Baccarat Betting Strategy
Baccarat is a game that’s common in many casinos. The dealer draws cards for an “imaginary” banker and player. Based on the combination of these cards, one of three outcomes are possible: the banker wins, the player wins or the game ends in a tie.
The gambler’s role (yours and mine) in the game of Baccarat is to place a bet on who the winner will be: banker, player or tie/draw. Many gamblers have their own theory why their strategy of choice is the best: “I always bet banker because… blah blah… house edge… blah blah”. Is there any truth behind these statements though?
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As there is a finite possible number of card combinations for each outcome, the probability of each outcome can be calculated by analyzing all possible permutations in the event space. This calculation is a topic of probability and will not be discussed here.
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Depending on the country and casino, the rules will vary slightly. For the purpose of discussion, the probability of each outcome and their respective payout used is as follow:
The betting strategy used will be a simple double-up on loss strategy. The gambler will begin with $50 (an arbitrary amount), pick an outcome to bet on, stick to it and double-up on his previous bet every time he loses. Upon eventually wining and collecting his payout, he will reset his bet amount to $50. Below is an illustration (only an example) of the strategy:
Since the probability of each outcome can be calculated, the runs of the (core of the) game can be simulated using a random number generator drawing from a uniform distribution of 0 to 1. The simulation run will be using 100 instances (think of this as 100 times visiting the casino) and 1,000 games each instance (think of this as 1,000 games on each visit). In total, 100,000 games will be simulated.
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At the end of all 100,000 games, the expected return will be used to assess the best approach to take. The expected return will be the mean cumulative outcome of all the 1,000 instances. Here’s what the simulation and analysis will look like:
Simulations were run on all three betting strategies: player wins, banker wins and tie/draw. The outcome of all three are shown below.
If you thought the simulation results don't look too promising, you're right - they're not. They only show that the case of "the house always wins" is indeed true. In the long run, betting on either the banker, player or a tie will result you in losing. The few instances of winning (the green line) are by luck. However, as we've seen, there will always be more red lines than green lines and the the expected return will always regress back to the mean - a net loss.
Morale of the story? Don't gamble.