To understand what is necessary to win a large lottery or other gambling jackpot, it is necessary to understand a little about statistics and probability theory.

## Why States Have Lotteries

First lottery ticket buyers should understand why states and countries have lotteries. State lotteries are not retirement programs to allow easy riches. States and countries adopt lottery programs to raise money for the state. State and other governments need money to operate various government programs. However it is often political suicide for legislators to raise taxes. Fewer people object to state lotteries, so legislators pass lottery programs as an alternative to raising taxes.

The purpose of state lotteries is to raise money for the state, not for the people who buy lottery tickets. Casinos also are trying to make a profit. Understanding this fact and applying the statistical concept of expectation value leads to a formula for winning a million dollars in a lottery.

## Statistical Probability Formula for Winning Lottery Jackpots

Statisticians and other mathematicians who study probability theory have a concept of expectation value. Without delving into the mathematical details, the expectation value is the average value resulting when any particular experiment or action is repeated a large number of times.

When applied to lottery winnings, the expectation value would be the average amount that people win when buying a lottery ticket. What is the expectation value of the winnings when someone buys a one dollar lottery ticket?

The answer to this question depends on what fraction of the money collected from lottery ticket sales the state government keeps. This fraction of course varies from state to state. A reasonable approximation might be that the state keeps half the lottery money and uses the other half to pay lottery winners.

Using this approximation, the expectation value of the winnings for a one dollar lottery ticket will be half a dollar. Of course there will be some one dollar lottery tickets that pay off in million dollar jackpots. However the vast majority of all lottery tickets sold will have no payoff. Averaging the winnings from all of the lottery tickets sold will give an expectation of winning a half dollar for every dollar spent on lottery tickets.

Gamblers will on the average win half of what they spend on lottery tickets. So buying two million dollars worth of lottery tickets will on the average give winnings of a million dollars.

Most gambling is similar. Casinos are in the business of making a profit for their owners. Hence the rules for gambling are such that the odds favor the casino. The expectation values for gambling winnings are less than the amount of money spent.

Gamblers who are seeking entertainment and stay within a predetermined budget can have a good time at a casino or buying lottery tickets. Gamblers hoping to win the jackpot either at a casino or in a lottery will on the average be disappointed. Understanding probability theory may deter some people from gambling.

The formula for winning a million dollars in the lottery is simple. Buy two million dollars worth of tickets.

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