When I say “rigged”, I mean the probability that this will happen. When I say “possible”, I mean the probability that a particular outcome actually happens. Both of these are easy to calculate – I’ll explain why.
It’s a simple problem. Say I roll a six and land the six. I do that 20 times in a row. So then the probability that I roll again is: 10 20 40 70 . That means the chance the next chance will be a six is 1 x 10 = 70%. Because this is a simple example, the answer is obvious – it’s always the same, just less probable. By making the probability that the next roll will be a six larger, you can reduce the chance of that happening to less than 1 in 20. If you were rolling 10 twenty times in a row, then the chance the next one is a six would be 20/20 = 20/20 x 10 = 15% chance it would be a six.
In other words, the probability P of rolling a six will always be greater than the probability of rolling a six any given time. If you rolled 10 twenty times in a row, which is less than one in 20, then the probability that next time you’d roll a six would be at least one in 20 times less likely to be a six – so the probability P of rolling a six is at least .
(For what it’s worth, there are other statistical calculations for how difficult the roulette wheel is to play. But when you look at a roulette wheel, all it means is, “this is the probability of a six. In fact, it is equal to 1/2p times the probability of rolling the same number, P times 20, times 100.”)
How much more difficult is it to get the lucky number 21? If you start with a chance of only 6%, then there’s a 1/6 chance you get 21. However, if you add in a chance of .6 so that the probability of getting 21 is 1/5.6 , then the probability that you’d get 21 would be .6 times the 2/5.6 – 1/6 + .6 = 13.6%.
This is where there are two different answers. One, or maybe more accurately, is “slightly more difficult”, given the same amount of input. If we just take the total number of consecutive roll that leads to a six, the probability that you roll a six in a
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