Bet the same fraction of the pot on every street and your whole stack goes in by the river. Change the sizes below and watch how much of your stack never makes it into the pot.
The idea. When a bet gets called, the pot grows by the bet twice — yours and theirs. Bet the same fraction f of the pot on every street and the pot grows by the same factor, 1 + 2f, each time. That's a geometric series, hence the name. There is exactly one fraction that makes your last bet put your remaining stack in on the river:
f = ((1 + 2·S/P)1/n − 1) / 2
where P is the flop pot, S the effective stack behind, and n the number of streets you bet.
Why small early bets hurt twice. A small flop bet doesn't just win less on the flop. Every later street starts from a smaller pot, so the same percentage buys fewer chips. The shortfall compounds — watch the red numbers grow from turn to river.
Why big early bets hurt too. Bet too big too early and you run out of chips before the river. The last street becomes a small, awkward jam instead of a real bet.
Set up a pot-size river jam. A simple rule most players use: bet enough on the flop and turn that you have at most about a pot-size shove left for the river. Bet too small early and the only way to get the rest in is a river shove far bigger than the pot — and those only get called by hands that beat you. The River all-in card turns red once that shove would be more than 110% of the pot. This rule is separate from geometric sizing: with very deep stacks, even the geometric line leaves more than a pot-size shove.
MDF (minimum defense frequency) = pot ÷ (pot + bet): how often the defender has to continue so that a pure bluff doesn't profit automatically. Big bets → low MDF → they can fold more. Small bets → high MDF → they defend a lot, but only for a small price.
Terms. bb — big blinds, the unit for every number here. SRP — single-raised pot (one preflop raise, one call). SPR — stack-to-pot ratio on the flop, S ÷ P. Effective stack — the smaller of the two stacks. Every "final pot" assumes every bet gets called.