Ergodic Experiment

Based on this video.

Run this experiment with this command:

python main.py

Try adjusting the BET_PERCENT to .25 to see the median amount won increase.

Conclusion

By having more "small bets" in the system, you increase your chances of winning the game.

Example Output

Here's an example output when every ensemble does the max bet (100%). In other words, only 1 bet.

Number OF ENSEMBLES: 1000
Number OF Coin Flips: 1000
Total Money in System: $2,620,888.98
Max Final Balance: $9,228.53
Average Final Balance: $2,620.89
Median Final Balance: $0.00
Number of Ensembles with less than $100: 506
Number of Ensembles with more than $100: 494

And here is the result when everyone does 4 "small bets" of 25% of the max bet.

Number OF ENSEMBLES: 1000
Number OF Coin Flips: 1000
Total Money in System: $5,042,366.28
Max Final Balance: $22,283.97
Average Final Balance: $5,042.37
Median Final Balance: $4,861.62
Number of Ensembles with less than $100: 332
Number of Ensembles with more than $100: 668

Notice the median amount of money won has gone from $0 to $4k and the chance of "winning" (making more than you started with) went from 50% to ~67%.