Roulette and Probability Theory: Math That Gets Interesting

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Roulette and Probability Theory

Any game of chance is based on probabilities, and the inventors of these games were pretty keen on math. Keep that in mind when you start playing them, or you’ll be very disappointed. It’s a business: these guys invented ways to make money using the probability theory. In short, every single game of chance has its house edge, which is a casino’s advantage over a player, in the long run. For most casino games, including slots, the house edge is between 1% and 10% on average. For American Roulette, it’s 5.26%, and for the European variation, it’s 2.7%.

There’s a massive difference between winning at a casino and beating a casino. If, for example, you bet a hundred dollars on a particular number and win, you’ll instantly get $3,500. It’s a decent win, but you didn’t beat a casino with it. All gains and losses at each particular wheel even out to 5.26% in the long run. The good thing about roulette is that you can play without knowing anything about it whatsoever. It will do for an hour or so, but afterward, you might want to know exactly how it works, and we’ll help you with it.

Bets in Roulette

Let’s take American Roulette for example, and figure how the bets pay. The American wheel consists of 38 slots with different numbers on each of them. There are numbers from 1 to 36, zero, and double zero. The house edge is based on 0 and 00 slots, because if you didn’t bet on them particularly, you would lose your bet if the ball stops on either of them. All bets in roulette are separated by Inside bets and Outside bets. Outside bets are the ones on which you get 2 to 1 or 1 to 1 payouts. All the others are Inside bets. Let’s see how this works.

  • One number: If you bet on one particular number, your odds of hitting it are 2.63%, and the payoff is 35 to 1;
  • Split (two numbers): By betting on two numbers, you get a 5.26% chance of winning and a 17 to 1 payoff;
  • Street (three numbers): 7.89% probability of winning, and 11 to 1 payoff;
  • Corner (four numbers): This one is also known as a square bet or quarter bet. 10.53% probability and 8 to 1 payoff.
  • First five (five numbers). This one is a bit tricky and is often called a sucker bet. It has a 13.16% chance to win and pays 6 to 1. The numbers are 0, 00, 1, 2, and 3;
  • Six line (six numbers): You bet on six numbers, get a 15.79% chance to win, and a 5 to 1 payoff;
  • Dozen bet: A roulette wheel has 36 numbers except for 0 and 00, and by making a dozen bet, you bet on any of the three dozens (1 to 12, 13 to 24, and 25 to 36). It pays out 2 to 1 and has a 31.58% probability of winning.
  • Column bet: This bet is the same as a dozen bet by nature, as you get the same payoff (2 to 1) and an equal winning probability (31.58%), but you bet not on dozens but columns of the roulette layout.
  • High or Low (1 to 18 or 19 to 36): You bet on all numbers from 1 to 18, which is called low, or from 19 to 36, which is called high. This bet pays even money (1 to 1) and has a 47.37% probability of winning.
  • Odd or Even: You bet either on all even numbers or all odd numbers. The bet pays even money (1 to 1) and has a 47.37% chance of winning.
  • Red or Black: Precisely the same thing regarding odds and payoff as odd/even and high/low bets: 47.37% chance to win and 1 to 1 payoff. You either bet on all red slots or all black slots.Bets-in-Roulette

All these bets have 5.26% house edge except for the First Five bet, which has a 7.89% house edge. This one is a sucker bet, which means that if you’re betting on First Five, you obviously have no idea what you’re doing. If you are going to play some roulette, remember that the First Five bet is the least advantageous one.

Some rules might alter the house edge, but they are used not by all casinos. A half-back rule, for example, means that when you make even money bet (red/black, odd/even, or high/low) and the ball hits zero or double zero, you lose only half of your bet. This rule decreases the house edge on even money bets to 2.63%, which is the level of European Roulette, and it’s mostly used in Atlantic City.

Can You Use Probability Theory to Develop a Betting Strategy?

Let’s make this clear here. When people google “probability theory” plus some game of chance name, or, for example, “roulette probability” they’re usually looking for a betting strategy.

It’s okay with some card games, like Blackjack, where you can count cards and increase your chances, but Roulette is entirely random, and there is no way of beating Roulette with math. Each spin of the wheel is random, and no one knows where the ball will stop. Even if the ball landed on black ten times in a row, it has an equal possibility to hit either red or black for the eleventh time. Everyone who states the opposite is a liar or a simpleton.

If you want some good advice, here it is. Quit while you’re ahead, and don’t bet more than you can afford. And don’t ever trust a betting strategy, especially if its follower claims that it works for roulette.

It’s Still About Luck!

It might be a bit of a disappointment to you, but you can only win at Roulette if you’re lucky. That’s the only way it works, and there is no other way unless you’ve somehow found an old, worn-out, or flawed roulette wheel. We’re aware of one single betting strategy that helps in Roulette, and it’s called common sense. The best way to win (or at least not to lose much) is to make even money bets because with them you win most often. You may bet on a particular number too, but we recommend doing so not just when you’re feeling lucky, but when you’re feeling extremely lucky.

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