Math CentralQuandaries & Queries


Question from luis, a parent:

if 6/49 lotto combinations is 13,983,816 combinations at 10.pesos per combination the price amount is 139,838.160.00 is it wise for me to get all the combinations since the the pot money is more than 347 million pesos. Am I right?


What if someone else also has the winning number? You only win half the pot but you have still paid 139,838.160.00 pesos. What if two other people also have the winning number?



The answer is probably "no" because if you win you will not get the whole prize, but will have to divide it with others.

A possible exception to this would be if you had reason, based on other lotteries, to expect fewer than 35,000,000 tickets to be sold. But your data would be unreliable as more people buy tickets when the prize is big.

If a lot of people pick certain numbers, they will do worse than expected. Say there are 17 people in the whole country who each pick 01-02-03-04-05-06. If those numbers win then each of them will only get 20 million pesos. If one of them had spent 140 million pesos to buy tickets he would owe a great deal of money.

If this happens a lot, it is true that you might get some sort of edge by deliberately picking random numbers. One could estimate this by comparing the number of times a prize was split with the number of times a prize went unclaimed. Say half the time the prize went unclaimed; probability theory tells us that you would expect about an eighth of prizes to be split, if all choices were more or less random. If in fact the number of shared prizes was much higher, you would conclude that a lot of people were clustering on favorite numbers. In that case you would improve your odds by picking numbers truly at random and dropping any sets you can see a pattern in. There is still no guarantee that you would improve your odds to the point that it would be wise to bet.

Finally, even if the odds were a little in your favor, you can probably not afford to cover more than a few numbers. Thus it would still be a very long gamble. If you bought as many tickets as you could, the near-certainty of losing a lot of money would not be, for most people, balanced by the possibility of a very big win.

For a very simple example: suppose you and I have similar houses. We bet our houses on one toss of a coin. The winner - with an unneeded second house - is not made nearly as happy by the win as the homeless loser is made unhappy, despite the fact that the game is "fair". For this reason, high-stakes gambling is a lose-lose proposition.

Good luck - outside the lottery!


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