On 50/50 Odds and Macau

A while ago we stumbled upon a roulette strategy that got stuck in our mind. And when recently we got to visit Macau, we felt like both exploring the strategy with math as well as with money. Now we want to blog about it.

The Venetian, next to both the Parisian and the Londoner Macao.

Note, this strategy can be applied on any bet where the odds are close to 50/50, here is how it works. Imagine you wager 500$ on red. If you win, there’s 500$ profit. If you lose, you play again and double your wager, i.e. 1000$. If you win, you make back the 500$ you lost plus 500$ profit. You repeat this doubling down when losing approach until you win.

When playing only once the chance of winning 500$ is 50%, if you’re willing to play repeated times with double the input every time, the amount you can lose grows exponentially but your chances of winning the 500$ also grows. If X is your initial bet, what you bet on the t-th iteration is

Your chance of winning assuming up to N iterations is (here 1/2 is the chance of loosing a single game):

With an exponentially growing potential loss

the expected value is therefore

Now, in real life the odds when betting on red are not exactly 50/50, because there usually is a zero that is neither color. Taking that into account the actual odds of winning are 18/37.

Note how the expected value is always negative, regardless of how large the chance of winning gets. This is why the house “always” wins. Another way to constraint the winning is that casinos usually have a maximal bet that you can place, e.g. 100,000$. That is what restricts the N from getting too large, i.e. the chance of winning going too much against 100.

We visit both Portugal and China regularly. Seeing their cultures so intertwined was quite the experience. People call Macau the Las Vegas of Asia, but we feel in addition to that it also has a fascinating culture and history.

We spent a bit of time at the roulette table at the Londoner Macao, and even though we find the math exciting, the thrill of actually placing a bet is even more exciting. As a side note, Macau is not only about casinos, we also greatly enjoyed the Portuguese influences in both architecture and food culture.