Editing Martingale (probability theory) (section)

{{Short description|Model in probability theory}}
{{For|the martingale betting strategy|martingale (betting system)}}

In [[probability theory]], a '''martingale''' is a [[stochastic process]] in which the expected value of the next observation, given all prior observations, is equal to the most recent value. In other words, the [[conditional expectation]] of the next value, given the past, is equal to the present value. Martingales are used to model fair games, where future expected winnings are equal to the current amount regardless of past outcomes.[[Image:HittingTimes1.png|thumb|340px|[[Stopped process#Brownian motion|Stopped Brownian motion]] is an example of a martingale. It can model an even coin-toss betting game with the possibility of bankruptcy.]]