I witnessed the following on a last hand where one player advances. Dealer hits soft 17. BJ pays 2-1. Insurance available. No Even money. Min bet = 25. Max bet = 2500. ...............BkRll...........Bet..........Cards Plyr1.........6300.........2500........10 + 5 Plyr2.........6150.........1500........10 + 6 Dealer.........................................A With the dealer having an 'A' up P1 takes full insurance and P2 also follows with full insurance. ..............The dealer does not have a BJ. P1 takes a hit to 18 and stands. P2 doubles for 1500 and gets a 5 for 21. Dealer eventually hits to a 4 card total of 21. P1 loses the hand and P2 pushes and advances. Comment about the bets and the play of the hands. This should be easy but their are several interesting points. ..............................BlueLight
Player 1 should have bet $125. Player 2 would have been forced to make a big bet to have an opportunity to win with the high.
Hope I've got my numbers right P1 Max bet: Ordinarily a mistake, but maybe he felt he had a read on P2. P2 1500 bet: Should have bet more. 1750 would allow a three bet win to beat a two bet win (double or 2:1 bj). If no surrender is allowed, then I can't see any reason to bet less than 2325, holding back one more chip than P1. If surrender is allowed then maybe bet a max of 2175, so that P1 cannot surrender (because P2 would then surrender for the win). P1 Takes Full Insurance Taking insurance seems like a good idea, because it prevents P2 from winning by taking insurance, and it gives P1 an extra way to win. But it gives P2 the high (in addition to the low he already has) if the dealer does not have a BJ. Insuring for 1200 would be enough to beat P2's BR of 6150 (meaning it is still pointless for P2 to also insure), but will still give up the high to P2 if the dealer does not have a BJ. Not sure what the right move should have been here. P2 Also Takes Full Insurance What on earth for? P1 has already insured, so will win if the dealer has a BJ. And the high that P1 just gave away has now been handed straight back! P1 Hits To 18 Seems fine to me. P2 doubles for 1500 (i.e. full amount) Doubling to take the high is good, but doubling for the full amount has given up the low. P2 only needs to double for 675 to take the high while retaining the low.
What I find interesting here is the insurance play. Since P1 took insurance for the full amount, P2 made a major mistake by also taking insurance as London Colin pointed out. If P2 did not take insurance then he/she has the high and low. In that case, P2's best play would have been to stand on his stiff because P1's 18 is not that strong against a dealer Ace especially since dealer hits a soft 17. In that case, a dealer total of 19,20,21, or bust gives P2 the victory. Nice teaser - has many "what if" possible discussions.
All the What Ifs These were very average players. All they know is to bet big when in doubt. A chip count was given before the hand was delt. As Moses pointed out a P1 bet of 125 (bet your lead minus a chip or hold what your opponent's BkRll is plus a chip) is the correct bet forcing P2 to win the hand. Also with a P1 bet of 125 he doesn't need to take insurance when the dealer's up card is an 'A'. P2's taking insurance can only save chips and not increase his bankroll if the dealer has BJ. In the end with a P1 bet of 125 it would have been P1 advancing instead of P2 as actually happened. As Colin points out: With a P1 bet of 2500 and P1 taking full insurance then P2 is only wasting chips on the insurance bet. If the dealer has a BJ then P1 wins the round reguardless of how much insurance P2 takes. Perhaps P2 was thinking of saving chips for a big double down - these were very average players. P2 does not insure: If I had been P2 I would have realized that insurance would have been a waste of chips. After P1 loses the insurance bet I would realize that I now would have more chips than P1 and I must confess that I would double for 1000 matching P1's bet of 2500 and knowing that I had more held back and thus would have the high and the low, and overlooking that a bet increase was not needed. Doubling for 1000 would give P2 (me) a .6758 probability to advance. With P2 not taking insurance then he has the high and low with no bet increase and as toolman says standing with the 16 is best with a .7101 probability of advancing. In fact if the dealer hits soft 17 then the P2 hard standing total is 14. If the dealer stands on soft 17 then P2 should hit to hard 18. After P2 insures: Now with both P1 and P2 losing the insurance bet, I would again realize that I have more chips than P1 and would double (now necessary to take the high) for 1000 matching P1's bet as above to take the high and low for the .6758 chance to advance. The full double as P2 played it gives up the low and gives only a .2533 chance to advance; although P2 was convinced he had played it correctly. In many situations players see a double down but overlook the double for less. ...............................BlueLight
I was slightly confused when I wrote the above. P1 does not need to worry about P2 taking insurance, since P2 has the low in any case. So P1's only reason to consider insurance is the 30%-or-so chance that the dealer may in fact have a BJ. My first thought was the the trade-off of giving up the high probably wasn't worth it, and that P1 insuring was a mistake. (70% of the time, P1 will find himself needing a swing to advance, having lost the insurance bet. Unless, of course P2 obliges by insuring also, as actually happened.) However, thinking about it some more, the fact that P1 has a total of 15 means that he will almost certainly only want to take just one card (i.e. he'd only want to hit again if he got an ace.), and even standing on 16, rather than hitting, isn't that much worse. So P1's best strategy could be to take insurance, and then to double down if the dealer does not have the BJ. That not only regains the high that was lost by insuring, it also puts P1 out of range of a double down from P2.
Player 1's bet was good if he felt there was at least a fair chance that Player 2 would match the max bet. If Player 1 bets 125 he has a 56% chance to advance. If he bets 2500 and Player 2 matches it, he has a >/=70% chance to advance. If he bets 2500 and Player 2 bets 1500, he has a >/=45% chance to advance. So if Player 1 thinks Player 2 has at least a 1/3 (fair) chance of matching his max bet lead off, then 2500 is the way to go. Player 1 taking insurance was actually a good plan, once Player 2 took the low. He had a 31% chance of advancing if the dealer turns blackjack, and a >/=30% chance of advancing if the dealer doesn't. This adds up to 31% + (>/=30% X 69%) = >/=52% chance of advancing. And that's a worst case scenario. It got much better once Player 2 made the bonehead mistake of insuring for the full amount too. If Player 1 does not take insurance, then Player 2 should not either, because he already has the low. This leaves player 1 with the high with a big losing hand. Player 1 gave Player 2 the opportunity to make a mistake not once, but twice. The 2500 bet was the first opportunity for Player 2 to make a mistake and the insurance bet was the second opportunity. Player 2 bit at the second opportunity. Player 1 was correct in taking a hit, because it gives him the best chance of winning his hand. Player 2 made a second mistake by doubling down. By doubling down he opted to take the high with his opponent having 18 against Ace. Player 2's correct play was to free hit with a hard standing number of 19. So Player 2 got away with two mistakes and advanced anyway at the expense of Player 1, who played it properly (provided his 2500 lead off bet was based on his assessment of Player 2's tendencies.) That's TBJ for you... :violin:
>/=30% Wow, I didn't account for the fact that after the lost insurance bets Player 2 had become BR1. That's what I get for posting on these teaser threads with a hangover... :joker: The rule of thumb is for BR1 to try to get the same money on the table as BR2 so the double for less was better. Nice work, London.
But surely that 30% figure is the general case when we don't know what cards we have. Here we want the probability that P1 wins the hand after doubling down on his total of 15 vs A (assuming that's higher than the probability of achieving a swing by hitting to some total, which I think it must be). It's reassuring to learn that even monkeys are human.
Another Right and Wronger The following situation occurred. Semifinal - one advance. Max bet all in. Min bet 25. Plyr........BkRll.............Bet................Cards.......Action P1........23500......11000+11000..........9+2...........DD.....K P2........25500..........11000...............10+2..........Hit.....A Dealer...............................................7 P1 doubles and gets a nice 10. P2 played basic strategy. After taking one hit he realized that even if he won the hand he would not advance. Dismayingly he waved off further hits to get the unpleasantness over with as soon as possible so he get up and leave. What's was wrong and/or right here? .............................BlueLight
Player 2 Player 2 should've doubled hard 12. He should double any hand in that predicament, even hard 20 (if he had bet too much to split, which he didn't.) After realizing his mistake he still had a long shot and could've tried to draw out to 21, hoping the dealer draws out to 21. This was an all in format. Player 1 had a better bet available. Player 1 might've used what I call the double plus holdback. Behind by 2000, he would hold back double that amount plus a chip and shove the rest in the betting circle. This holds back enough so he can still double to cover Player 2. In this case he would hold back 4025 and shove the rest in, for a bet of 19,475. If he gets a BJ, it's like a walk off home run; Player 2 can't cover it with a double.
Match Agreed, Sweet. I should've added that to my previous answer. Player 2's bet was correct, matching Player 1. That forced Player 1 to double virtually any hand. Keeping in the spirit of using position and the lead, Player 2 should've followed up matching Player 1's bet by matching Player 1's double. He would also match Player 1's surrender, insurance, double for less, etc.
I expected most people to realize that P2 (BR1) needed to double down also. However Monkeysystem pointed out the hidden resourse P2 had by not giving up on the hand after hitting. He could still win the round by by hitting to 21 and then the dealer had to hit to 21 also, only a 1% chance of this happening. A 1% chance is better than no chance. As for P1 holding back 2 times the deficit plus a chip works fine for doubling or getting a BJ. But what about if P1 is delt a pair of tens? I got stung when I bet the max of 500 of my 800 and couldn't split the 10's. Of course splitting the 10's don't guarantee a win. Is it 6 of one or half a dozen of the other? ....................................BlueLight
Splitting Tens If P1 is the chaser and is dealt 20, he has a good chance of getting a swing. He probably doesn't need to split.
Sim Result The day I read my first gambling book (which recommended some progressive betting scheme for black jack) I wrote a quick simulation program to test it out.The sim, exposed the flaw (bankroll constraints) in the system and, ever since then, I've been expanding my simulator's capabilities in order to find answers to questions I've had and to verify things that I've read. Most recently, since becoming interested in black jack tournaments, I've been working on analysis of tournament situations, such as this one. This group of threads (strategy & teasers) has been of particular value in testing my work (thanks!). I am now confident enough in the results I'm getting to share them here and to hopefully help in deciding the answer to this question posed by BlueLight: One of the things my sim can do is to generate the correct playing strategy for any situation given the bets, the state of the cards (both on the table and remaining in the deck) and the goal of the player. It can then simulate the results of applying that strategy to the situation. Often this is of more academic use than practical, since it is not practical to memorize the variations of basic strategy for random situations, however in cases like this one, which I think is quite common, it can compute the answer to the question of "which bet is better" or "which play is better". While BlueLight hi-lighted the particular case of not being able to split 10's when using the double plus holdback, I interpreted his final question as "which is the better overall bet: split bankroll or double plus holdback?" I ran sims of the following conditions in an attempt to find out: Sim1 (split bankroll) P1: BR: 23500 Bet: 11750 P2: BR 25500 Bet: 13725 Sim2 (double plus holdback) P1: BR: 23500 Bet: 19475 P2: BR: 25500 Bet: 21450 Note that in both cases, P2 makes the optimal bet to counter what P1 has done. Both players employ the strategy generated by my sim with the goal of both players being to finish first. Other conditions (some more relevant than others): 8 deck shoe, 75% pen, S17, split any equally ranked cards, 1 card on split aces, late surrender, double any 2 cards, DAS, double on blackjack allowed. The results of simulating these conditions on 1 billion hands dealt from the simulated shoe are: Split Bankroll : P1 finishes first 28.88% of the time Double Plus Holdback: P1 finishes first 26.35% of the time So while it's a fairly close call, it seems that the ability to split vs double wins out (theoretically). Note that while a blackjack is a walk off home run for P1, it is the same for P2, so there is no advantage there. Also, P2 can double to cover a double by P1 in both scenarios. For the split bankroll scenario, the generated strategy for P1 when P2 gets black jack (i.e. P1 needs to win 2 bets) is View attachment win2-strategy.txt We see that almost every split is preferred over doubling (exceptions 5,5 vs 9, T and A). Some notes on the strategy table: 1) All plays are listed in order of preference for (probability of) achieving the player's goal 2) Plays which follow a '+' are plays for which the probability of achieving the player's goal is non-zero 3) Plays which follow a '-' are plays for which the probability of achieving the player's goal is zero (but he has to do something!). 4) The line for 20 is a hard total which is not a pair, so doubling is not available in this situation. 5) The lines for 21 and A,T represent 21s which are not black jack, so doubling is not available in these situations I hope that this helps with the question. I apologise for the long post, but given that it was my first sim result, I wanted it to be detailed in order to hopefully lend some credibility to the result.
Matching P1 would be better in the first case (and wouldn't actually be any worse than the 21450 bet, in the second case). In the first case, P2 has given up the ability to split, and might be obliged to double down on very unfavourable terms. Holding back just a chip more than your opponent comes into its own if it allows you to cover your opponent's possible blackjack, or conversely allows your possible blackjack to cover a double. When that's not the case, it can actually hurt rather than help. Even if the bet had not been more than half the BR, making it impossible to split, splitting can give up the low if your bet is more than half your lead above your opponent's bet. And similar problems can occur with doubling, if doubling for less is not possible. I think P1 does gain more from the possibility of receiving a blackjack in case 2 than in case 1, though. Because it blunts the power of Curt's Revenge. The situation in case 2: If P1 alone gets a BJ, he wins. If P2 alone gets a BJ, he wins. If both get a BJ, P2 wins. The situation in case 1: If P1 alone gets a BJ (and stands), P2 knows he must double down and hope to win the hand. If P2 gets a BJ, P1 knows he must double down and hope to win the hand. (Obviously true even if P1 also got a BJ). But then P2 can also double to retake the high and low. (Assuming he can either double for less, or has matched P1's bet, rather than bet 13725) So it looks to me that the drawback of acting first means that overall P1 will finish first less of the time, when one, the other or both get a BJ, for case 1 than for case 2. (Though in fact, for case 2, P1 finishing first would be confined to the specific outcome of P1 getting the sole BJ.)
Makes sense, for the same reason that giving up the ability to split was a slightly worse choice for P1. Further simulation supports this. If P2 matches P1's bet in case 1 (p1 split bankroll), he reduces p1's chances of finishing first to 27.10% (was 28.88%). However, P1's case 1 bet is still better off than the case 2 bet (double plus hold back) which yielded 26.35%. Also, you are correct that P2 matching P1's bet makes no difference in case 2 (double plus hold back). My sim was able to detect that the original and matching bet both represent the same situation (thanks for pointing out a good test case!).
