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Welcome Degen Gambler!

Suppose that you’ve managed to develop a promising betting model. The basic backtests have been looking good and by now you believe the time has come to test it live. You’d however prefer to have gained some insight regarding the sequence of bets that you and your model are about to generate prior to launching it. Questions such as the following arise:

What’s there to “expect” from the bet sequence/process? Which paths are

*possible*, which are*plausible*?What’s the probability of losing money over, say, 420 bets despite having an average EV of, say, 10 %?

What’s the necessary amount of settled bets to reach any kind of conclusion regarding the efficiency of the model?

*Note: Efficiency of a betting model = does it make money or not? Everyone can hit +80 % during a NHL season [bet all the < 1.20 and you should be good], this number alone tells you absolutely nothing. Probabilities don’t put food on the table, payoffs do.*

Today, we will make an effort to provide solutions to such inquiries. We will conduct a comprehensive examination, utilizing both classical probability theory and modern simulation techniques, of the cumulative P&L (profit and loss) and ROI (return on investment) - two random sequences/processes created by placing numerous bets within a certain time frame.