First, a big thank you to Ken for his two eBooks--they're full of actionable information, and I look forward to rereading them many times as I learn. The weekly tournament I play in divides the pot with 50% to first, 30% to second, and 20% to third. Most of the advice I see on here about play of the final hand seems to focus on betting by BR1 and BR2, with relatively little attention paid to the players behind BR2, and none to the allocation of the pot. This makes sense for early elimination rounds when only two advance, of course. But with respect to the final money round, I'm hoping that people can help me out regarding when it makes sense to aggressively shoot for first place (and risk finishing out of the money) versus trying to lock-in second or third place. At a minimum, it seems that how the pot is paid out is a relevant factor which is rarely discussed. For those with the mathematical facility, I'm sure it's child's play to fill in multiple branches of a decision tree by determining the chances of success of multiple betting choices and then multiplying by the appropriate percentage of the pot, but that's simply not a feasible choice for me. So what I'm wondering is whether there are some rules of thumb I can use for the final hand when I'm BR2 or BR3 to determine when it's better to fend off the people who are out of the money and settle for my existing position, or when to bet more aggressively to win a larger share of the pot, but risk ending up with nothing. I understand that this can be viewed as a naive or stupid question, since perhaps it's a question that can only be answered by doing the mathematical work, and others may see it as just a matter of having an aggressive or conservative psychology. I'm hoping there is a third alternative, since I'm bad at calculating on the fly, but am pretty good at pattern recognition. Thoughts?
As a rule of thumb, at the final table, if the increased reward for the spot I'm considering is greater than the penalty for the possible loss of position, then I am more inclined to go for it. For example, in your tournament, the increase from 30% of the pot to 50% of the pot for improving from 2nd to 1st represents a reward of 66.6%, while the penalty for dropping to 3rd is only 33.3%.. This is not the final decision criteria, but it is enough to get me thinking about it. The probability of improving vs worsening my position must also be weighed. In a crowd, as a rule of thumb, I am more inclined to bet to win, since it is unlikely that everyone behind me will lose. At the very least, I try to correlate with as many challengers as possible. I try to never bet so much as to fall out of the money if everyone loses. Being able to lock in a payday is also a strong consideration. These are good questions. Keep them coming!
One thing to remember at a final table is many players are loathe to risk their relative position against most of the other players. You don't necessarily have to go broke and take the high for first place. Say you're BR1 acting first on the last hand of a final table. A big bet that takes the high would be the optimal play in a one-advance elimination round. But in a final table taking second-high may be all that's needed if it leaves your remaining bankroll somewhere in the middle of your opponents' bankrolls. Some of them may not want to make a tiny bet that takes the low on you but not necessarily against one or more of the other players. BR2 may not go for broke and take first high if it risks ending up in last place if he loses his hand. The rule of thumb is to find a bet that forces the other players to look at each others' bankrolls and bets, and not just yours.
I like these rules of thumb. Let me try a scenario: BR2 is on the button with 1000. BR1 has 1100. BR2 bets 400 (max bet is 500). BR1 bets 305 (and is prepared to double any hand he gets if BR2 gets a natural or doubles his bet for any reason). BR2 is dealt a stiff 15 and (for some unknown reason) elects to stand against the dealer's 7. BR1 is dealt 12. Question 1: I believe that the advice for BR1 to correlate refers not only to bet sizing, but also play of the hand, in order to reduce the chances of a swing. In this situation, BR1 should deviate from BS (draw to 17) and instead draw only to 15, since it reduces the chances of BR1 busting and if both players lose, BR1 remains in the lead--correct? Now change the facts: There is now a BR3 who has 950 and bets after BR1. Question 2: I think that BR3 will either want to lock the low by betting 5, or try for first by betting 155 more than whatever BR1 decides to bet (subject to the max). Because BR1 uncannily thinks like I do, he implicitly concedes the low to BR3, and tries to take the high by betting 350. BR1 isn't too worried about BR2 doubling his bet or getting a natural since BR1 can correlate, but he's not sure what he can do if BR3 bets 500 and then correlates to whatever double BR1 may then attempt. If BR1 instead bets 500 (with the intention of doubling later to block a double by BR3), BR1 will finish out of the money if he loses to the dealer. Does BR1 have a better bet than 350? Question 3: If BR1 decides to bet either 350 or 500, wouldn't the best bet for BR3 be 5, since he is guaranteed third place (20% of the pot), and wins either second (30% of the pot) if BR2 loses, or first (50% of the pot) if both BR1 and BR2 lose to the dealer? Question 4: If BR3 ends up making a max bet of 500, should BR1 simply revert to playing BS (instead of hitting to 15 as in the original two person scenario) to have the best chance of beating the dealer? Does the answer depend on the first two cards dealt to BR3? Thanks to Monkeysystem for his rule of thumb of trying to find a bet that forces the other players to look at each others' bankrolls and bets, and not just yours.
In your first example BR1 should stand. He will have locked out BR2 by standing. My rule of thumb when I'm the chip leader is I don't want to bust. There are a few busting hands that you need to hit if BR2 has a good hand. But if BR2 makes the terrible mistake of standing as in your first example, BR1 could wave off 2-2 and be a lock. In your second example BR3 shouldn't bet 5, unless there are lower bankrolls that can be locked out by this tiny bet. If he is going to take the low he should hold back one more chip than BR1. Good things might happen if he gets a blackjack. However, one from three advancing if he can he should take the high. The probability of winning a hand is greater than the probability of two opponents both losing theirs. In your third example it depends on your goals. For me personally, I want to take 1st. It's not a bad policy to reflexively play for 1st, and it's often actually got the best EV. For me this game is about more than just the money. I want to have fun, and there's nothing more fun than taking 1st. I have a job that pays me money. If you want another rule of thumb, here's one for you - have fun. In your first example the answer is no. BS is designed to maximize EV against the dealer. In a tournament your goal is not to maximize your EV against the dealer, but to finish with more chips than your opponents. A push could be as bad as a loss, or as good as a win, depending on how your opponents do in their hands.
If it's the final hand, with no other contenders to worry about, then BR1 should stand on 12 for a lock. The dealer's card is irrelevant; if BR2 stands stiff, BR1 has a lock and has no need to risk busting by drawing a card. With regard to BR1's bet size, 305 is too small to cover a double down from BR2. The lead is 100, so if BR2 wins 800 by doubling, BR1 needs to win > 700, which means a bet > 350. The simplest thing to do with a small lead is simply to match BR2's bet.
Another rule of thumb: In most cases there is a range of bets that you can make which will all allow you to take the low. As a rule of thumb, I try to bet the high end of that range. The reason is that it automatically gives you options to make a counter-move on the greatest number of high scenarios should the low scenario you were betting on not pan out. In your initial example. BR1 can bet 305 to cover BR2's win, but he can bet up to 495 without giving up the low. As Colin has pointed out, the bet of 305 makes it impossible to cover BR2's double. The minimum required bet is 355. Once again, you could calculate this and bet 355, but in the heat of battle I would bet 495 for two reasons: It's easy to size the bet, by holding back one more chip than BR2 Just in case there is another high option that could be covered if needed. Now, it turns out that in this case, betting 495 has no actual advantage over betting 355. However, I'm a believer in simplifying things at the table and I think that the bet of 495 is easier to size and automatically leaves you with more possible options, if they exist. Why is this important? Because sometimes, under time pressure, you can overlook a scenario that you could have covered had you only bet a little more. If we change the bankrolls in your example to BR2: 1200 -- bets 400 BR1: 1300 ---bets 355 There is now the possibility that BR2 splits and then doubles one of his hands for a possible win of 1200. This may not have been on BR1's radar when making his bet, but if he had had simply bet the max for taking the low (i.e. 495), then he would still have a small chance of countering BR2's move by doing the same (with a split and a double for less). I know that this is along shot scenario, but why not cover all possible situations when it can be done easily?
Thank you all for your quick (and deflating) responses. I knew this was complicated, but this is much more complicated than I realized. I will have to read and reread your responses to be able to extract all of the juice from them.
Don't be deflated. This topic of reducing complex situations to simple rules of thumb will prove to be valuable to many.
Actually, it does have an advantage. A natural will win enough to cover a BR2 double - BR1: 1100 + 495*3/2 = 1842.50 BR2: 1000 + 2*400 = 1800 It also has a disadvantage, the magnitude of which is rule dependent - All my experience has been in the UK, Europe or online, and doubling for less has not generally been allowed. That would make the upper limit of my range 445, so that I am not forced to give up the low if I need to double after BR2 does so. It shows how easy it is to fall into habits of thought and then forget the reasoning behind them, that I completely failed to consider betting any higher than this range when I looked at this example. Even where doubling for less is allowed, there is still a slight disadvantage in that you may be dealt a high pair and compelled to keep the low by doubling for less, rather than lose it by splitting. But it's my understanding that the advantage from the first (natural) scenario outweighs this.
