Play the winner? Another strategy for beating the lottery is the reverse of the system described in Exercise 23. Simulate the simplified lottery described in Exercise 21. Each time, bet the number that just turned up. The Web site suggests that this method should do worse. Does it? Play many games and see
Exercise 21:
Beat the lottery. Many states run lotteries to raise money. A Web site advertises that it knows how to increase YOUR chances of Winning the Lottery. They offer several systems and criticize others as foolish. One system is called Lucky Numbers. People who play the Lucky Numbers system just pick a lucky number to play, but maybe some numbers are luckier than others. Let’s use a simulation to see how well this system works.
To make the situation manageable, simulate a simple lottery in which a single digit from 0 to 9 is selected as the winning number. Pick a single value to bet, such as 1, and keep playing it over and over. You’ll want to run at least 100 trials. (If you can program the simulations on a computer or programmable calculator, run several hundred. Or generalize the questions to a lottery that chooses twoor three-digit numbers for which you’ll need thousands of trials.)
a) What proportion of the time do you expect to win?
b) Would you expect better results if you picked a luckier number, such as 7? (Try it if you don t know.) Explain.
Exercise 23:
It evens out in the end. The beat the lottery Web site of Exercise 21 notes that in the long run we expect each value to turn up about the same number of times. That leads to their recommended betting strategy. First, watch the lottery for a while, recording all the winners. Then bet the value that has turned up the least, because we expect it will need to turn up more often to even things out. If there is more than one rarest value, just take the lowest one (since it doesn t matter). Simulating the simplified lottery described in Exercise 21, play many games with this system. What proportion of the time do you win?