like this, based on "element of risk" or what-have-you makes sense......but for the most part, no. Just no.

Quote: MathExtremist

That should put it in perspective, no?

Point taken.

However, the issue is not so esoteric when it comes to Extra Draw keno. As mentioned in the original post, if the player catches 3 out of balls 4, he can either accept a win of 12, or spend 1 credit for a 5% chance at increasing it to a gross win of 31. If he doesn't get the 31, he still gets his win of 12, so he is betting on an extra 19. So, it is like a side bet with a 5% chance at a win of 19. The expected return of that is 0.05*31=95%. Using the classical way of expressing the return, the return of the pick-4 game with the 1-12-31 pay table is 85.07%. The player will win 12 after the initial 20 balls with probability 0.043247891. What's better, a return of 85% or 95%? So, we're not talking about 0.0005% here.

Also, IGT calculates their return for the game with the player buying the extra ball in that situation. In other words, the strategy that maximizes what I defined as the "Element of Return" previously. Then again, in their video poker games involving supplemental bets their returns seem to be based on the way I do it, maximizing the EV for the hand, not the overall game.

At the very least, should you ever work with them, consider this a warning about how they think about keno games. I think a very strong argument could be made that they are right.

I like math in general, and always try to solve those brain teasers where the trains are leaving Chicago and New York, or where Tom has twice as many apples as Sally's nephew's mother's husband. But this thread has me tearing my hair out trying to follow it, until unconsciousness puts me out of my misery. At least I can ignore the Keno and craps parts (this forum does have "blackjack" at the top, right?)

Is there a simple answer? I hit a soft 17 against a 2., 6Deck, H17 AND S17.

WOO's charts say that hitting has an expected return of -.000491, doubling -.007043. So hitting is less worse, correct? And since by doubling I am putting out, let's see, twice as much, isn't my net loss even greater, since I lose more often, with more money at risk?

Is this a discussion amongst the Mathemaniacs that mere mortals need not trouble themselves with, especially since the difference is out there in the insignificant digits way out there to the far right of the decimal point?

Quote: racquet

I like math in general, and always try to solve those brain teasers where the trains are leaving Chicago and New York, or where Tom has twice as many apples as Sally's nephew's mother's husband. But this thread has me tearing my hair out trying to follow it, until unconsciousness puts me out of my misery. At least I can ignore the Keno and craps parts (this forum does have "blackjack" at the top, right?)

Is there a simple answer? I hit a soft 17 against a 2., 6Deck, H17 AND S17.

WOO's charts say that hitting has an expected return of -.000491, doubling -.007043. So hitting is less worse, correct? And since by doubling I am putting out, let's see, twice as much, isn't my net loss even greater, since I lose more often, with more money at risk?

Is this a discussion amongst the Mathemaniacs that mere mortals need not trouble themselves with, especially since the difference is out there in the insignificant digits way out there to the far right of the decimal point?

The idea is, if you're going to be making $25 bets at -0.5%, then it's a good bet to put out a $25 bet at -0.05% (or whatever the actual numbers are). Sometimes, stuff like this makes sense. Other times it doesn't. Sometimes it's practically useless. Other times it's very useful.

Quote: Wizard

Point taken.

However, the issue is not so esoteric when it comes to Extra Draw keno. As mentioned in the original post, if the player catches 3 out of balls 4, he can either accept a win of 12, or spend 1 credit for a 5% chance at increasing it to a gross win of 31. If he doesn't get the 31, he still gets his win of 12, so he is betting on an extra 19. So, it is like a side bet with a 5% chance at a win of 19. The expected return of that is 0.05*31=95%. Using the classical way of expressing the return, the return of the pick-4 game with the 1-12-31 pay table is 85.07%. The player will win 12 after the initial 20 balls with probability 0.043247891. What's better, a return of 85% or 95%? So, we're not talking about 0.0005% here.

In order to look at the question from a practical standpoint, I think the relevant thing we should be asking is whether or not the player is ever going to play a draw of Extra Draw Keno again (whether or not the player buys the extra three balls) as long as he or she lives. If the player is not going to play Extra Draw Keno ever again, then the player should decline the Extra Draw in this situation because (in and of itself) it has a negative EV, as you have pointed out. If the player would continue to play the game, then the player should pay for the Extra Draw as it has a better EV on that extra unit bet than would a completely new draw.

One can also look at the result in terms of totals:

No Extra Draw:

12 -1 =Profit of 11 units (100%)

Extra Draw:

12 -2 = Profit of 10 units (95%)

31 -2 = Profit of 29 units (5%)

(29 * .05) + (10 * .95) = 10.95

______________

Unlike the Blackjack hand mentioned, the thing about Extra Draw Keno is that the player has already won. That also separates the Extra Draw Keno from the Craps Odds comparison, the player doesn't know the result of that hand, either.

In this case, the player's overall profit is expected to be 1/20th of a unit lower than just refusing the Extra Draw given the fact that the player has already won. However, the Expected Loss of 5% on that one unit bet is less than the Expected Loss of betting the unit on a completely new draw.

In other words, if we assume that the player will be betting one of those units again, and remember, those twelve units can effectively be added to the player's credits even though they haven't been yet, then the player should go ahead and accept the Extra Draw because that is better than playing a new draw from scratch again.

If, for some reason, the Extra Draw player decides that he/she is never going to play Extra Draw again, then the player should walk away with the profit of eleven credits.

Perhaps the way IGT decided to figure it was just to assume that the player would play again either way.

I have a different philosophy. No matter what the game I'm playing, I like to know what the very close call decisions are: like Hit or Double A6 vs 2, 6 deck, S17. When I see I have a very close decision I immediately try get more information! I peek at any other players cards that I can see and take into account any cards that are exposed during the play of hands that act before me.

In the example of A-6 vs 2, 6 Deck,S17 I simply watch to see if any A-4 cards are out of the deck vs cards 5-9, realizing that the prospect of getting a 3 or 4 is where the real advantage is in doubling. I don't do any real math in my head, I just keep it simple. If I see one or more cards 5-9 dealt to the hands of other players and no cards A-4 are exposed before I must make my decision, then I'm doubling A6 vs 2. If I see a 3 or 4 in another players hand then I'm likely going to Hit A6 vs 2 unless I see a lot of other cards in the range of 5 to 9.

Its not card counting - because I'm not trying to track prior hands and I'm not varying my bet size. It's just playing smart and it makes the game more fun.

But if I'm playing 1 on 1 vs a BJ dealer in the situation that the Wiz gave us: an A-6 vs 2, 6-deck, S17 then I personally would play optimal strategy and HIT the A-6.

The more intriguing question is: if you have Double vs HIT decision where the DOUBLE is better than HIT by less than 0.003, do you accept the greater volatility involved in doubling and chase the tiny edge?

Quote: MathExtremist

If someone brings $500 to a casino and wants to play $25 blackjack for some arbitrary timeframe. . .

What if someone brings $500 to a casino and wants to turn it into $10,000 at the blackjack table while minimizing their chance of losing it all. Doubling would be the correct play.

I can definitely accept that "basic" strategy should be whatever maximizes EV. But that also means that unless you are counting or have some other way to change the EV, the correct strategy is to never play.

I guess if someone decides they want to donate money to the casino in exchange for them letting you breathe their second hand smoke, either way is fine: Lose less money or lose money at a lower rate. For an informational chart I would say just go with what everyone else has, because that's what the community has decided is preferred, even if some individuals may have other ideas.

Quote: racquet

WOO's charts say that hitting has an expected return of -.000491, doubling -.007043. So hitting is less worse, correct? And since by doubling I am putting out, let's see, twice as much, isn't my net loss even greater, since I lose more often, with more money at risk?

No. The -0.007043 is the expected amount of UNITS lost, after considering you doubling your bet.

Quote: Mission146

Perhaps the way IGT decided to figure it was just to assume that the player would play again either way.

They assume the player will buy the extra ball if the house edge in doing so is less than that of the overall game.

BTW, does anyone know if the player earns player card points for the supplemental bet in Extra Draw keno? I tend to think he would, but welcome anyone to confirm or deny.

Quote: Wizard

BTW, does anyone know if the player earns player card points for the supplemental bet in Extra Draw keno? I tend to think he would, but welcome anyone to confirm or deny.

I would be surprised if anyone here plays it with any regularity. I'll be happy to find out at earliest opportunity if you want, which I would suggest would be in about four days, you'll probably owe me anywhere from $0.75-$10.00 (depending on how many plays before I hit some kind of play that results in making the decision) next time you see me...lol...The $0.50-$10.00 represents my expected loss because the easiest way to do it is bet $5.00/play and see if I get more than one point after making the decision, points are awarded at 1 point for $5.00 coin-in.

If I win overall, I'll ignore my negative EV and just let you know the result. ;)

(Kidding, of course, I'll just find out for you if you really want to know)

Quote: Mission146

I'll just find out for you if you really want to know)

That's okay. I could do the same thing myself but it isn't that important to me.

Here's some thoughts on this:

A practical use for the strategy presented here (as opposed to the usual strategy) would be when you need to have bet a certain amount to receive a bonus, etc. (e.g. some online casinos). Making a double/split that is wrong by less than the HE is an advantageous way to reach the total faster. (If the target was a certain number of hands played, you'd follow the modified strategy with splitting but not doubling, assuming that each post-split hand counts as another one.)

Another benefit of the conventional strategy is it's independent of any other rules that would normally not have any effect on such a decision (e.g. DAS/nDAS for non-pair hands, S/H17 for 7-10 upcards, BJ payout for any other decision). With the modified strategy a double/split decision would maybe flip if it was a game with worse rules but not so with better rules, even if said rule change would not affect the decision under the usual strategy as I described. (As a side-note if it were a game with a player edge, then there might be some doubles/splits you'd refrain from making under the modified strategy if the cost would be more than your advantage.)

Quote: Wizard

Again, to discuss this in depth, the question needs to be asked about why negative EV gamblers gamble in the first place.

Extending your line of thought about doubling on A-6 vs 2, perhaps the "correct" Blackjack strategy is to not play it at all.

Quote: gordonm888

Extending your line of thought about doubling on A-6 vs 2, perhaps the "correct" Blackjack strategy is to not play it at all.

Exactly. Same conclusion the computer came to in War Games.

However, I have no problem accepting that for some people, playing has an entertainment value. If the player gets x units of happiness for every $1 bet, including on doubles, then he will achieve more happiness per dollar by doubling on that hand.

Quote: Wizard

Exactly. Same conclusion the computer came to in War Games.

However, I have no problem accepting that for some people, playing has an entertainment value. If the player gets x units of happiness for every $1 bet, including on doubles, then he will achieve more happiness per dollar by doubling on that hand.

Fair enough. Then let me answer in kind: I think there is far more entertainment value in being dealt a new hand than in doubling my bet on an A-6 vs 2. My reasoning is:
- In BJ, as in most card games, there is an adrenaline rush/entertainment value in turning over the first cards you've been dealt in anticipation of the prospect of having been dealt a great hand.
- am I the only person who has a mild dislike for playing against a dealer 2? Its because sometimes the dealer slaps down four or 5 small cards so fast that I can't add them up in real time leaving me bewildered for a moment as to what the bloody outcome what. Definitely not fun.
- also a dealer 2 is morally ambiguous. With a dealer upcard that is a 5, 6,7 or a 10 or Ace, you have some idea as to what the righteous outcome ought to be -and you hope to achieve it or to dodge a bullet. With a dealer 2, I feel like the dealer's final hand is almost random and unknowable and, for me, this reduces the tension of the hand and the drama of the outcome.

So, I would choose to maximize my entertainment value and Hit (instead of double) the A-6 vs 2, thereby preserving one betting unit for the deal of one additional hand.

I think it's best to give the best strategy as the one which makes most (or loses least) at every stage. There are occasions where a choice of bet, typically split or double, have a lower HE than the base game - that is your extra $1 to split or double is now worth (say) 99.9c and this is better than making the wager on the next hand. However this presupposes that you're down to your last few dollars.

Personally I prefer looking at sitting at (say) a $5 table and minimising my cost per hand. Then, in theory this can be compared with other games and given the number of hands per hour etc. an informed choice of games made.

Interestingly if you were playing BJ to make money (e.g. an AP) then you might double because it reduces the time of this hand and gets you to the next one quicker. Similarly, under close decisions, you might not split as you want to make the next "large" bet while the count remains good and splitting might taken too many good cards.

However the "correct" strategy should be the one that ignores all these side issues.

Afterthought The correct strategy in Three Card Poker is to fold Q63, but you could argue that your raise on such a marginal hand is better than using the $1 on a new hand. I should like to suggest that you shouldn't propose a change the strategy to raise on slightly worse hands. It seems reasonable to state that Q63 should be folded and in a similar way the correct play on Blackjack hands should be the ones with higher EV to the player.