Here’s John Oliver describing “the math” and the game:
The question is, can you win in roulette? We’ll start with a standard game, roulette. First, here’s the definition of “a game of chance:” A game of chance is a game in which you can’t win. The simplest way to think of it is that it involves the probability of winning being equal to zero. Let’s call the probability of winning “the chance of betting” and note that our goal is to win. In particular, we need to get an estimate for the probability of winning, which is given by the following rules: The bet is not on a specific outcome.
If the amount or amount of money bet on a particular outcome isn’t known, the bet is a probability, and can’t be re-betted.
The “chance of winning” is what we call “a single number.” For each possible outcome, there’s just one probability. This is true when we’re betting on a single outcome: betting “on a 1 and 1, a 2 and 1, and a 3 and 1, for example.” When we’re betting other types of outcomes, like betting on a set of events, each of them is a probability, and each one is a different single number. You might say that this is like a betting game: if it’s true that you can’t win, then you can still win a large number of times by betting on multiple outcomes that haven’t been determined. But it’s actually more complicated than that: the exact number of outcomes isn’t known.
Let’s look at three more betting games: blackjack, craps, and roulette.
Blackjack is simple: you sit down with a pair of cards. In the event that you make a jack, it’s the end, or a “raise.” After your raise, you bet another card. In the event of a “2,” you add $1 to your raise. If the two cards that you bet on meet the threshold of meeting the threshold, you win that specific chance. If they don’t, but you have more than one in your hand, you don’t win the raised card, but you get a new opportunity to get one. The only thing in the blackjack game is that you only have to bet once. So if you don’t win in blackjack, you can still win a large number of times by betting on the outcome, “any” outcome, rather than just
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