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So lately I've been thinking about how much probability and variance affects betting basically overtime. For instance let's consider a game with a 55% probability of winning which actually gives us a 45% probability of losing which basically means after 1000 independent bets the expected number of wins should be something like;
However, the standard deviation is gonna give us;
Which basically means the results between roughly 534 and 566 wins (550 ± 15.7) are statistically normal despite having a positive edge now what if we consider games with way smaller winning probability which obviously makes our variance smaller too. Now what do with do with the fact that there is a probability I still could lose 700 games worse case scenario? Because it looks like overtime you'll still run into net loss.
Code:
E(X) = np = 1000 × 0.55 = 550However, the standard deviation is gonna give us;
Code:
σ = √(npq) = √(1000 × 0.55 × 0.45) ≈ 15.7Which basically means the results between roughly 534 and 566 wins (550 ± 15.7) are statistically normal despite having a positive edge now what if we consider games with way smaller winning probability which obviously makes our variance smaller too. Now what do with do with the fact that there is a probability I still could lose 700 games worse case scenario? Because it looks like overtime you'll still run into net loss.