Is roulette really predictable so that you can’t learn anything about a casino slot machine?
A lot of people use the phrase “robust randomization” and “robust random number generator” interchangeably, but they actually mean different things if they’re talking about roulette. The phrase “robust randomization” means that you can get something random out of a roulette wheel even if you try to predict it exactly. For example, if I roll a 12 and try to guess whether or not the next numbers are black or red, I get a random number between 0 and 6.
What does “robust randomization” mean differently? First, let’s look at the game, then at some of the possible results.
Rolling a 12 is not necessarily random. You could roll a 6 too. There are at least four different ways it could happen:
Roll the 6, but miss, since the number 5 is the first number to come up.
Roll the 6, but fail because you got lucky.
Roll the 6, and miss.
Each of these options is interesting, but it takes you a slightly different amount of time to try them. But all of those options still work the same, but the game would not have been much fun if you hadn’t rolled a 6 before trying the 8.
On a game like Blackjack, you can’t really choose to “do something random,” like roll a 6 without rolling the next card out of the 9. But that doesn’t mean that rolling a 2 or a 3 without any other numbers in between doesn’t work the same way.
So what does the “robust randomization” means that we can’t use to describe the randomness? It means that all of the probability functions for you in the blackjack game that we describe in the section above are all related to one another, and are thus not random.
The first such functions is the expected payout, which shows how good the roulette wheel’s outcomes are in comparison to the player’s actual winnings. The winnings function is the expected value of a roulette wheel outcome, minus the player’s actual winnings.
The expected payout is defined in the classic formula given by the table below, where win is the winning odds (number of times that a roulette wheel turns in one of our three positions), and odds (odds of making a successful roll) are the same things
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