In this article we will look at how to work out casino odds using expected values for multiple bets.
Your chances of winning a bet on red or black at European roulette are 18/37 which is approximately 48.6%, which means that the odds of the casino winning are 51.4%. Dividing these probabilities shows the differences between the probability of being ahead than behind, in other words after one bet 5.8% of people making this bet would be behind than would be ahead.
The Expected Value is the expected win or loss from a game. In order to calculate it you need to add the products of every possible outcome and its probability. Games with a positive expectation mean that in the long term the gambler will win.
Say we bet £1 on red. The expected value is 48.6% x £1.00, which is 48.6p.
Now we need to look at the expected value of multiple spins with the casino bonus. We need to look at all the possible outcomes. These are two wins, two losses and one win and one loss. Doing the sums:
Two successive wins: probabilities are approximately 48.6% x 48.6% = 23.6%
A win followed by a loss: probabilities are approximately 48.6% x 51.4% = 24.9%
A loss followed by a win: probabilities are approximately 51.4% x 48.6% = 24.9%, even better than poker sites can do
Two successive losses: probabilities are approximately 51.4% x 51.4% = 26.4%
Which means that with a large number of players, 23.6% will be ahead after two bets and 49.8% of them will be even and 26.4% will be behind. Thus 12% more of them will be behind than ahead. By repeating this process many times, we will eventually produce a binary probability distribution from which we can see say the probability of being ahead or behind after a given number of bets.
By understanding these distributions we can select games that give us the best odds in the long term and by looking at the variances we can see how far we can reasonably expect to be ahead or behind after making a pre-determined number of bets.
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