Four players, three paid, everyone on 10 big blinds: the numbers behind a famous poker saying.
"Shove wide, call tight" is the best known piece of bubble advice. Here are the numbers for one clean case: four players left, three get paid (50 / 30 / 20 percent), everyone has 10 big blinds. Compare what chip EV says with what ICM says.
| Seat | Chip EV shove | ICM shove |
|---|---|---|
| Cutoff | 34% | 44% |
| Button | 43% | 63% |
| Small blind | 72% | 100% |
Under chip EV the cutoff shoves 34% of hands. Under ICM he shoves 44%. The small blind, heads-up against the big blind, shoves 100% under ICM against 72% in chip EV.
The same spot from the other side: the cutoff shoves and the three players behind decide whether to call.
| Caller | Chip EV call | ICM call |
|---|---|---|
| Button | 16% | 4% |
| Small blind | 21% | 5% |
| Big blind | 29% | 7% |
The calling ranges collapse. Where chip EV calls with 16% to 29% of hands, ICM calls with only 4% to 7%.
A caller who loses is out of the tournament without a payout. A caller who wins gains chips, but the extra chips are worth less than the chips he risks. That is the bubble factor: calling needs far more equity than pot odds say. The shover is protected by that fear. Because everyone behind folds so often, a shove wins the blinds and antes most of the time, and hands that would be folds in chip EV become profitable shoves.
They come from our own push/fold model of the whole hand. Every player, in turn, can fold, go all-in or call an all-in. The payouts use the Malmuth-Harville ICM, and the ranges are found by repeated best responses until they settle (they move by about a percentage point between runs; a second, independent solver agrees with the chip EV numbers to within about a point and a half). The blinds are 0.5 and 1 BB and the antes total 1 BB. Stacks are before posting. There is no postflop play, because an all-in and a call run to showdown. It is an approximation of the real game, and ICM itself ignores skill and position after the flop. It is a map for study, not an exact solution.
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On the bubble, first-in all-ins should be wider than in chip EV because callers fold so often, and calling ranges should be much tighter because a loss costs the whole payout.
In our model he shoves 44% of hands under ICM against 34% in chip EV.
Not directly. A big stack and a short stack behave differently from equal stacks, as the unequal-stack guide shows.
progressGTO guides use our own solution book (v13, 8-max tournaments with ante, chip EV): an approximation of equilibrium with a modelled postflop, not an exact solution. Numbers are computed from the book and from the exact ICM model.
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