David Sklansky
11-01-2004, 04:44 AM
Vince Lepore's adamant insistence on avoiding most go broke situations when there is a short stack in third place takes on added validity when the prizes are so high that marginal utility comes into play (assuming there is no extra value to the publicity of winning). Of course the assumption is that you are on a fairly short bankroll.
Here's an example:
Say first prize is $500,000, second is $300,000 and third is $100,000. I will call this 5, 3 and 1 in the calculations.
Suppose the third guy is basically broke and you and the other guy have equal chips., So your EV if you don't gamble is 4. But now your opponent moves in and the tiny stack folds. If you have a coin flip and you call your EV drops to 3. See why? To play in this extreme situation you have to be a 3-1 favorite since you risk 3 to gain 1. This of course assumes that the short stack has zero chance of a comeback. Playing with less than a 75% chance actually lowers your EV
But now lets say that the extra 200k above second place is not worth that more incrementally to you. Say that to you, first place is only worth 400K in incremental dollars. Thus waiting for the other guy to go broke gives you an EV in marginal utility dollars of 3.5. Playing a coin flip reduces it to 2.5. And the degree of a favorite you need to be to fight is now FIVE to one.
In real life what I am saying is this:
Not only do slightly negative EV plays become positive EV when the third stack is short, negative EV plays that REMAIN negative might still be right if they increase your chances of finishing seond (at the expense of finishing first) and second place money (but not third) can change your life. By this criteria Vince's call with AQ is probably the right play.
Here's an example:
Say first prize is $500,000, second is $300,000 and third is $100,000. I will call this 5, 3 and 1 in the calculations.
Suppose the third guy is basically broke and you and the other guy have equal chips., So your EV if you don't gamble is 4. But now your opponent moves in and the tiny stack folds. If you have a coin flip and you call your EV drops to 3. See why? To play in this extreme situation you have to be a 3-1 favorite since you risk 3 to gain 1. This of course assumes that the short stack has zero chance of a comeback. Playing with less than a 75% chance actually lowers your EV
But now lets say that the extra 200k above second place is not worth that more incrementally to you. Say that to you, first place is only worth 400K in incremental dollars. Thus waiting for the other guy to go broke gives you an EV in marginal utility dollars of 3.5. Playing a coin flip reduces it to 2.5. And the degree of a favorite you need to be to fight is now FIVE to one.
In real life what I am saying is this:
Not only do slightly negative EV plays become positive EV when the third stack is short, negative EV plays that REMAIN negative might still be right if they increase your chances of finishing seond (at the expense of finishing first) and second place money (but not third) can change your life. By this criteria Vince's call with AQ is probably the right play.