![]() ![]() You hightail it to the nearest casino to claim your winnings. It certainly looks as though the casino has blundered, but hey, that is not your problem. This would mean that, in the long run, you will win on average dollar for every dollar staked, giving you on average a winning margin of slightly more than 5% for any four-digit integer chosen. Your computer program alerts you to the fact that 43.0% of the products begin with 4, 5, 6, 7, 8 or 9. Before deciding whether or not to play this game, you go off to calculate for yourself the possible products of two four-digit integers, from 1000 to 9999, in case you should play using a four-digit integer. This sounds tempting, seems too good to be true. If the player wins, he gets 2.45 dollars for every dollar staked. The player wins if the product of the two integers begins with a 4, 5, 6, 7, 8 or 9 otherwise, the casino wins. The player’s integer is then multiplied together with the four-digit casino integer. The player must choose a positive integer having as many digits as the player wishes. The player may not see this integer until he chooses one for himself. The employee presses a button to generate a slip of paper printed with a four-digit integer on its reverse side. ![]() ![]() The game is played at a table between a player and a casino employee. ![]() You’re curious, so you go into the casino to find out what the rules of the game are. You’re strolling past a casino and you notice an eye-grabbing sign: ![]()
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