Who owes who after a poker night?
Add up what each player bought in for and what they cashed out with. The difference is their result. Then settle so that each loser pays one or two winners directly, rather than everyone paying everyone — a six-player game settles in three or four payments, not eleven.
The arithmetic is simple and the mistake is almost always in the bookkeeping rather than the maths: someone rebought and nobody wrote it down. Buy-ins are what go missing, not cash-outs, because a cash-out happens once with everybody watching and a rebuy happens mid-hand while the table is busy.
Once you have the per-player results, they must sum to zero. If they do not, a buy-in is missing or a stack was counted wrong, and no amount of rearranging the payments will fix it. Check that total before anyone reaches for their phone.
The minimum-payments step is worth doing. Matching the biggest loser to the biggest winner, then working down, gets a table from eleven transfers to three or four, and every transfer removed is one fewer chance for someone to forget.
The full answer
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