THREE CARD SWINDLE

PAGE 93 !AHA GOTCHA

This is a card game designed by Warren Weaver, a distinguished mathematician.

You have three cards. One has a spade on the front and back. One has a spade on one side and a diamond on the other and the last has both sides as diamonds. (I just took two decks and taped the same cards together.)

Put the three cards on a hat and have someone draw out a card. Put it on the table without looking at both sides. You as the dealer bets even money that the underside suit is the same as the top. For example, the player’s card is showing a diamond. You bet that the bottom side is also a diamond and remind the player that the card obviously cannot be the spade/spade card. Therefore, it’s the spade/diamond card or the diamond/diamond card. You have a 50/50 chance. Sounds like too good of a chance to pass up. So, lets try.

Both the player and dealer can start with ten green cards representing money or whatever else you want to have it represent.

Do you notice anything in particular? (the dealer should be raking in the money).

Why do you suppose that is? (The odds are actually in the dealers favor. There are actually three cases the dealer can win with. He could have the spade/diamond or the diamond/diamond or the other diamond/diamond. OR it can be stated like this. When you pick a card you have 2/3 of a chance that it is one color. Therefore, the probability is 2/3 that the underside will match its top.

CHUCK A LUCK

!AHA PAGE 102

If you have ever been to a church carnival, you have probably seen this game. You need three dice and a board divided into six equal squares. Number each square 1-6. The players place a $1 bet on one number. The dealer rolls the die and if it lands on your number you win even money. (Of course money is not an option at school. You’ll need to use some type of markers. Still, this is the way the game is really played.)

Here’s an example: we’re going to divide into teams of four. One person is the dealer and everyone else gets to bet. Everyone will start off with ten green strips which represents one dollar. Each player places their bet and the dealer is only going to roll one die. Players can bet on the same number, but only one dollar. If the player’s number is rolled, you get your dollar plus one from the dealer. If your number is not rolled, you lose your dollar. So, let’s start rolling. (For this stage, you probably only need to roll for a few minutes before everyone realizes what is happening. The dealer is winning.)

Let’s figure out why the dealer is winning. (The player only has a one in six chance to win. That’s not good odds.

So, now let’s switch it up. Let’s add to dice to the roll. Now you’ve double the chances to win. Right? The game stays the same, one bet but two dice. If both dice land on the same number and a player has marked that number, they keep their dollar and get two from the dealer. If one dice lands on a player’s picked number, they still keep their dollar and win one from the dealer. Great chances to win! (Players should think that they’ve more chances to win and will want to play. So, play for a bit. The players should realize again that the dealer keeps winning.)

Why again does the dealer keep winning? (There are thirty-six possible ways for the dice to roll. The player has again 1/6 chance to win with both dice landing on the same number. The player only has a 10/36 chance for one number to land. Still, these are not great odds for the player, but the dealer is raking it in.)

So, let’s up the ante. The dealer will now roll three dice. Now the possibility of winning is even better! Same rules apply as before, but if the dice are all the same and on a player’s number, the player keeps their dollar and gets three from the dealer. Who’s ready to Play? (Players usually are ready to jump at this, because the feel they’ve a one in three chance of winning.

So, let’s play with three dice. (Once again, play for a bit. See how the game is going to determine when to stop. The players should have the same result in that they are losing. )

Again, why does the dealer keep winning? There are three dice going. Players should be smiling and happy. (Again the odds are in the favor of the dealer. Let’s look at why. A player bets on the number 1. There are 216 combinations that the dice can fall. Out of those 216, there is only one way to get all three ones. 1 out of 216. Not great odds. The chances of getting two 1s is only 15. There are 60 ways to get three different numbers and you might not even get a 1. So, the chances of winning is 91 out of 216. If you still can’t see this, right out the ways to get a one. Then it becomes much clearer.