Here is a situation from the recent New Orleans tournament where either one: betting, playing, and especially the method of analysis should qualify it as an interesting teaser. Out of seven players only four were left going into next to last hand. Bankrolls: 22,250......14,000........5,000.......4,500 I had 22,250 and in the first position had bet 2,100 in anticipation of BR2 betting max 10,000 from his bankroll of 14,000. BR2 had bet max (10K), both of the other two players had bet less than their all-in (these kind of bets always make me wonder whether all tournament participants really grasp the idea of one player per round advancing, however the prevailing bet on most tables on the last hand was max of 10k, even though, often times a smaller bet would give them as much upside but could offer some benefits in case of losing). A brief explanation of my bet. Though, against many experienced players I would cover their chance of winning double down by my single win (and definitely I could afford it comparing my bankroll to BR2’s), here I was still measuring my main opponent’s skills. He made a couple minimum bets when medium bet would protect him from losing the lead, but earlier he also made a couple of medium bets not afraid of the risks losing them would have created. Winning my bet of 2,100 leaves me with a small lead over BR2 if he wins maximum bet and my lead would be greater than the max bet if he would win doubled minimum bet. Also, that black one-hundred chip nicely and legally covered two dark yellow chips resting under it. And finally, losing that bet still leaves me with more that twice the bankrolls of both BR3 and BR4 if they win all-in (and at the same time more than max bet). I received a 16, BR2 got 13, the dealer showed an Ace, nobody insured, and unfortunately there was no blackjack. Do you stay or hit my 16? .. .. .. My objective here is to avoid the swing, so I unhesitatingly stood. BR2’s hit produced a beautiful (for him) 8 for a total of 21. The other players... to be honest, I stopped paying attention, I think they lost. Now came last bet carrying a twist – it was a secret bet, revealed after two initial cards were dealt to all players but before we had to act on it. Basically it was a two man contest; I had 20,150 and my opponent had 24,000. What would be your bet in my place and why? S. Yama
First of all, I do stay on the 16. I'm pretty sure that the odds of a swing go way down when you stay on that hand. If the dealer beats your opponent, you've won regardless what you do, so you should do your best to hold onto the lead assuming that your opponent beats the dealer. And, I think the best way to do that is to stand on 16. As for your secret bet, I hate these as teasers, since, as BR2, your goal needs to be unpredictible. I think that your best options are 4,000 and 10,000. The max bet allows you to control your own destiny. But since your opponent could suspect that (and 10K is a common last bet), you should consider something counter to that. 4K wins a win-tie situation and is far enough away from 10K to give you a chance at the low (assuming no surrender). Of course, a 7K bet from an expert opponent would cover both of them, but couldn't cover a 10K DD, so it's less likely your opp would be 7K. I think I would make a 50-50 random selection between 4000 and 10000.
First off let me say I hate, I really really HATE, secret bets. But in this situation BR2 gets little more chance to win since it gives BR1 a better chance to screw up. From what I read about BR1 it seems to me that he will either go minimum or maximum. I don't think he's smart enough to do anything else. To narrow it down further, a max bet is most likely by BR1 since most players in the tournament seem to bet max on the last hand and BR1 has no reservations about putting out a max bet. So with that in mind, my vote is for BR2 to bet $4,100. BR2 is naturally under the gun and must count on winning the last hand. Winning a $4100 bet will give BR2 a victory as long as BR1 does not win his hand - irregardless of BR1's bet. It also gives BR2 victory if both lose - assuming BR1 bets at least $8,000. Naturally, a max win by BR1 just about locks out BR2 with his $4,100 bet but you have to sacrifice something in this situation. By the way, did I mention that I really HATE secret bets.
OK, I like $4100 better than $4000 as it covers a min bet double without additional risk. But $4200 is too much, because $8000 would be a good possibility by a smart player.
hhhhmmmm....I think you've seen that miracle eight before From your post, you play AFTER he does on the final hand - that's your only edge - He leads you by 3,850, so a bet of 3,800 gives him the low, if he loses and you lose or push; a bet of 6,200 gives him the high, even if you win a max bet. players don't have to be that skilled to do these simple calculations for the last hand - so I would put him on one of these two bets. A bet of 2,300 or less would give you the low if he bets the 6,200, if he loses - no matter what happens with your hand - and gives you a swing possibility if he pushes and you double or split. A bet of 7,700 gives you the high if he bets 3,800, and a shot of beating his straight win if he bets the 6,200 with a double or split - but won't give you a low under any circumstance. I would go with 2,300; if he loses, you should be ok - if he looks like a likely push, then go for the double or split.
Reading Your Player Good to see you posting teasers on here again S Yama! First of all, in your situation your deficit was too much to take the low on a max bet with the option to double for the high. So you were left with just trying to avoid correlation by your opponent. Did you read your opponent as weak/passive? BR1 demonstrated a willingness to bet the max but that doesn't mean he's not a weak/passive player. It just means he wasn't totally lost. If you read your player as weak/passive, then you could assign only a 1/3 possibility he would bet the max on the last hand. You'd bet the max, giving you a 2/3 possibility of having the high and a 1/3 possibility of being correlated. You would want to double aggressively to cover your opponent's strong single bet hands. If you bet to barely cover a win-push you have a 2/3 possibility of being correlated and a 1/3 possibility of having the low. You could double to cover BR1's low bet but you have a 1/3 possibility to actually double your way into a correlation you want to avoid. Your probability of winning if you have the high is 44%. Your probability of winning if you barely cover the win-push and have the low is a coin flip. Your probability of winning if you are correlated is 20-30%. You calculate your possibility of winning for each decision by multiplying the possibilities of each opponent decision by the probabilities of the outcomes. 44%*2/3 + 20%*1/3 > 50%*1/3 + 20%*2/3. .36 > .30 Your possibility of winning is actually greater than .36 because you will aggressively double. .36+ sucks but it's the best you can do given the uncertainty of what your opponent did and the fact you're playing from behind. Do you need to do all this calculating with the clock ticking, everyone watching, and your heart pounding? No. Just remember: when behind, bet the max and double aggressively with secrets working and a weak/passive opponent.
Monkey, I have a question about your response: You used the phrase "weak/passive" quite often in your reply. Ya, I know what the word "weak" means but I'm not sure what you meant by "passive". Could you define?
Do people not believe in the concept of mixed strategies in this forum? Poker players talke about them all the time. For example, if you have aces under the gun in a no limit holdem game, books might suggest that you raise 80% of the time varying between 3x and 5x and that you smooth call 20% of the time. The idea is to avoid being predictable. So, how can we talk about secret bets and decide that the best bet is a single bet in cases like this, when 2nd level thinking will assign the perfect bet to counter your bet.
I think the assumption here is that BR1, based on his play so far, will not be giving a moment's thought to the possibility of correlating his bet with yours. Of course, he could always spring a surprise! I guess if you assess your opponent as skilled, then introducing a random element is a good idea, though harder than it sounds, unless you have some dice handy . But otherwise, it's a question of predicting their bet and responding to it, rather than worrying about the response to your response.
Actually, most people have a pretty good random number generator on them. Harrington recommends using the second hand on your watch. For example, if your decision is to use $4100 67% of the time and $10,000 33% of the time, take a quick glance at your watch. If the second hand is between 12 and 8, bet $4100, and if the second hand is between 8 and 12, bet $10,000. I doubt that a glance at your watch will give your action away.
lively conversation Very lively conversation, isn’t it? A small correction, I was not betting first on the next-to-last hand. I was actually betting second, but in front of my main, and almost only, opponent, hence I wrote first – but that means that I was first to act on the last hand, once our secret bets were revealed. It definitely lowers my chance but does not change analysis itself. So let’s continue with the real case. Toolman, I can relate to your feelings of [size=+1]HATING[/size] it, I also used to hate secret bets. In my case it was hate of relying on pure luck, the sense of hollowness caused by incompleteness of information, and hopeless lack of control. However, if you analyze and compartmentalize them, and get familiar with relations and consequences, then they become just another kind of fun puzzle, or at least hopefuly you just may only [size=-2]hate[/size] them. The bet of 4,100 you proposed is definitely better than 4,000. Toonces, very good and concise analysis; that’s what would be most practical in real live casino tournament. By the way, thank you for mentioning my name as one of the contributors – I appreciate it. You also talked about using randomized decision in bj tournament –very interesting subject. We could talk about it in a separate thread. Personally, I rarely use it- if at all- and think that only not very advanced players would benefit from it, as it is by its nature is a defensive move, along the lines of London Colin's post. RKuczek, sure I remember “that” 8 double down on 13 and me screwing up, though I rarely remember my hands from the past tournaments. Your bet of 2,300 is interesting, though value of doubling is diminished because it may work only for BR2 small bets, or when the opponent would push; with BR2 medium and big bets your double could work at the risk of giving up the low. It may be the best bet depending on how you weigh chances of your opponent different bets. Monkeysystem, fantastic analysis! That’s exactly where I hoped it would go in the end. You also used weighing example for easily to imagine groups (1/3 and 2/3, and low, high, and correlate), where I, with my tendencies to go into countless fine points and details, would lose most of the readers. There are a few other minor points but they may be helpful to create a full picture of this teaser, which I will try to post by the end of this weekend. It is really too bad that you are not playing for the highest stakes tournaments -you would be extremely successful. S. Yama
Weak/Passive I try to categorize opponents, to simplify my decision process. Weak/passive is a poker term for someone who doesn't understand the game well, and has tendencies toward smaller, conservative betting. In this case S Yama may well have profiled his opponent as such, so I provided an analysis in the case that it's true. The fact that the secret bets are revealed after the first two cards are dealt means you can make more intelligent playing decisions than if you're still uncertain. It actually favors the max bet option because you can increase your chance of winning from 20-30%. All this analysis is just for weak/passive opponents. It's out the window if BR1 is the kind of player you find in this forum. There are indeed multi levels of thinking in that case but it's all still random. You might think your strong opponent will read you likewise, play it safe, and take the low, so you take the high. But maybe, just maybe, BR1 will assume you do that and try to correlate you with a high bet. But then you might think another level and try to outguess BR1 and take the low. Which comes first the chicken or the egg? The main thing is not to establish a pattern over the course of many tournaments.
