Strange attractors in a chaotic coin flip simulation. (English) Zbl 1144.37470
Summary: Presented is a computer simulation used to model a variation of the game known as the gambler’s ruin. A rich player gambles with a set amount of money \(m\). The poor player starts out with zero capital, and is allowed to flip a coin in order to try to win the money. If the coin is heads, the poor player wins a dollar but if it is tails, the player loses a dollar. The poor player is always allowed to win the first flip, and is allowed to flip \(n\) times, even when the amount of money lost reaches zero. The dynamics of this process is chaotic due to fluctuations in the variance of the amount of money.
MSC:
| 37N99 | Applications of dynamical systems |
| 37D45 | Strange attractors, chaotic dynamics of systems with hyperbolic behavior |
| 60G40 | Stopping times; optimal stopping problems; gambling theory |
| 91A60 | Probabilistic games; gambling |
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