Wizard's Simple Strategy question
Quote: 78687Just starting to learn about optimal blackjack strategy...I'm confused why you don't double when you have a hard 16 and the Dealer's Up Card is 7 to ace. The cutoff to hit is 16, so no matter what you will only hit once. Why not double? Thanks!
Because with hard 16 the most likely outcome is a loss. The last thing you want to do is get more money on the table. So since hitting costs the least amount in the long run that is what we do.
Quote: 78687Just starting to learn about optimal blackjack strategy...I'm confused why you don't double when you have a hard 16 and the Dealer's Up Card is 7 to ace. The cutoff to hit is 16, so no matter what you will only hit once. Why not double? Thanks!
You have 16, and only 5 of 13 cards will keep you from busting. If you're going to lose 8/13ths of the time, why add money to the hand?
Note with splits this logic doesn't always apply, as sometimes you're converting a really bad hand (16) into two slightly bad hands (8-8), and other times converting a really good hand (e.g. 18) into two quite good hands (9 9).
Quote: charliepatrickThe thing about doubling is whether, in the long run, you are better hitting than doubling. Where the chances of winning are less than 1/2, it is clear that you are better hitting (even if you know you're only taking one more card whatever happens). The reason is your existing BJ bet goes the way it goes, while you have a chance to add another bet (double). If most the time your bet wins, then the additional bet will be worth making (e.g. doubling soft 17) - as you win more than you lose on the "double" part. If it's the other way round, then you're better off leaving the "double" part in your pocket.
Note with splits this logic doesn't always apply, as sometimes you're converting a really bad hand (16) into two slightly bad hands (8-8), and other times converting a really good hand (e.g. 18) into two quite good hands (9 9).
Probably doesn't matter for this OP, but a couple refinements for anyone else who may read it. If your chances were 50/50, it is still clear you would not double, your hand must be stronger than the dealers up card. Also, 18 is not a good hand. Two 9s is better, but never justifies the cost of a split versus a 10.
Quote: 78687Just starting to learn about optimal blackjack strategy...I'm confused why you don't double when you have a hard 16 and the Dealer's Up Card is 7 to ace. The cutoff to hit is 16, so no matter what you will only hit once. Why not double? Thanks!
You Double when you have a Positive EV AND that positive EV is higher than the positive EV of a Hit.
You never Double with a Negative EV.
The point that you will take only one card means that the Double EV is twice the Hit EV. If the Hit EV is negative then the Double EV will be twice that negative.
When you have a Positive EV for a Hit and you will take one card in any case then the Double EV will be twice that positive and you always Double.
When you have Positive EV for a Hit but you will take more than one card then the Double EV is NOT twice that (not being able to hit again costs). The EV of the Double will be less than twice the Hit EV but in most cases it will still be higher than the Hit EV and the BS is Double. In some cases it will be less than the Hit EV and then you Hit.
Quote: AceTwoYou Double when you have a Positive EV AND that positive EV is higher than the positive EV of a Hit.
You never Double with a Negative EV.
The point that you will take only one card means that the Double EV is twice the Hit EV. If the Hit EV is negative then the Double EV will be twice that negative.
When you have a Positive EV for a Hit and you will take one card in any case then the Double EV will be twice that positive and you always Double.
When you have Positive EV for a Hit but you will take more than one card then the Double EV is NOT twice that (not being able to hit again costs). The EV of the Double will be less than twice the Hit EV but in most cases it will still be higher than the Hit EV and the BS is Double. In some cases it will be less than the Hit EV and then you Hit.
Another couple refinements. Soft 17 v. 4-6 and 11 v. 4-6 are the only doubles that double EV, if playing proper basic strategy; using the Wizard's simple strategy, include doubling against the 3 for those hands I imagine. Doubling a negative EV hand can far more than double the negative EV, it can more than quadruple it.
Quote: MangoJSo in short: the double EV is always equal to double the EV for a one-hit.
There is no 'one-hit' EV. One hit could give you any random card, which would elicit another random card--you can't calculate EV based on incomplete data. Generally, only being able to take one-hit costs you EV. It only has no cost on the above listed hands. In those cases, EV is double that of taking one-hit because if it were a non-double situation, it would be incorrect to take a second hit.
I think 10 v. 4-6 also applies. The reason is that the Ace gives you 21, and anything else 12+; so you'd never take a second hit. (This assumes it isn't correct to hit 12 vs 4 - which with multiple decks and no Tens in your hand, is correct.)Quote: SonuvabishAnother couple refinements. Soft 17 v. 4-6 and 11 v. 4-6 are the only doubles that double EV...
The reason it doesn't apply to doubling vs 2 or 3, is if you got 12 you would have wanted to take another card.
Similarly with soft totals (v 4-6) you would never want to hit any result after doubling (say) soft 18, however you are taking an initial trade-off by taking an extra card rather than standing, but since it's for twice as much it's the better option.
Quote: SonuvabishThere is no 'one-hit' EV. One hit could give you any random card, which would elicit another random card--you can't calculate EV based on incomplete data.
I'm sorry, can you explain more what you mean by your statement ?
If you follow the "strategy" to hit only once and then stand whatever card you get, this gives you a precise EV which I called "one-hit EV". Whether or not to play this strategy is not a question here. Clearly it is not a favourable strategy, because the usual hit will always be favourable (or at least equal). My statement is that the "double EV" is twice the "one-hit EV", because this is exactly what you do: You double the EV of your current hand (by doubling the stake), but you a forced on a strategy that only takes one hit.
Also I don't get your incomplete data argument. Sure, any drawn card is random. But the card does not fall from the sky but is drawn from a shuffled deck with precisely known statistical properties.
Quote: MangoJYou double the EV of your current hand (by doubling the stake)
Not sure what is meant by this
The Wizard lays it out with the below. He says it shows cost or profit in "cents per original dollar bet".
https://wizardofodds.com/games/blackjack/appendix/1/
With soft 18 against a dealer 2, the EVs he lists are below, and you stand simply because the EV is best.
0.121742 standing
0.119750 doubling
0.062905 hitting
You don't figure that doubling the EV of 0.119750 is better than 0.121742 by being 2 times or 0.2395
So I'm not sure what you mean
PS: also doubling 0.062905 is 0.12581 not 0.119750, so doubling the standing EV or the hitting EV is not how this is derived.
Quote: odiousgambitNot sure what is meant by this
The Wizard lays it out with the below. He says it shows cost or profit in "cents per original dollar bet".
https://wizardofodds.com/games/blackjack/appendix/1/
With soft 18 against a dealer 2, the EVs he lists are below, and you stand simply because the EV is best.
0.121742 standing
0.119750 doubling
0.062905 hitting
You don't figure that doubling the EV of 0.119750 is better than 0.121742 by being 2 times or 0.2395
So I'm not sure what you mean
PS: also doubling 0.062905 is 0.12581 not 0.119750, so doubling the standing EV or the hitting EV is not how this is derived.
Soft 18 vs 2 is a bad example, as if you hit and end up drawing a 4, you would then hit again. MangoJ is talking about cases where you would hit exactly one time - never more than that.
If you look at 10 vs 6, hit is 0.287795, while double is 0.575590 - exactly 2x the EV of hitting. This is because regardless of what card you have drawn on a single hit, you are not going to hit again against a 6.
The same even goes for hard 20 vs, say a 2. Hit is -0.855230, while double is -1.710461, again 2x.
Quote: odiousgambit
https://wizardofodds.com/games/blackjack/appendix/1/
With soft 18 against a dealer 2, the EVs he lists are below, and you stand simply because the EV is best.
0.121742 standing
0.119750 doubling
0.062905 hitting
I have been trying to understand the concept of Element of Risk. Is it correct to say that doubling soft 18 vs dealer 2 improves your Element of Risk even though it slightly reduces your EV? You get twice as much money in action for almost the same EV.
Edit: Reading my own question, I see that I am clearly quite wrong. Carry on.
Quote: MangoJI'm sorry, can you explain more what you mean by your statement ?
If you follow the "strategy" to hit only once and then stand whatever card you get, this gives you a precise EV which I called "one-hit EV". Whether or not to play this strategy is not a question here. Clearly it is not a favourable strategy, because the usual hit will always be favourable (or at least equal). My statement is that the "double EV" is twice the "one-hit EV", because this is exactly what you do: You double the EV of your current hand (by doubling the stake), but you a forced on a strategy that only takes one hit.
Also I don't get your incomplete data argument. Sure, any drawn card is random. But the card does not fall from the sky but is drawn from a shuffled deck with precisely known statistical properties.
OK, reading what wudged said about your statements, I think I understand what you're saying. If you are asking if doubling a 10, 11 and soft 17 v. 4-6 is exactly twice that of taking "one-hit" on those hands, then the answer is yes. I took your question to mean that dpubling would double EV for the first hit on any hand. By incomplete data, I meant you can't know the EV of a hand that you do not finish, which you can disregard. Please excuse the miscommunication.
The usual EV for a hit is calculated by an implied strategy you will follow optimal play (or fixed strategy) after your card. This EV is of no use for calculating double EV. That's why you need to look at the "one-hit" EV, that means the EV following the strategy that you always stand (unless you are bust) after taking the hit card.
Of course the "one-hit" EV is always equal or less than the "hit" EV.
Then for calculating the double EV, it is trivially double the "one-hit" EV. This is not also true for 11 vs. 6, but especially true for 11 vs. 9 or any other hand.
If you don't believe it, go to the Wizards blackjack appendix tables and calculate the "one-hit" EV: Consult the stand table and weighting each possible drawing card by it's probability of drawing, and multiply with the corresponding stand EV of the resulting hand. Double that amount, and you get the value for the double EV, which you can confirm in the different table.
Quote: JimRockfordI have been trying to understand the concept of Element of Risk. Is it correct to say that doubling soft 18 vs dealer 2 improves your Element of Risk even though it slightly reduces your EV? You get twice as much money in action for almost the same EV.
Edit: Reading my own question, I see that I am clearly quite wrong. Carry on.
Durn it; I was just working up the courage to attempt an answer and see if I got it right. Maybe next time. (my best understanding is, you are correct that you were wrong in your original statement). Or maybe this time, fully expecting corrections as necessary.
Element of Risk takes into account that you are making BJ bets beyond your initial ante in order to double or split, based on optimal strategy for each play. The numbers in appendix 1 (though labeled "returns") already have that figured in. It's Wizard's attempt to give you apple-for-apple evaluations of what to do in any particular case, rather than having to guesstimate whether you would be getting value for 2x your bet on a double or split.
To figure BJ EOR, he's taking the average bet, which is a bit over 1 unit because of the doubles and splits possible at the decision point, and dividing it into the house edge of the BJ game under the rules he stated in the intro. If the BJ game has surrender, that's also figured into the EOR, but he didn't list that in this appendix. In craps/roulette, there is no decision point, so your EOR and EV/HE are always the same. To the other extreme, in a game like Mississippi Stud, where you have 3 decision points and can bet another 9 units max after your ante, EOR is very different than HE, because your average bet under optimal strategy is (from the Wizard's page) 3.59 units, not just the 1 unit ante. So, with MS Stud, the HE is 4.91%, which is pretty high, but 4.91/3.59 leaves your element of risk at a more acceptable 1.37%.
Quote: MangoJWell, EV is not a property of a hand or of a single choice of action. It is a property of a strategy, i.e. the collection of all choices under all future possible scenarios. If you talk about EV of a hit, you need to first specify how you play afterwards when you receive your card (which may of course depend on that card).
The usual EV for a hit is calculated by an implied strategy you will follow optimal play (or fixed strategy) after your card. This EV is of no use for calculating double EV. That's why you need to look at the "one-hit" EV, that means the EV following the strategy that you always stand (unless you are bust) after taking the hit card.
Of course the "one-hit" EV is always equal or less than the "hit" EV.
Then for calculating the double EV, it is trivially double the "one-hit" EV. This is not also true for 11 vs. 6, but especially true for 11 vs. 9 or any other hand.
If you don't believe it, go to the Wizards blackjack appendix tables and calculate the "one-hit" EV: Consult the stand table and weighting each possible drawing card by it's probability of drawing, and multiply with the corresponding stand EV of the resulting hand. Double that amount, and you get the value for the double EV, which you can confirm in the different table.
Wait, I think we are back to where we started. As I said, there is no such thing as 'one-hit' EV. Doubling can more than quadruple your losses. I suppose you are saying if you purposely play extremely poorly, you can make it so doubling always exactly doubles your losses. Yeah, I guess you could.
Quote: SonuvabishYeah, I guess you could.
You are twisting my words. I'm not saying you should ever play a "one-hit" strategy. I'm saying that the EV of a "one-hit" strategy is fairly simple to calculate, and once you have the "one-hit" EV you can calculate the EV of a double down strategy.
Quote: AceTwo
The point that you will take only one card means that the Double EV is twice the Hit EV. If the Hit EV is negative then the Double EV will be twice that negative.
When you have a Positive EV for a Hit and you will take one card in any case then the Double EV will be twice that positive and you always Double.
Not necessarily, but pretty much correct. Sometimes doubling is +EV, but hitting is more +EV, for example, 9v7. Hitting is ~0.17, while doubling is ~0.11. Hitting 12v7 is ~-.21, while doubling is ~-.50. Doubling is more than 2x the -EV in such a situation because you give up the option to hit again. When you get to higher stiff hands, the EV gets closer and closer to 2x the EV (negative EV*), due to the fact that you aren't going to be giving up a chance to hit again (ie: only time you'd hit 15v7 twice is if the first time you catch an Ace....but if you have a 12v7, you have multiple chances to hit again (draw A-4,,,then draw again...)).
edit: Over-read the "and will only take one card" part. =\
Quote: MangoJYou are twisting my words. I'm not saying you should ever play a "one-hit" strategy. I'm saying that the EV of a "one-hit" strategy is fairly simple to calculate, and once you have the "one-hit" EV you can calculate the EV of a double down strategy.
But there is no such thing as a one-hit strategy. Why would you hit on 5 and stand on 7? What happens when you double a 6, and 1/13 times you get an Ace, which gives you a stronger hand that you would normally never stand on? You can calculate the EV of doubling, but what is the "one-hit' EV? I'm not twisting your words, I'm trying to make sense of them. A one-hit strategy is purposefully playing poorly, is it not? If you wish to calculate EV in this fashion in some manner, don't let me stop you. I don't care.
Quote: SonuvabishBut there is no such thing as a one-hit strategy. Why would you hit on 5 and stand on 7? What happens when you double a 6, and 1/13 times you get an Ace, which gives you a stronger hand that you would normally never stand on? You can calculate the EV of doubling, but what is the "one-hit' EV? I'm not twisting your words, I'm trying to make sense of them. A one-hit strategy is purposefully playing poorly, is it not? If you wish to calculate EV in this fashion in some manner, don't let me stop you. I don't care.
I believe the "one-hit" strategy isn't a strategy in general, but for specific hands. If you have 12v2 or 12v3, you're only going to hit once. If you have 10v4,5,6, you're only going to hit (well, double, actuall), once, sit you're never going to hit again. If you have 16v7,8,9,T,A, you're only going to hit once, never twice.
Quote: SonuvabishI'm trying to make sense of them. A one-hit strategy is purposefully playing poorly, is it not? If you wish to calculate EV in this fashion in some manner, don't let me stop you. I don't care.
Ok, I will try simple words: one-hit EV is a tool. It's not in any way meant to be played, it's meant to be analyzed to gain further insight into the game.
For some people tools might look rather funny than useful. That's okay. Surgical instruments look to me also rather funny than useful. But I don't make the mistake and judge surgeons by their look of their funny tools, I judge them by what they can do with them. As any sane man should also on their next time visiting a hospital.
Soo .... you think the "one-hit" EV is of no use on a hand like 11 vs 8, as you would likely re-hit your hand. Again, it's a tool. Although noone should play it, let's calculate it (all stand EV data is taken from Wizards Blackjack Appendix 1 for the infinite deck analysis against a S17 dealer).
| hit card | probability | Stand | EV against 8 | partial sum |
|---|---|---|---|---|
| A | 1/13 | 12 | -0.510518 | -0.039270 |
| 2 | 1/13 | 13 | -0.510518 | -0.039270 |
| 3 | 1/13 | 14 | -0.510518 | -0.039270 |
| 4 | 1/13 | 15 | -0.510518 | -0.039270 |
| 5 | 1/13 | 16 | -0.510518 | -0.039270 |
| 6 | 1/13 | 17 | -0.381951 | -0.029380 |
| 7 | 1/13 | 18 | 0.105951 | 0.008150 |
| 8 | 1/13 | 19 | 0.593854 | 0.045681 |
| 9 | 1/13 | 20 | 0.791815 | 0.060908 |
| T | 4/13 | 21 | 0.930605 | 0.286340 |
| Total | 1 | 0.175346 |
So the "one-hit" EV gives +0.175346. Pretty lame against the usual hit EV (+0.229982 from the same appendix). Do you still see no use ?
Because - as said before a couple of times - twice the "one-hit EV" (2 * 0.175346 = 0.350692) exactly matches the "double EV" (0.350693, from the same appendix). And that is not only 11 vs. 8, it is any hand against any dealer upcard. For the reasons given some posts earlier. But as you said, what do you care....
There is nothing illogical seeing the double down as equivalent to "double your stake but forfeit right to re-hit" whose EV is thus equivalent to double the one-hit EV.
How about a different application ? Some player (obvious a bad one) offers you to double down his hand on his initial bet. That's not uncommon at least, I've read some discussion in this thread. Which hands should you double down from your perspective ? Obviously it's quite more hands than the basic-strategy would indicate, as you don't risk the initial bet when doubling down for this someone else. The answer is: whenever the one-hit EV is positive.
Not sure where our discussion will converge. Again it's a tool, not a strategy to be played. Whoopps... I just gave you a specific strategy example.
Quote: SonuvabishIt's not a tool for anything, it is utter nonsense. Perhaps it's a tool for someone like the Wizard to calculate the table, there's always an exception, I don't know--but it's not useful here. it's convenient when you use a hand like 11 that automatically turns to stiff or pat hand, and looks more reasonable than others, to try and salvage some type of argument, since a 12-16 have the same value and you will normally double 11. What if your hand is 5 v. A? Show me your one-hit EV table. Exactly as I said, if you purposely play extremely poorly, yes, you can make the double EV exactly equal to double the EV for the extremely poor strategy of taking one hit. It is extremely poor strategy to only take one hit on 11 v. 8, so why not look at a clearer example? Why you think this information is at all relevant is beyond me, unless you are attempting to prove me wrong for the sake of it. As I said, I don't care if you want to play with this information for whatever reason. I personally find this has now become potentially very misleading to an uninformed player. You are posting mathematically accurate conclusions backed with illogical reasoning. I may not have been clear earlier: I concede, you are technically correct in that employing a nonsensical strategy can result in your conclusion. I hope that quells it.
Maybe you should stop posting and re-read what's been said.
The return from 1-hit strategies are used to determine whether a double down is a better or worse play than standing or hitting.
Quote: RSMaybe you should stop posting and re-read what's been said.
The return from 1-hit strategies are used to determine whether a double down is a better or worse play than standing or hitting.
????
There is no such thing as a one-hit strategy. Of course 1 is half of 2. You don't need an EV table to know that. Are you saying the information is useful to determine how much playing sub-optimally, outside of double situations, would cost you in the long run for particular hands? No you are not, but I guess that somewhat trivial information could be learned and it is not nonsensical. When you want to determine whether it is best to stand, hit, or double, you follow the basic strategy chart. If you are implying this is in fact how the Wizard calculates his table, then of what use is the information outside of a combinatorial analysis used to create a chart? I make a further concession--if this information is known to have no practical application whatsoever, then it is not necessarily without value to a mathematician. Really, I don't think you guys were too clear on all the conditions your one-hit strategy has. You wanna just list all them so I can stop divining them for you?
Quote: SonuvabishIt's not a tool for anything, it is utter nonsense. Perhaps it's a tool for someone like the Wizard to calculate the table, there's always an exception, I don't know--but it's not useful here.
So we are trying to find a practical application for this information. Ok.
Say you are backbetting on another's players box (very common outside US).
The Hand is 9 v 7 and the Front bettor decides to Double.
Backbettor has the option to follow the Double or stay with the initial bet (standard rule in most places allowing backbeting).
Does the 9 v 7 Hit only once EV help now?
The discussion about the Hit One card only EV was just a point made to the initial poster to explain in which cases the Double EV is twice the Hit EV.
But knowing the HIT one EV (when the EV is positive) as I show above does have practical application anyway.
Quote: AceTwoSo we are trying to find a practical application for this information. Ok.
Say you are backbetting on another's players box (very common outside US).
The Hand is 9 v 7 and the Front bettor decides to Double.
Backbettor has the option to follow the Double or stay with the initial bet (standard rule in most places allowing backbeting).
Does the 9 v 7 Hit only once EV help now?
The discussion about the Hit One card only EV was just a point made to the initial poster to explain in which cases the Double EV is twice the Hit EV.
But knowing the HIT one EV (when the EV is positive) as I show above does have practical application anyway.
No. The answer would be to stay with the initial bet. The loss in EV from giving up the ability to hit thru doubling can be found by dividing the double EV by 2 and subtracting it from the hit EV. In this case, you lose about .2 EV by giving up the ability to take multiple hits. I did that in my head. Further, and simpler, anytime you double a negative expectation hand your EV decreases, which makes it an auto-NO DOUBLE without needing the prior analysis--since 9 v. 7 optimum is only slightly positive EV. Have Mango calculate one of his charts. Like I tried to say in an earlier post, this is the type of precise information you can garner that is trivial, but not nonsensical, that I had not thought of at first. It's trivial because you do not need to know it; even in this extremely unusual situation you describe that will never happen to most of us, I still wouldn't need to know, I'd simply have to understand blackjack as much as I already do. It's trivial because I might use information like this when trying to explain to someone the cost of their errors--it is academic. But admittedly, yours AceTwo, was an excellent try. I had to look up backbetting.
But backbetting is still a very good example: In a S17 game you would like to follow the double on 9 vs 2 or 11 vs A, and some of the soft hands (I would let you find out which of those).
Quote: MangoJYou are right, you would not want to double 9 vs 7 while you backbet.
But backbetting is still a very good example: In a S17 game you would like to follow the double on 9 vs 2 or 11 vs A, and some of the soft hands (I would let you find out which of those).
I wouldn't play this backbetting game, solo. It puts you in an inferior situation, at the mercy of the original bettor's strategy decisions. There is obvious AP potential in a big bettor gleaning the benefits of defensive splits without the risk, and probably some reckless splits by the low bettor to defend the big bettor. Not the case with doubles. But you are still arguing that this information is useful in order to play wrong. Wouldn't playing properly be more useful to a bad player than this information? It would be wrong to back-bet a terrible player's hand. If I bet $5, and someone backbets 300, if someone guarantees me $10 to do so, I'm gonna bust on purpose.
Quote: SonuvabishI wouldn't play this backbetting game, solo. It puts you in an inferior situation, at the mercy of the original bettor's strategy decisions. There is obvious AP potential in a big bettor gleaning the benefits of defensive splits without the risk, and probably some reckless splits by the low bettor to defend the big bettor. Not the case with doubles. But you are still arguing that this information is useful in order to play wrong. Wouldn't playing properly be more useful to a bad player than this information? It would be wrong to back-bet a terrible player's hand. If I bet $5, and someone backbets 300, if someone guarantees me $10 to do so, I'm gonna bust on purpose.
You've mentioned a couple of reasons why Foxwoods did away with back betting or back lining as it was called there.
