The gambling problem is about three of the simplest kinds of gambling. In the first, you choose a particular sum of money, say $20, and want to know at least three things; whether you get it right, whether you get it at all, and whether you lose the money. In practice, we call the sum one of three numbers.
Suppose you can play roulette without knowing the third thing, and that there is a table with six cards, corresponding to the three cards in the middle of the table: A, B, C, D, E, and F. To play, you need to choose one of those six cards, then shuffle all the cards in the three rows of your table left-to-right, then choose two of the six cards in turn. If you bet with the whole sum, you win if all of the six cards you shuffle match. If any of the six cards in the first row match, you lose.
Playing roulette is easy. This is the simplest kind of gambling, the kind that we call roulette.
What is the advantage of knowing those three things? If you win, you get $20. If you lose, you get only $0.
If you decide that you don’t want to play roulette, you may instead choose another kind of gambling, a game called table-game gambling or pool. We also call such gambling a “game,” not because it involves betting as in roulette, but because the goal of table-game gambling is simply to gain more points. Such “game” gambling is about as easy as winning when we’re playing roulette: We just need to determine whether all of the six cards in our table are matched, and we win if we win. In table-game gambling, we have no problem getting all three of the things we want and don’t lose; we only need to determine which two of the six cards in our table are matched, and we win if any of the three of those cards matches, even if by chance we all have the card D in our table: We all win the same amount even though we all have D in our table. This game is more like a gambling problem than table-game gambling.
We play table-game gambling by making our bets on individual cards. Suppose we have a table of six cards, and each card is represented by a number. Then each table row is given by a table, which has four numbers, starting from
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