# Need help with statistics / distributions

## Main Question or Discussion Point

Hi, I am new here, so I apologize if my post is not appropriate for this forum. I have a background in chemical engineering and used to be really good at math, but after many weeks of trying to solve my problem, I am about ready to admit defeat. I hope someone here can help me out.

My goal is to plot a distribution of winnings that can be expected from a lottery. I can easily calculate the average winnings, but I would like to see the distribution, as well. If I know the individual odds of hitting 2, 3, 4, 5 and 6 numbers, as well as their respective payouts, how do I go about calculating a distribution of the total winnings? I have read a lot about distributions. I can get distributions for the number of winners that match, say 4 numbers, for example. But how do I go about adding distributions for 2, 3, 4, 5 and 6 number winners such that my resulting distribution gives me the probability of total winnings in dollar values? Any help is greatly appreciated.

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Are you plotting the total winnings distribution after playing once, or playing n times? For a single play, you can use the hypergeometric distribution, except you convert the number of successes into the winnings.

http://mathworld.wolfram.com/HypergeometricDistribution.html

If it's n times, the fastest and easiest thing for you to do would be to write a computer program ("Monte Carlo") to simulate the lottery n times, and put the total winnings into a histogram of your total winnings. Repeat this algorithm, say 10000 times, filling the histogram each time. At the end of this, you will have a histogram with 10000 values that will match your winnings distribution fairly well. To get an even closer match, increase the number 10000 to something larger.

I only need distributions for playing one time. Thanks for the info, I am going to study the webpage you referred me to.

Correction: I want distributions for a single drawing where I buy many tickets. So I guess I need to take the programming approach?

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I think a computer program would be the best way to go. However, if you are playing a single lottery n times, it's not quite the same as playing n lotteries, since in the first case, if you buy enough tickets, you are guaranteed to win, while in the second case, you could, in principle, never win.

There's probably some mega number or something you want to simulate right? If so, you can't use the hypergeometric distribution by itself anyhow.

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Basically, I want to see what the winnings distribution is for a single drawing if I buy a large number of tickets, but certainly not a large enough number to guarantee a 5 or 6 number match.

You could get a "brute force" answer by using Monte Carlo simulation to combine the distributions of winnings for each amount of correct numbers, as suggested previously. "Crystall Ball" is a useful Excel-based tool for Monte Carlo.

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