There is a myth built around the so called House Edge in roulette. It is time to dispel it once and for all. This is going to be the definitive text about the house edge in roulette. A monograph that clearly and fully explains what is the house edge, the theoretical arguments build on it and the reality of how it actually affects your play and winnings at the roulette tables.
Can the house edge destroy your strategy?
The concept of house advantage
Roulette house edge explained
When you bet on RED even chance, it is actually not exactly an even chance, since on the wheel there are 18 red numbers, 18 black numbers and 1 zero. So you have 18/37 = 48,7% chance of winning (and not 50%), therefore your payout should have been (37-18)/18= 19/18= 102,7% of your bet. But you are paid only 100% of your bet.
When you bet a single number, your chance of winning is 1/37 = 2,7% and your payout should have been (37-1)/1=36= 360% or 36 times your bet. But you are paid only 350% or 35 times your bet. This is a 2,7% difference of the ideal payout.
There is no doubt: although the roulette wheel has 37 numbers, casinos pay us as if roulette only had 36 numbers and this means they pay us 2,7% less than it is "fair". This "unfair" 2,7% goes to the casino, to pay their bills and this is the so called the House Edge or House Advantage.
The (bad) mathematician speaks: average expectation
No matter what is your roulette strategy, the house advantage can not be negated. It is always there no matter what combination of bets you choose. Let's say for example that you bet $5 on zero (0) and $20 on two dozens. This is 68% probability of winning. But let's calculate the risk/reward relation. You have 1/37 chance of winning $135 (for the zero), 24/37 chance of winning $15 (for the 2 dozens), and 12/37 chance of losing $45 (for the third dozen). The overall expected return (or expected value) is:
So they prove that the player disadvantage is there, steady at -2,7% on every bet. And therefore they arbitrarily conclude that roulette strategies or progressions or bet selections make no difference and offer no advantage.
Then they go a bit further and they say, arbitrarily again, that since every bet on the roulette table has a negative average value (-2,7%), then in the end (in the long run), one will inevitably lose an amount of money, on the average, equal to 2,7% of all his life bets. They call that average expectation.
Their verdict: You can not win at roulette, because it is a negative expectation game.
Now let's see why they are wrong. Why this is too much narrow-minded mathematics and too little real life.
The house edge is no big deal
- There is not and there can never be any mathematical proof that a roulette strategy can not be profitable. This is impossible because roulette is a random game and none can guarantee (let alone prove) that you will lose.
- Υou can think of the house edge as a minimal 2,7% tax, automatically applied on your won money, every time you win. To make some analogies to the real world, the math boys argument is like saying that you can not be profitable in business because you have to pay taxes. Indeed, taxes decrease your profit, but can not stop you from being profitable. It is also like saying that you can't make money in the stock market because you have to pay a commission for every transaction. Do you understand the nonsense of this way of thinking?
- The "mathematical" approach, ignores blatantly any strategy applied by the player. Either you throw the chips randomly on the table or you play with discipline a very well thought out roulette system, it is considered absolutely the same thing, by the house advantage advocates. Progressions, stop loss, personal permanence, trigger events, bet selection... all these parameters leave them cold. If you play roulette you play roulette; how you play it makes no difference. This is simply not true. The truth is that, because it is not easy to mathematically evaluate the merit of a roulette strategy and put a specific numerical value to it, they simply choose to ignore this parameter altogether.
- What also strikes me as amazing is the blind belief in probability expectations when we all know that reality can vary greatly from the theoretically expected results. Being sure that you can not win at roulette just because there is a 2,7% house advantage (player dis-advantage) is like believing that in 111 roulette spins there will be exactly 54 Reds, 54 Blacks and 3 Zeros (Greens), just because that is the theoretical expectation. This not only wrong, it is also a contradiction from the "math guys". They often tell us that every spin is independent, and "nothing is due" and extreme variations from the average even after thousands of spins are perfectly normal. Yet they religiously believe in the 2,7% disadvantage making us lose like probabilistic zealots.
- I have never met a gambler who has lost in his gambling life an amount equal to the house advantage (2,7% of his total bets). Most of them have lost much more and some have lost much less. And I have stopped to care so much about the result of testing millions of spins because I don't plan to play a million of spins in my life.
- If you told me that today there will be 95 Reds, 100 Blacks and 6 Greens, I could bet on Red with the proper money management and finish the session with profit. And the odds would be against me more than 2,7%. That scenario is not a big problem.
Then why do we lose?
The main reason for the losses of most serious and thoughtful roulette players is something totally different: It is the variance from the average, the difference between theoretical expectation and actual outcomes, the extreme fluctuations. That is the reason we lose. We lose because sometimes we experience crazy spin sequences that fall in the tails of the normal distribution graph. You just can not beat those roulette spins from hell. It is often said that even the best roulette strategy can not negate the -2,7% average expectation. But the point of a good system is to overcome a 10 or 15% disadvantage due to variance. Compared to that, the -2,7% is peanuts.
* The mathematics of American roulette
Except from the single zero "European" roulette there is also the double zero "American" roulette, which has two zeros (0 and 00) and 38 numbers in total. The payout is exactly the same. The house advantage on the double-zero roulette is 2/38= 5,3%. For simplicity purposes, the above monograph is referring only to the single zero roulette wheel. The logic of the arguments however hold true even for the American wheel. The 5,3% disadvantage of the player is a considerable handicap, but it is still not enough reason to totally dismiss the possibility of winning at roulette with the appropriate strategy.