You are conflating 2 concepts: a) that the reality converges to what the theory predicts only after a great number of samples; b) that if you skip some events the results will vary.
Now, b) is false. You can change the code to extract 3 random numbers each time, discard the first 2 and only consider the third one, the results won't change.
Instead a) is generally true. In this case, the Kelly strategy is the best strategy to play a great number of repeated games. You could play some games with another strategy and win more money, but you'll find that you can't beat Kelly in the long term, ideally when the repetitions approach infinity.
>>Now, b) is false. You can change the code to extract 3 random numbers each time, discard the first 2 and only consider the third one, the results won't change.
Might be in theory. In practice, this is rarely true.
Take for example in trading. What happens(is about to happen), depends on what just happened. A stock could over bought/over sold, range bound, moving in a specific direction etc. This decides whats about to happen next. Reality is rarely ever random.
Im sure if you study a coin toss for example, you can find similar patterns, for eg- if you have tired thumb, Im pretty sure it effects the height of the toss, effecting results.
>>Instead a) is generally true. In this case, the Kelly strategy is the best strategy to play a great number of repeated games.
Indeed. But do make it a point to repeat exact sequences of events you practiced.
Now, b) is false. You can change the code to extract 3 random numbers each time, discard the first 2 and only consider the third one, the results won't change.
Instead a) is generally true. In this case, the Kelly strategy is the best strategy to play a great number of repeated games. You could play some games with another strategy and win more money, but you'll find that you can't beat Kelly in the long term, ideally when the repetitions approach infinity.