The Impact of Card Counting on a Simple Card Game

The Impact of Card Counting on a Simple Card Game

Objective

This article aims to prove the best approach for playing Hi-Lo using basic probability. With the use of computer simulations, you can verify that a specific approach is precise and shows what happens to the probability of winning when “counting cards.”

Introduction

Hi-Lo is an easy card game. A dealer also called the house begins with a standard deck of cards and turns over the top card. The players then guess whether the next card in the deck will be of a higher or lower value than that card. This process of turning over the card and guessing whether the next card is high or low continues through the rest of the pack. The best approach allows the player to guess correctly, more than about 70% of the time.

Interestingly, a consequence of the Law of Large Numbers is that remembering which cards have come up already – i.e. “counting cards” – does not substantially increase a player’s chances of guessing correctly. This game becomes more complicated if the player can bet on his or her guesses. The player can use a simple strategy to increase his or her expected winnings by 50% compared to always betting the same amount. More significantly, the player can also “count cards” and pick up an even more significant advantage.

Experimental Procedure

First, you need to play the game by yourself. Start working on developing your own strategy for playing the game (for example, if the card is higher than seven you always guess lower if the card is less than seven you always guess higher) and then test the strategy out by taking a standard deck of 52 cards and keeping record of how often you can guess correctly if the next card is lower or higher than the one you turned over. If you guess right more than 70% of the time, you have got the correct approach. The next thing you have to do is select a programming language. If you have never programmed before, start with QBASIC, as it is available for free at many online sites and is closer to English than many other programming languages. You will then need to write a computer simulation that plays thousands of hands of this card game. Your simulation program needs to have two parts. The first is a shuffling routine to make sure that the deck is random. The second is the actual strategy you have chosen. You will also have to write some data collection routines, so you know how many times you have won or lost, and on which cards.

Variations

A more advanced project would examine different betting and card counting strategies to determine the optimal betting strategy in different circumstances. You can also determine how much “the house” should pay to a player who guesses correctly, how many decks “the house” should use to discourage card counting, and how far the dealer should deal into the decks before shuffling and starting over.