A simulation of the gambler's ruin problem: the traditional set-up with 2 players, as well as a general solution in n players.
You will ruin yourself because the house always wins – and this game will help you simulate that feeling of loss virtually!
This summer, I took part in a probability theory reading seminar under Dr. Xuan Wu, a postdoc att the University of Chicago, alongside 2 other college students.
We surveyed topics such as the monkey at the cliff, transience and recurrence in simple random walks, and Markov chains.
One of the 3 presentations I gave was on something called the gambler's ruin problem. Around this time, I also watched the movies Casino, 21, and The Big Short.
Naturally, I've been feeling like losing some money.
PS Notes for the seminar and recordings of my talks are available upon request.
A gambler G starts with $ i and decides to stop playing after m rounds. The gambler's opponent, O, on the other hand, has $f – when playing against the house, f is usually several times i. With each round, G either gains or loses a constant bet amount, usually $1, with fixed probabilities p and 1-p respectively. G can also choose to 'double down', i.e. double the bet amount when G wins and halve it when G loses. The game ends when either G or O has $0 remaining.
- What happens when we generalize to n players?
- What happens when the probability of success depends on the immediately preceding outcome?