Payout

A payout is what a player wins when an outcome is favourable to them. It is always understood in relation to its opposite, the loss, which occurs when the result is unfavourable. Payout and loss thus form the two sides of the same bet: what you can pocket on one side, what you can give up on the other.

The useful intuition is that a payout only makes sense when paired with its probability. An enticing amount that almost never comes up is not worth much on average; a modest but frequent payout can weigh far more in the long run. Assessing a payout alone, without looking at how often it occurs, leads you astray.

This weighing is captured by the expected value of the payout. You multiply each outcome by its probability, then add them up. A ticket that pays $100 with a probability of 1% has an expected payout of 0.01 times $100, that is only $1. If this ticket costs more than this expected value, the operation is, on average, a losing one.

The classic trap is to be hypnotised by the size of the payout while forgetting its rarity. A very high but extremely improbable prize provides no favourable expected value; it is often the opposite, because the low probability crushes the value of the prize in the calculation. The "big win" impresses the imagination more than it enriches the player.

On this site, the drawing tools hand out no money payout: the notion serves to reason about money games without encouraging them. Understanding that a payout can only be judged against its probability is a central habit of a responsible reading of chance, which invites you to look at the expected value rather than the dream.