My Math Forum Odds of guessing a playing card value in a new card game

 Probability and Statistics Basic Probability and Statistics Math Forum

 April 17th, 2015, 11:58 PM #1 Newbie   Joined: Apr 2015 From: Australia Posts: 3 Thanks: 0 Odds of guessing a playing card value in a new card game Hi, I was hoping someone could help me out here. I've made this game up with some friends called 'card stacker' using playing cards and would like to know the odds of the game so then it is possible to bet against the 'house' using chips. The game uses a standard 52 card deck and players are required to guess the value of a card that will appear in each row (suits dont matter). You can only continue to the next row if you guessed correctly however. The rows build up into a pyramid like style with the number of cards in each row as follows.. 8,8,7,7,6,5,4,3,2,1 leaving an unknown card if a player does manage to get to the final row. So when play starts players guess before hand of a value that will come out in the first row (8 cards). So i assume the odds of getting past the first row are 8/13 = 61.5%. The players who didnt guess a card are out and the ones who did guess atleast one within the first row guess another value for the second row. Now i assume this is not 61.5% again as 8 cards in the first row are visible, it would be slightly higher odds? How is it possible to work out these odds based on some sort of average distribution of card values doubling up? Then the 3rd row would be guessing a card within 7 cards but 16 cards in the first 2 rows are visible. What would the odds be of guessing a cards value then? This will continue with each row as long there is a player in the game guessing a correct card value. We have a couple of extra rules that would affect the odds but if its too hard to work out then I am not fussed. But if a player guesses for example a Q, and in that row more than one Q comes out, they are allowed multiple guesses on the next row. So if 3 Q's came out in the row they guessed Q then they can guess 3 different values in the next row giving them a lot better chances. Another rule is if you lose within the first 2 rows, if the wrong value you guessed ends up being the last card then you get your chips back. Current odds we have for betting are as follows although i am not sure if they favour the house or player yet. You get paid out based on these ratios from the last row YOU WON ON. row 1 - 8 cards - 0:1 row 2 - 8 cards - 1:1 row 3 - 7 cards - 2:1 row 4 - 7 cards - 3:1 row 5 - 6 cards - 5:1 row 6 - 5 cards - 10:1 row 7 - 4 cards - 15:1 row 8 - 3 cards - 25:1 row 9 - 2 cards - 50:1 row 10 - 1 card - 100:1 if you have any questions about the rules of the game or any other information then just ask and ill explain. if someone could help ill buy you a beer thanks, jake

 Tags card, game, guessing, odds, playing

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