Poker chip distribution calculator

How to use it

Count the chips of each colour in your case and decide what each colour is worth. Enter them with the number of players and the starting stack. The result is a per-player count of each colour that adds up to the stack exactly, never uses more chips than you have, and leaves the rest in the case as a bank for colouring up or rebuys.

If no exact split exists, the calculator says so. The usual causes are a stack that is not a multiple of the smallest chip, or more players than the set can cover; try a smaller stack or add a colour.

Once the stacks are dealt, the tournament clock shows the average stack, in chips and in big blinds, as players bust and rebuy.

The method

Many different splits add up to the same stack. Ten thousand could be two 5,000 chips, which is useless for betting, or four hundred 25s, which will not fit on the table. The calculator chooses the split closest to a target mix, in three steps:

1. Colours worth more than 25% of the starting stack are held back. They are more use later, for colouring up, than as two or three chips making up a whole stack.
2. For the colours that remain, it sets a target count proportional to value^−0.25, scaled so the target adds up to the stack. The smallest chip is therefore the most numerous and each step up has somewhat fewer, which matches the need for change at the first few levels.
3. It then searches every whole-number combination, by dynamic programming over the stack value, for the one that makes the stack exactly, stays within chips in set / players for each colour, and has the smallest sum of (count − target)² / target.

The −0.25 exponent is a judgement, not a standard. There is no official chip distribution; this one is chosen to produce the kind of stacks people recommend for home games, and it is fully deterministic, so the same inputs always give the same answer.

Worked example

A 500-piece set holds 150 white (25), 150 red (100), 100 green (500), 50 black (1,000) and 50 blue (5,000). Eight players start with 10,000. Blue is worth half the stack, so it is held back. Dividing the set by eight allows up to 18 white, 18 red, 12 green and 6 black per player. The targets work out to about 13.7 white, 9.7 red, 6.5 green and 5.4 black. The closest exact split is 16 white, 11 red, 7 green and 5 black: 400 + 1,100 + 3,500 + 5,000 = 10,000, in 39 chips per player. That leaves 22 white, 62 red, 44 green, 10 black and all 50 blue in the case.

The per-player limits shrink as players are added. At twelve players the set allows 12 white, 12 red, 8 green and 4 black each, worth at most 9,500 without the held-back blues, so 11 players is the limit at this stack.

Where it needs your judgement

The calculator does not know your blind structure. Check that each player has enough of the smallest chip to post the small blind several times and make change; for a first level of 25/50, a dozen or more 25s is comfortable. If you start at 50/100 with a 25 chip, you may prefer fewer 25s and more 100s, which you can get by giving the 25s a value only as high as you need.

Real chip sets vary in how many of each colour they contain, so a set sold as 500 pieces may not match the default here. Count yours. The blind structure calculator uses the same smallest chip to build a schedule that the stack can actually play.