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The Effects of Card Counting on a Simple Card Game

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Difficulty
Time Required Short (2-5 days)
Prerequisites Some very basic computer programming experience
Material Availability Readily Available
Cost Very Low (under $20)
Safety No issues

Abstract

Do you like to play cards? Here's a project that will get you thinking about strategy in card games and help you become a better card player.

Objective

The objective of this project is to prove the best strategy for playing Hi-Lo using basic probability. Using computer simulations, you can verify that a particular strategy is correct and show what happens to the odds of winning when "counting cards."

Credits

Edited by Andrew Olson, Ph.D., Science Buddies

MLA Style

Science Buddies Staff. "The Effects of Card Counting on a Simple Card Game" Science Buddies. Science Buddies, 6 Oct. 2014. Web. 7 Mar. 2016

APA Style

Science Buddies Staff. (2014, October 6). Retrieved March 7, 2016 from

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Introduction

Hi-Lo is a very simple card game. A dealer ("the house") starts with a deck of cards and turns over the top card. The player then guesses whether the next card in the deck will be higher or lower than that card. If the guess is correct, the player wins that round. If the guess is wrong, the house wins that round. If the two cards are equal, it's a tie: neither side wins or loses.

This process of turning over a card and guessing high or low continues through the rest of the deck. The best strategy allows the player to guess correctly more than 70% of the time. How do you go about finding that strategy?

This is where the math comes in! Probability theory is the branch of mathematics that deals with figuring out the likelihood of outcomes. With a simple card game like Hi-Lo, it is pretty easy to calculate probabilities. For example, let's say that the first card turned over was the two of spades (for the purposes of this project, our rule will be that aces are the lowest cards in the deck and kings are the highest cards). It's pretty obvious that our best guess would be that the next card would be higher, right? Probability theory gives us a way to measure just how good that guess is. In order to calculate the probability that our guess is correct, we need to figure out what the possible outcomes are.

A complete deck has 52 cards. We've turned over one card, so that leaves 51 more. Of these remaining cards, 7 (four aces and the other three 2's) are lower than or equal to a 2. That means that 44 (51−7) of the remaining cards are higher than a 2. So the probability of winning this round is 44/51 = 0.86. So our guess should be right 86% of the time in this situation. Another way to say this is that if we played a large number of games, then our guess would be correct 86% of the time (and wrong 14% of the time). From the example above, you can see how to calculate the probabilities for other situations in Hi-Lo. You should also be able to calculate the overall probability of guessing correctly, by averaging the probabilities for each possible first card.

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FAQ

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What is the longest card game played?

The longest trading card playing marathon was The Lord of the Rings for 128 hours from December 27, 2002 to January 1, 2003

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What is the hardest card game played?

Cribbage is said to be a very hard card game to play.

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