[Aisthesis]

The following are selected results matching a hand to a maximum stack-size given a number of opponents. The main application I’m thinking of on this is with a short-stack in tournament situations, where one is often faced with the alternative of moving in or folding.

The calculation does not include any special status for the blinds, who might have odds to call with inferior hands. I assume here that your opponents know exactly what you have and simply fold every inferior hand (hands that are inferior but would have odds to call are not considered). The result is a MAXIMUM stack size for which it is exactly 0 EV to move in in the given situation.

The stack-size is expressed as a multiple of the total pot prior to seeing any cards. This seemed to make more sense to me (rather than using BB as starting point) because it also provides a way to figure antes into the equation. For example, with blinds at 100/200 with no antes. The pot-size is 300 before any cards are seen, so a value of “6” would mean that moving in with the given hand is plus EV as long as your stack is smaller than 1,800. But with 100/200 blinds and an ante of 25 at a 9 player table, the pot is 525 before any cards are seen. So, a plus EV here is possible with the same value of “6” up to a stack size of 3,150—large enough that moving in is probably not the best play even though it should be plus EV for a stack of 3,000.

For this reason, I’ve tried in my calculations up until now to focus on those hands where the stack-size is between 3 and 9 times the pot before cards are seen. Those should provide some insight into the hands that one can consider in short-stack situations where this move is often a viable way to play the hand.

Anyhow, here are some selected results up to now (sorry about the format--I'm copying it from Word and the tabs don't seem to translate here. The first "column" is the hand in question, then the stack-sizes for 9 down to 3 players):

9 players 8 7 6 5 4 3
99 7.91 9.15 10.80 13.11 16.59 22.37 33.95
AQo 6.60 7.82 9.46 11.77 15.24 21.05 32.69
88 6.50 7.54 8.92 10.85 13.76 18.61 28.30
AJs 6.43 7.62 9.21 11.44 14.80 20.42 31.68
77 5.39 6.27 7.45 9.11 11.59 15.74 24.03
AJo 4.51 5.38 6.55 8.19 10.66 14.81 23.12
66 4.48 5.24 6.27 7.70 9.86 13.47 20.69
A9s 3.14 3.80 4.67 5.91 7.79 10.94 17.26
A8o 2.07 2.52 3.12 3.97 5.26 7.42 11.78
22 1.97 2.40 2.98 3.80 5.05 7.15 11.37
A6o 1.51 1.85 2.32 3.00 4.02 5.74 9.21
A2o 0.99 1.25 1.62 2.14 2.95 4.31 7.09
KJo 0.85 1.12 1.51 2.08 2.97 4.51 7.68
K7s 0.52 0.71 0.98 1.39 2.04 3.17 5.51
JTs 0.13 0.21 0.36 0.63 1.12 2.09 4.28
K2o 0.20 0.29 0.42 0.63 0.98 1.59 2.90

Those are the most important hands I’ve run up to now. For background as to how all this is calculated and how we arrived at this idea, see PairTheBoard’s thread “Median Best Starting Hand Part II.”