| Interesting exercise. I like the concept of trying to factor in the probability of winning the tournament, as well as the hand, based on one decision in a big pot when its heads-up.
Other factors to consider:
1. Difficulty in projecting outs.
When its heads-up, there is a much greater probability that your opponent is bluffing, or at least does not have a solid hand. In any calculation, its safe to assume that your opponent is bluffing at least 10% of the time (as Harrington recommends). During heads-up play, the probability is likely much higher than 10% on any given hand. This would need to be added to the calculations.
In addition, its more difficult to distinguish a “bluff” from a regular bet. Say you are on a draw with K8 on a board of 976. Your opponent might go all in with QT, thinking you are on a draw with low cards like 54. Is this a bluff? Not really, since his bet is premised upon the fact that he thinks he has the best hand at the moment with queen high. The point is, this makes counting your outs more difficult, AND you may already have the winning hand with king high.
2. Absolute cash value of remaining tournament chips at a short table.
At the start of our QTOC, we each get T1500 for $20, so T1500 = $20.
First place was $90 and second place was $54. Each of the final 2 players is guaranteed $54, and they are now playing for $36 as the difference between first and second. There are T13,500 chips on the table, so when its heads-up, T13,500 = $36.
Consider the value when three players are left: each player is guaranteed $36, and the three players are playing for the remaining $72. So, T13,500 = $72 in the aggregate. Further, when there are 3 players left and if a player is down to 100 chips and is faced with a decision to call all-in or fold, but one of the other players is all-in and might bust out on this hand, then that T100 = $18, as the difference between third and second place money, and leaves the door open to another potential $36.
Tournament chips can have wildly different values late in the game, depending on the circumstances. This analysis is important to keep in mind when doing these exercises involving all-in plays late in a tournament. A decision you make with 3 or 4 players left can be vastly more important, in terms of cash in your pocket, than when you are heads-up, and does not necessarily relate to a comparison of your remaining tournament chips to the pot odds on a particular hand. |