Strategy for next card when an opponent plays after you.

I was wondering if this is covered somewhere or not. In BJ against the casino there is no benefit to trying to decide whether your situation has you better deciding one way or another based on the dealers upcard when playing third base since you don't know the dealers hole card but only see his upcard. You can't tell if a card that hurts you will help or hurt the dealer. But in a tournament you are playing against the other players in a table ranking move on situation so you know what ranks help or hurt the opponent playing after you and their affect on your hand.

You are late in the tournament but not so late that your strategy is cut and dried. You need to make a move out of position in the next few rounds. So if you have the only close competitor close competitor playing and betting IMMEDIATELY AFTER YOU it is tough to make a move. The one power you have is taking the next card or leaving it for him if you know he must hit. Like if you have hard 17 and the player you are competing against is playing after you with a total of 12. The A, 2, 3 and 4 improve your hand but have your opponent hitting 13 thru 16 after taking the card. 5, 6, 7, 8 and 9 make your opponents hand but would bust you (the 5 would tie you if the opponent gets it or bust you if you take it). The 10, J, Q and K bust both you and your opponent. So:

5 ranks you would definitely want to give to your opponent: 4 T's, that would bust whoever gets them and a 5 which busts you and has the opponent tie you

4 ranks bust you or makes your opponents hand: 6-9, obviously you are better off not busting but any hope of a swing is gone with these cards. If you are lucky you will have the same result as your opponent.

4 ranks make your hand or have the opponent hitting a stiff 13-16 with the second card if he hits: A-4, you would like to have a better hand but there is value to having the opponent hitting a worse stiff than 12. Each addition of 1 to his total adds 1 rank to what busts him.

The next thing that must be considered is the dealers upcard. It will affect how the player plays his hand and the likelihood the 17 will get you a swing if your opponent busts.

Now I know there are strategy tables for general playing situations where the card you take or don't take doesn't automatically become the card that your opponent has to take if you decline to take it. My question is, if it is a case where the next card is yours or your opponents should you decline to take it is there a strategy table for your hand, your opponents hand and the dealer upcard given the fact that if you decline the card your opponent will have to take or decline the SAME card? I probably picked a bad example for making it a strategic call but I was just illustrating the way your decision to decline a card affects the next players outcomes compared to what yours would have been if you took the card.

 

It's not clear from your post, but this sounds like a situation where you know what the next card is. i.e. you have seen it flashed inadvertently by the dealer. Otherwise, the usual principal of not knowing the exact order of the cards would apply, the same as for normal blackjack play.

I can already generate similar strategies for seeing the hole card combined with a specific tournament situation and goal. With a small software enhancement I could generate strategies for when you have next-card information instead or for if you had both.

 

Combinations, Permutations and other statistical analyses are accurate mathematically, but apply only to very large samplings. When applied empirically with an extremely small sampling such as a shoe of cards, it's almost no better than a guess as to what the next card might be. It was certainly a good subject/question to raise, but I recommend concentrating on applying a good betting strategy (before the deal) to set up as many possible action strategies after the deal.

 

No. I was referring to the difference between the common tournament table strategies that don't assume the next card will be yours or the opponent you are trying to make a move on in the next few hands to be in a position to play the last round and if the opponent played directly after you. Thus if you don't take the next card it would be the card that opponent would either take with a hit or double or stand on. There should be a difference between the opponent you are trying to make a move on being the next player after you and getting the card you waive off and playing another position after you and getting a different card than the card you waived off. Many times it may not make a difference but there is an additional relationship when the card you take or waive off becomes the opponents decision card. It may be trivial or it may be significant.

The difference can be illustrated easily. Using 17v8: with the opponent having a 12
If the opponent acts after you:
If you hit/If you stand:
Next card A: You have 18 and the opponent is hitting a 12/ You have 17 and the opponent is hitting 13 (after taking the next card)
Next card 2: You have 19 and the opponent is hitting a 12/ You have 17 and the opponent is hitting 14
Next card 3: You have 20 and the opponent is hitting 12/ You have 17 and the opponent is hitting 15
Next card 4: You have 21 and the opponent is hitting 12/ You have 17 and the opponent is hitting 16
Next card 5: You bust and the opponent is hitting 12/ You have 17 and so does your opponent
Next card 6: You bust and the opponent is hitting 12/ You have 17 and the opponent as 18
Next card 7: You bust and the opponent is hitting 12/ You have 17 and the opponent has 19
Next card 8: you bust and the opponent is hitting 12/ You have 17 and the opponent has 20
Next card 9: You bust and the opponent is hitting 12/ You have 17 and the opponent has 21
Next card T: You bust and the opponent is hitting 12/ You have 17 and your opponent busts

In the more general situation where your opponent won't get the card you waive off, the left side is unchanged but the right side has your opponent hitting 12 in each instance since his first hit is not the card you waived off. The cases of the opponent getting the card you waive off and the opponent getting a different card are not the same but the strategy may not change. I was asking if anyone figured out what matchups, if any, where the correlation between the next card being yours or your opponents changes the correct play. I think it is pretty obvious the case I am talking about is a specific subset of the cases that the tables we use consider. The question is what matchups (your hand, opponents had and dealer upcard), if any, does this special subset change the strategy. remember your decision dictates if your situation is the one on the left or right. Only in the special case I am describing do you pair the right side with a further play of your opponents hand. If he isn't getting the card you waive off the card he gets is just random card not the card that you would have got had you hit.

 

That's not the reason that there's no benefit. It's much more fundamental than that. You don't know the identity of the next card, nor the one after that. Regardless of how much information you have about the hand to be played on your immediate left (be it the dealer or another player), you can't alter their prospects by any hit/stand decision you make.

To go through all the combinations of outcomes that result from choosing to either take the next random card for yourself or give it to your opponent must necessarily reveal a zero sum game, in which every instance of a waived off card hurting your opponent is matched by an instance of it helping them, and every time hitting and taking the next card for yourself hurts your opponent is similarly matched.

 

I must still be missing something, because, as Colin says, how does any of this matter unless you have information about which card it is that you're taking or waving off?

 

Still trying to wrap my head around the question ...

Chairman, is your question about situations where, even assuming that the next card is random, you can see that there are more ranks that improve the probability of accomplishing your goal for that hand depending on whether you hit or stand and assuming that the player to your left will take the card if you stand?

 

I am pretty sure there is a measurable difference with the next card falling to either you or your opponent. It may be negligible in most cases but I am sure it will make a difference in some. You are eliminating a large percentage of the possible outcomes . I guess some of the more interesting results may be soft pat hands versus an opponent stiff with a strong dealer upcard. Like say soft 18v 9-A with opponent hard 14. The T doesn't change your total but busts your opponent. the cards you want to get would be really useful to fall to your opponent (He would have 15 to 17 against your 18 and the dealer 9-A). The cards your opponent wants would bust you. This is obviously standing situation yet BS says to hit. I know on the last hand the decision is the same but what I am talking about is trying to make a move out of position to be prepared for play on the last hand. You may have a few hands to make your play before the last rounds. Now in this example (soft 18v 9-A and an opponent playing directly after you has hard 14 with 3-5 hands left to go I wouldn't expect an alteration in BS to be much). But in this situation you are in a much better situation if you stand because:
Next card A-3: You have 19-21v dealer 9-A and your opponent is hitting 14/ You stand you have 18 and your opponent is hitting 15 or 16 or standing on 17
Next card 4-7: You are hitting 12-15 and your opponent is hitting 14/ You have 18 and your opponent has 18-21
Next card 8: you have 16 and hit again with your opponent hitting 14/ You have 18 and your opponent busts
Next card 9: You stand on 17 and your opponent is hitting 14/ You have 18 and your opponent busts
Next card T: You still have 18 and your opponent is hitting 14/ You have 18 and your opponent busts

In a situation your opponent gets a different card if you waived that card off the right side would always be:
......./You have 18 and your opponent is hitting 14.

The correct BS play is to hit but 6/13 times your opponent busts if you stand OR you wouldn't improve your hand if you took the card. Obviously you would stand in the shared card situation. The 3/13 times that the next card helps improve your hand it also puts you in a better situation against your opponent if you waive it off. There are 3/13 times that the next card has you hitting a stiff OR your opponent has a better hand than you. 1/13 times you are hitting a 12 and your opponent is hitting a 14 OR you both have 18. It seems to me that it is pretty obvious in this situation standing is the stronger move. I may be surprised if the actual numbers were presented but with 6/13 being no brainer stands and only 3/13 being somewhat of a hit it looks obvious you want to break BS if the next card is going to your opponent if you waive it off. Now if someone else would get it you would hit.

 

Yes. I am wondering about the difference between your opponent gets a totally different card so your decision is based on you hit soft 18v9 and your opponent hits hard 14v9 with totally different cards (as an example) and the specific case that the next card will either be taken by you or your opponent. That added correlation between the possible outcomes in the more specific case should affect the success rate of standing, hitting or doubling. I am sure most of the time it won't change the decision but I suspect there are certain matchups where the added correlation of outcomes will affect the decision. Perhaps a few where the difference is quiste significant.

I figure if you are looking to make a move out of position to get where you need to be for the last round or 2 identifying these cases will increase your chances. Like say the guy is matching your bets and you are hoping to get a full swing or a push/opponent loss.

 

I love to play against players who think like that, knowing that only half the time are they right, and some of those times they hurt themselves as well.

 

This sort of reasoning can be very seductive, and I too have fallen prey to it in the past. But it is entirely wrong.

There are reasons to make strategy variations in a tournament, based on your hand and that of your opponent, but none of them are impacted by the shared potential next card. and hence they don't just apply to the player on your immediate left.

In non-tournament BJ there are two common myths - the player at 3rd base 'controlling' the table by choosing which cards to give to the dealer, and bad players somehow influencing the results of other players at the table. I think I recall seeing some rigorous, mathematical proofs of the falsehood of these, though intuitively it seems pretty clear that they have to be false.

This tournament situation is just the same, but with additional confusing factor of the players not being wedded to basic strategy, but instead one of them seeking to play for a swing, while the other may seek to correlate their results.

Imagine playing in the way you suggest at a real-money table - We can choose to deviate from basic strategy, but this necessarily means our EV for the hand is reduced. All well and good, but for what you say to be correct, the EV of the other player must be reduced too, since we are supposed to be gaining an advantage over him. Thus we would have the mythical 'bad' player reducing the EV of another player.

If you meticulously go through all the permutations for the next two cards for the example you proposed (or any other), you are guaranteed to find that the other player's possible outcomes are unaffected by your decision to hit or stand. (At least if they play basic strategy. If they are seeking to correlate, then change to your hand total brought about by hitting may have an impact on their strategy, but, again, this has nothing to do with the shared next card; it would be just as true if you were each being dealt cards from a different shoe.)

 

OK, I see what you're asking now. Sure, each possible card rank when taken or left by you will improve/degrade/retain your situation while at the same time improve/degrade/retain your opponent's situation assuming that he will hit if you do not. You have enumerated them in your 17 vs 8 vs opponent 12 example. However, counting the number of ranks which make things better for one of you while making things worse for the other would provide an extremely weak correlation, if at all for determining your optimal decision. This is because each card rank+decision combination leaves you and your opponent in positions of different levels of strength. This came up recently in another thread. Colin is also right in that while you're decision may have a weak correlation with respect to your individual hand positions for the next card to be dealt, it will have no effect on the distribution of your opponent's actual cards nor the distribution of his his final hand results (the latter assuming he plays basic strategy).

For example, in your 17 vs 8 vs opponent 12 example, receiving a 4 leaves you much stronger if you hit and receive it than receiving an ace, even though they are both equally probable. Similarly, standing would leave your opponent much weaker if he were to receive a 4 vs an ace. It's also possible that a rank which leaves you both stronger or both weaker could be a net gain due to the relative levels of those strengths/weaknesses.

In order to evaluate the strength of each action that you're contemplating you instead have to enumerate each possible outcome of that action along with it's probability and then multiply that by the probability of achieving your goal from that position given your opponent's assumed action(s) and the probabilities of their outcomes. This quickly branches into a complex probability tree if there is the possibility that either might need to act more than once (i.e. hit more than once) and/or if you need to assign probabilities to the likelyhood of of your opponents possible responses and/or it is not the final hand and you're trying to evaluate the effectiveness of an earlier move..

I can generate the proper strategy for a given goal from a given playing position (bankrolls and bets, tournament rules and limits, etc.) given a variety of possible responses by opponent(s), but I do it by simulation rather than by combinatorial analysis. For tournament situations, the size of the probability tree becomes computationally infeasible very quickly.

 

As part of this discussion, I would like to let everyone know that Chairman is an extremely knowledgeable advantage player who understands the subtleties of gaming probability math and of blackjack play. I think that he may be simply looking for an advantage based on what I believe to be a very weak 1 card correlation that is not worth pursuing.

 

Apologies if I laboured some obvious points, then, concerning the blackjack myths.

But I really don't see how this case is any different. -

If someone were to swoop down after the hit/stand decision has been made and transfer the shoe, dealer's upcard, and opponent's hand to a regular BJ table, a player asked to complete that hand obviously has the same expectation as any other player encountering that same hand.

And if the hand's EV is unchanged, regardless of the preceding hit/stand choice, then a choice that deviated from BS cannot have gained a relative advantage over the opponent.

All that is different is whether or not one more random card has been removed from the shoe before the next hand is played.

Even if we have knowledge of the count, the fact that a waived off card goes to the opponent has no bearing on the decision making process, since the order of the unseen cards is the key unknown quantity.

Surely?

 

Oh, yes, I think we agree that there's nothing that we (the first player) can do to affect the outcome of the second player's hand.

However, we can say that, assuming that the second player will hit if we stand, there are A card ranks which when taken by us, will improve our position and B (=13-A) which will degrade it. Similarly, there are C card ranks which when deferred to player 2 will improve our position, knowing that he will hit, and D (=13-C) which will degrade it. I think what Chairman is asking is whether, in order to engineer a swing, the decision about whether to hit or stand can be based on the values of A and C, i..e., based on the notion that, even with a random distribution of cards remaining, we can calculate the relative probabilities, A/13 and C/13, that our position will be temporarily improved after either hitting or standing respectively. i.e. hit if A > C and stand if A < C.

My position is that the correlation of the values of A and C to the probability of succeeding in creating the swing will be weak, if there is any correlation at all and that the decision should be based on the actual probability of generating the swing by either hitting or standing knowing that player 2 will hit at least once.

Chairman will no doubt correct me if I have it wrong.

 

So you are thinking about it in terms of variance, rather than expectation or probability of winning the hand, since engineering a swing really means increasing the probability of getting a different result to your opponent, which could just as easily prove to be lose/win as win/lose?


That might make sense, but I think the only correlation would come from cards that would be helpful to either player. Thus, if you get lucky and draw such a card, then you also remove it from the remaining pool of cards for your opponent. Conversely, if you hit and don't draw such a card, there is a slightly higher probability that the opponent will draw it.

[Edit: Which may be closer to what you are saying than I realised, re-reading your post. i.e. 'improve our position' refers to the net effect on both hands of a particular card's location -

• either added to our hand and thus made unavailable to the opponent's
• or left in the pool of cards which the opponent may draw ]

 

Gron came real close to expressing my thoughts. You are not trying to have the biggest edge in EV on your opponent. EV is about the long run. What you need is to make the swing be the most likely. If a lot of your EV is on an outcome that will not achieve your goal then it is worthless in terms of achieving your goal.

I think you are right about EV though. I know the odds of winning if you stand are independent of the common card. So your chances of winning standing haven't changed. If you hit there is no common card. So that situation hasn't changed either. Given these two statements which I believe are both correct there is no room for EV to be different than before. But when you switch your focus from maximizing EV gain to maximizing the likelihood of the swing you need there may be value in the common card.

 

Hi three
I think I understood what you trying to say, I hope. But the issue I have is about the card that follows the next card. So, we do not know any information about either card. So, for example you have soft 18 and the person after you has 12. The next card is 3 will help and hurt your opponent. You have a small bet and your opponent has a big one. So, you would rather pass the 3 to him. If the next card is 9, you would rather take it but not if it is 10. So, there are more chances to pass a bad card to him. However, that same situation would still exist after you take the next card because the following card value is independent. Only if you have some information about the actual card or the true count. The latter can be helpful probably only incrementally I think. I might be totally off, so excuse me if so.

 

Indeed. That's the principle behind any deviation from BS in a tournament. You deliberately hurt your own EV in a hand, so that when success does come it also achieves a particular goal - such as a swing to get ahead of someone, or a correlation to stay ahead of them. Maximising the probability of the particular goal, rather than maximizing the EV gives rise to a different strategy table.

I think we are on the same page now. It seemed as if you were arguing something else to begin with. Poor comprehension skills on my part, perhaps.

But I think for there to be any impact on strategy due to this correlation effect, we would have to be dealing with a very small set of remaining cards, and make use of perfect knowledge of the distribution of each the rank. So a perfect-play, card-counting, tournament playing computer might be able to benefit if the game was dealt deep enough, but I don't think there could be any generalised strategy tables for human players.

 

I think the way this problem is presented it mixes up different subjects: conventionally understood EV, necessity and value of creating a swing, and optimal tournament strategies.
For some of them specific circumstances (brls, positions) would have to be given to make general statements.

If a player who needs to create a swing has a very small (insignificant) bet then it is not creating a swing but trying to make opponent lose or not win his/her hand.
There is no way to affect the opponent’s result without any additional knowledge of any particular card – even if you know the exact composition of the remaining cards.
Let’s simplify it; assume that there are 13 cards left, one of each denomination. If you stay your opponent will have 1/13 chance of getting each of them, if you take a hit his chances are 1/12 of each. Nothing changes.

If your bet is big enough that losing/winning it versus your opponent winning/losing his in the same round of play will effect your chances of advancing, then it becomes tournament strategy that sometimes is different than regular table play which usually is based on best EV.
Once again, you should apply correct tournament strategies, and whether you hit or stand does not influence your opponent chances to win.
Let’s say you both have 16 vs. dealer’s T and there are only 4 cards left (including the hole card for the dealer). The cards are three Tens and one Five. If you stay (and know that your opponent will hit) he gets 21 once (out of 4) and swings you; he busts 3 times and one of those 3 dealer busts and twice makes a hand. Net swing for you 25% and negative swing 25%.
If you hit you get 21 once in four, the other three times twice you have the same result and once he gets 21 and you lose.
Of course tournament play is to hit if the value of 25% positive and negative swings and 50% of correlation is better than 4 times full correlation (and possibly doubling if there is a chance that you opponent will not double, esp. if you get an Ace or deuce, lol).

However, there are some situations where it may look like you took a card to influence the dealer’s outcome but it is tournament strategy. For example, your opponents have a lead and have big doubles with stiff hands. Dealer has six showing, and you have a stiff hand, too. You may be better off hitting (or even doubling) if the dealer bust makes your opponents have more than twice maximum bet, or more than twice your bankroll and they may bet minimum to lock you out.

S. Yama