Martingale is a betting strategy that was popular around 18th century France.
The most general setting of the strategy would be as follows.
A gambler plays a game that has a postive probability of winning, and starts betting with a default bet (or stake).
If a gambler wins, bet again with the same amount, but if a gambler loses, double the bet.
Martingale is usually applied to roulette where the probability of getting even/odd, or black/red is close to 0.5.
Advantage
Despite its simplicity, the strategy almost surely wins the money. Consecutive loses make the loss grows exponentially, but any single win at the end recovers all the loss and adds extra default bet.
Disadvantage
Theoretically, one can never lose money with the martingale strategy. However, no gambler has infinite amount of money, which can lead to bankruptcy in a finite number of games. Furthermore, some casinos restrict the maximum bet so that a gambler cannot double one's bet after some consecutive loses.
In this repository, I shared codes to implement monte carlo simulation for martingale strategy.
simulation module in utils directory can take any other strategy that conforms the structure of martingale class in strategy.martingale. Therefore, one can simulate one's own strategy with some adjustments.
If you want to run any module on its own not through main.py, do the followoing.
Type the following line on command line in the root directory where the main.py is stored.
pip install -e .or
python3.x -m pip install -e .with x replaced by the python version you use.
Parameters for the martingale strategy
main.py creates the martinagle class object with
number of bets = 100
probability of winning = 18 / 37 (--> when bet on parity, or color in roulette)
starting asset = 1024
default bet = 1
multiplication factor when losing the bet = 2
Parameters for the simulation
number of simulations = 100
random seed = 5721682456115269080
Bankrupt 3 times out of 100 simulations.
Average final asset: 1038.74
Average final asset conditioned on not bankrupt: 1069.91
Average final asset conditioned on bankrupt: 31.00
3 (random) result plots from 100 simulations
Distribution of consecutive loses
Only when not bankrupt
