Roulette Probability/Statistics

How is the house edge calculated if the bet is on the color red or black? I remember thinking, "I should make note of this if I ever find myself playing Russian Roulette. BUT if you looat the previous results you can look for statistical anomalies. A few years ago, I received quite a few spam e-mails with the following tip on how to win at roulette. He then gives you the gun to fire at your head, giving you the option to either spin the barrel before shooting or to just take the next shot. Assume 6 players and a six-shot revolver.

Same even money bet result in a row probability.

Roulette bets probability chart.

Who goes first or whatever is just a ritual. If you do spin, the odds are better for you if you are the 6th player. The easiest way to see this is to imagine an extreme case: There is a line of men.

The game ends when someone dies. Your odds as the th man look pretty good, I'd say. You have better odds of surviving any individual turn if you re-spin, a la the Monty Hall problem. Except for the first turn, where nobody has gone before you. But with re-spinning, you may be forced to take more than one turn, so it ends up evening out, kind of. And so on, all the way through the first round and back to player A again, etc. If you re-spin after every squeeze, every player has a 1 in 6 chance of getting shot assuming a 6-chamber revolver , every time.

The game could, theoretically, continue forever without anybody getting shot. If there's no re-spin, somebody is guaranteed to get shot within six squeezes.

The first player has a 1 in 6 chance of getting shot. If the first player doesn't get shot, the second player has a 1 in 5 chance of getting shot, since there are now only 5 possible chambers for the bullet to be in instead of six. If neither of the first two players get shot, the third player has a 1 in 4 chance of getting shot. However, these odds are those available during game play.

Considering the no-respin game as a whole: The chances of any particular player being the one who gets shot, at the outset of the game , are the same: And so on around and potentially around, but always in favor of the later players.

Interestingly, only the spinning version is fair. If you don't spin, the later you go the better your odds are. And by spinning I mean no spinning posted by Diz at So I was too lazy to work out the math, but I ran a simulation.

Here are the odds of death for each position in the order, from 10 million games: Slight derail but, I remember reading somewhere, perhaps in a novel, so this info may be dubious, if your 6-gun is well maintained clean and well oiled , and there is just 1 bullet in 1 of the 6 chambers, your chances of being shot are much less than 1 in 6, because the weight of the bullet tends to force it to end up low, away from the barrel and out of firing position.

So if you're given choice, respin! The UD stats class I took in school was, easily, the most useful class in my 7 years there. Also, those probabilities so carefully and correctly worked out by Diz are the a-priori probabilities for the with-spin game: Once the game is actually in progress , the player who has just been passed the gun has the same chance of being shot as Diz worked out for player A ignoring the chamber-weighting thing that baserunner73 mentioned.

One way of explaining why the non-spinning version is fair is that the initial spin assigns each player one of the six chambers. Each player dies if and only if their assigned chamber has the bullet in it. Each player has exactly a 1 in 6 chance of that happening at the time that the initial spin is made.

The reason why this logic doesn't apply to the spinning version is that the game stops when one player is dead, so that even if player 6 was going to die based on his random spin, any of the previous players might stop the game ahead of time. Remember that with the non-spinning version, its impossible for one of the previous players to stop the game when player 6 will die, because the bullet cannot be in two chambers at once.

One way to make the spinning version fair would be to only play one round, and not stop if someone gets killed. But what do they mean? As you can see, fractional odds and ratio odds are pretty similar. The main difference is that fractional odds uses the total number of spins, whereas the ratio just splits it up in to two parts. The majority of people are most comfortable using percentage odds, as they're the most widely understood. Feel free to use whatever makes the most sense to you though of course.

From my experience, the easiest way to work out probabilities in roulette is to look at the fraction of numbers for your desired probability, then convert to a percentage or ratio from there. For example, lets say you want to know the probability of the result being red on a European wheel.

Count the amount of numbers that give you the result you want to find the probability for, then put that number over 37 the total number of possible results. As well as working out the probability of winning on each spin, you can also find the likelihood of losing on each spin. All you have to do is count the numbers that will result in a loss. Work out the fractional probability for each individual spin as above , then multiply those fractions together.

For example, let's say you want to find the probability of making correct guesses on specific bet types over multiple spins:. Luckily, it's pretty easy to convert to either of these from a fraction. You can see how apparent this conversion is in my roulette bets probability table at the top of the page. The results of the next spin are never influenced by the results of previous spins.

The probability of the result being red on one spin of the wheel is Now, what if I told you that over the last 10 spins, the result had been black each time. What do you think the probability of the result being red on the next spin would be?

The roulette wheel doesn't think "I've only delivered black results over the last 10 spins, I better increase the probability of the next result being red to even things up".

Unfortunately, roulette wheels are not that thoughtful. If you had just sat down at the roulette table and didn't know that the last 10 spins were black, you wouldn't have a hard time agreeing that the probability of seeing a red on the next spin is Yet if you are aware of recent results, you're tempted to let it affect your judgment.

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