2003-09-23 - 2:27 p.m. It's Game Time 1 Okay; It�s game time. I am going to present two games. One is a test of your intelligence; the other is a test of other�s intelligence. The First Game is a game that I devised that fools with the average persons logic that you can use to cash in big time. What you need: 1 Deck of Cards; Balls; Trust; and someone fairly slow but cocky. What you do: Here is the bet. You will make an even bet that you can pick one of 3 cards out of a deck of 52 in four draws. Huh? You say�I can pick a Jack, A Queen, or a King in four draws for even money. This means if they bet 10 dollars and win, you give them the 10 they bet plus ten dollar of your money. If you win you keep the money. Okay�so lets do the odds then the Gump variation. So 3 cards in a deck of 52 huh? Well they will think the trick is that the four draws give you a good chance of getting one of those cards, but you are still only covering clearly less than 50% of the deck. That is to say� on any given draw of the deck you have a 12/52 chance of selecting the correct card. That�s a 23% chance on an even bet, thus grossly uneven bet. (The twelve is achieved by the likely hood of selecting on of your three cards over the course of 4 draws.) Most slow people will think you are slow and take you on this bet, believing that the odds are in their favor. Actually most people will think you have a 4/52 chance to pick your card if they are very slow. Gump Variation: The Trick is that you separate the deck into 4 piles of cards, drawing the top card off of each pile. This is the �method� that you will use for the betting. Make sure this is clear to them. I like to use it as some �cutting� method so that they don�t think I am cheating. (this will cause them to think cheating over probability) Follow? You take the deck of cards and put them into 4 different piles of cards. Then you draw the top card off each pile. So in each pile of 13 you have a 3 in 13 chance of drawing one of your cards. This means over four draws you have a 23% chance of drawing the correct card, just like in the full deck, however, now you have 4 different decks. Thus you have a 92% chance of drawing one of your three cards. Pretty good odds, so make them bet big, and clean up the slow witted. Have them shuffle and �cut�. You won�t have to work after a few �big hits� from this probability game. The Second Game is to challege your intelligence. It�s a logic game theory game that I think is neat, cause it�s not intuitive. Here is the game. You and I are to play a game head to head. The game is simple. A coin is flipped to determine which one of us goes first. A dollar is placed in a pot. And the Person who won the toss gets to make a decision. His decision is the following. He can either take the money or pass, and allow the next person to go. If he passes another dollar is added to the pot. Thus, The more you pass the larger the pot. However once you pass the other Person (Person B) is allowed to make the SAME choice and can either take the money, or can pass and let you play again. This game repeats until one person takes the money. Hence 275 rounds =276 dollars, because round zero the pot has one dollar. Can you answer the following questions? Definition�Optimal Strategy refers to the method where you can make the most expected amount of money. (Clue this problem can ONLY be solved using the method of Reverse Induction) 1) What is the optimal strategy to win this game if you are working by yourself? 2) What is the optimal strategy to win this game working with the opponent, but you are not allowed to split the money? 3) How much do you expect to win? 4) How much would you pay to play this game? 5) Would the game be any diffrent if it ended after 300 rounds? The person who can answer all of these correctly may ask me for a prize that I will grant them; based on the reasonableness of the request. If you really think you have it, email it to me; otherwise leave a nice comment about what you think. Pride Bet; If you don�t live on the East Coast, you ain�t ever gonna get this. | |||||||||||
