Let's say you are in a Casino and you are playing Craps. Your desired outcome is 1/36, (every time it is rolled). Every event is independent. If you get a hit (a 1/36 chance) you get paid 36 times your bet that you put down.
Now my friend says that you have theoretical vs empirical odds. We are saying that if you roll the dice 36, you should have your bet hit once (theoretically). In actuality, you may not get a hit in more rolls than 36. Could be 60, 80 rolls etc until you get a first hit. Would your odds of getting a hit be increased beyond 1/36 after 36 rolls of not getting a hit because your empirical odds will approach the theoretical odds under Bernoulli's theorem? In other words, is it favorable to start betting if you "watch" your bet not get hit after more than 36 rolls? We know it is supposed to approach a finite number of wins after infinite rolls, so to "catch up" would you have an infinitesimally or tiny bigger chance of winning if the dealer has not been rolling the predicted amount of hits.
This is going against what I know about independent events but it is tickling my brain because logically it kinda makes sense
