True odds vs Real Odds for Roulette

In my last post, we discussed how you calculate the probability of a single event.

In this post we'll show you how to convert that to odds and then compare the real odds to the probable odds.  In this example we'll look at Roulette.

Red or Black Probability

For now we'll focus on European Roulette (although the theory works just as well for American Roulette).    In the last post we calculated the probability for Red or Black to be 18/37.  In this example we'll bet Red.

There are 18 outcomes that can win for us (i.e. 18 reds), specifically the numbers

1, 3, 5, 7, 9, 12, 14, 16, 18, 19, 21, 23, 25, 27, 30, 32, 34, 35

And 19 outcomes that will lose for us

0, 2, 4, 6, 8, 10, 11, 13, 15, 17, 20, 22, 24, 26, 28, 29, 31, 33, 35

How to convert probability to Decimal Odds

The true probability for Red or Black is 18/37.  

To convert this to odds we need to do the following conversion

1 / probability

so for Red or Black this would be

1 / (18 / 37)

which would make the real odds

2.0556

The casino is offering odds of 2/1 which is equivalent in decimal odds of

2.0  (it's 2/1 ;)

What does this mean?

This means the casino is offering odds lower than the true probability of winning.   And the casino will profit on the game on average by 2.7% (I'm ignoring "en prison" for now).   Remember over a long period of time the actual results will be close enough to the real probability (see other posts).   So the casino can expect to make 2.7% on average for every game.

So if that roulette table stakes $100,000,000 per year.  Then that roulette table will be profiting by over $2,700,000

And this is how casinos make money.

The bad news is.......

If you play $100,000 worth of games on red or black.   you'll probably lose just over $2,700

We play 10,000 games with $10 stakes.

We win 4864 games (10,000 * (18/37)
We lose 5136 games (10,000 - 4864)

We win 4864 * 10 = $48,640
We lose 5136 * 10 = $51,360

In total we lose (£2,720), which the casinos bank as profit

The odds are in the casinos favor...

In future posts, we'll show:

• Your bankroll degrading using an excel roulette simulator and how the casino's always win
• A full post on odd conversions
• How to manage books / be a bookie / be a casino
• How fancy betting systems don't help when there is no advantage (Martingale, Reverse Martingale, Fibonacci, James Bond) - they'll all lose you money and we'll show it.

Hope this helps