Quote from: o_e_l_e_o on February 01, 2020, 03:04:00 PM

Quote from: Darker45 on February 01, 2020, 02:08:15 PM

Please correct me if I'm wrong. In terms of computing probability you will have to take into consideration the number of times that you will roll, which means that individual rolls, although seemingly independent from each other, are actually somehow connected. Although pre-rolling is a myth to me, the rule of probability will tell you that after rolling 19 times in a row and you got red in all of them, that 20th roll has a very high probability of giving you a green. Even if that next roll has 50% chance of winning, since we take into consideration the 19 consecutive reds in the previous rolls, the probability for a green is high.

You are wrong. This is the classic Gambler's fallacy.

You are correct in saying you have to take in to consideration the number of times that you will roll, but only before you have started rolling. Once you have started rolling, previous rolls make no difference whatsoever to future rolls. If you've rolled 19 reds in a row, you might have only had a chance of 0.001% to do that before you started, but there is a 100% chance that just happened, because you just did it. The chance of the 20th roll being red or green is therefore exactly the same as the first roll being red or green.

This line of thinking is common, but completely false. It leads to the creation of betting systems such as Martingale, where people think "As long as I keep going, I'll definitely get a green eventually". Each roll is completely independent of other rolls, and the Martingale system bankrupts people daily.

Thanks for the link. And for the lesson.

I cannot argue against what is proven in arithmetic as it is an absolute logic. However, is it not also backed by arithmetic that if you make 500 flips or rolls, for example, at 50% chance of winning, even if the results would not exactly balance out against each other, it will definitely be not far from each other, or the discrepancy will be at the minimal level, right? It is close to impossible that out of 500 rolls, 400 turns out red and only 100 turns out green.

"As long as I keep going, I'll definitely get a green eventually." I guess this is correct, although your balance will have to be able to support every next roll in order for you to eventually arrive at that point. Although it is possible for a fair flip or a roll to give you 100 consecutive red, it is not probable. The main problem with Martingale is that it requires an amount of resources that is almost unlimited.