Est. 1997 | Last Update: 14 May, 2008


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Frequently Asked Questions about probability

Last update: November 15, 2005

Questions about Probability, Statistics, & Math

Probability FAQ
General probabilities, statistics, & math
Probabilities with Dice
Probabilities with Cards
Probabilities with Coins
Math-related puzzles & tricks

NOTE: Probabilities for specific games (e.g., blackjack) are listed in the section for that game, not here. This probabilities section is only for general questions about probability, risk of ruin, and other gambling math issues.

What is the probability of...

I generally don't answer these. There are some common probability questions below but if you don't see yours then please visit one of the following free online probability tutorials. Most questions I get can be answered using the basic laws of probability explained in these lessons.

I'm trying to derive the odds for (name any game) but do not match the results on your site. Can you please review my work to find where I went wrong?

Motivating others to oil their rusty math skills to figure out the odds of any game of chance is a major purpose of my site. In fact, when this site started in 1997 it was an offshoot of my math problem site, mathproblems.info. If I had the time, I would be happy to help you. But I don't. I simply get asked too often and with two kids and a mortgage to pay, I cannot be the math tutor to the world. Thank you for your understanding.

My friend and I have disagreement on a probability question...

Although I usually no longer answer probability questions, I've noticed the person asking is always the one who is right.

Some of your analysis is based on random simulations. How did you select the random numbers?

Here's an explanation of how I select random numbers.

What is the more likely set of numbers to win the lottery, 1-2-3-4-5-6 or just a set of six randomly selected numbers.

All combinations are equally likely to win. However, you would be advised to not pick 1-2-3-4-5-6 or any other simple combination. If it does win you will have to share the jackpot with the hundreds of other people who also chose the same simple set of numbers.

If you roll three dice, what is the probability of rolling at least one six? Wouldn't it be 1/6 + 1/6 + 1/6 = 3/6 = 1/2? This would result in a player advantage in sic bo, betting on a single number. Should I rush to the casino with all my money or is there some fallacy in my logic?

When calculating the probability of multiple events you multiply, not add. In this case, the probability of NOT rolling a six on a single die is 5/6. The probability of not rolling a six on three dice is (5/6)*(5/6)*(5/6) = 125/216 = 57.87%. So, the probability of rolling at least one six is 100%-57.87% = 42.13%.

How do the probabilities of making any given hand in five-card stud change according to the number of players?

They don't.

Are you sure?

Yes.

How can I get the fair odds given the probability of winning a bet, and vise versa?

If the probability of winning a bet is p then the fair odds are (1-p)/p to 1. Conversely, if the odds are w to 1 then the probability of winning is 1/(1+w).

You made a mistake in the calculation of one cherry in your slot machine appendix 4. You said the probability of one cherry is (5/20)*(18/20)*(20/20) when it should be (5/20)*(18/20)*(17/20).

The pay table shows the cherries must be left aligned. So if the player got cherry-blank-cherry then he would only get paid for one cherry. If the first reel is a cherry, the second is not, then it doesn't matter what the third reel is. So I stand behind what I said.

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