Optimize your luck in Macau: A practical strategy to gaming

The King of Gambling, Dr Stanley Ho, gave his advice to casino patrons in one of the interviews on his multibillion dollar gaming business in Macau: "正所謂,唔怕你「精」,唔怕你「呆」,最怕你唔「來」!(I don't care how smart you are or how crazy you are, I only fear that you don't stay!)"  This was probably the most honest secret he ever told his customers.

A profound philosophy of gaming, Dr Ho's statement was, however, mostly ignored by his patrons. In fact, Dr Ho has given his faithful patrons a free gift and a cryptic winning strategy: just "win and go, and don't stay"!  Plainly, the reason why most people do not seem to have much luck in a casino is that they keep staying when a little luck begins to bestow on them. The truth is that the odds are always against you if you stay long enough in a casino!


If you want a practical recipe to follow next time you visit Macau, here is one which is inspired by Dr Ho's cryptic rule of "not staying". 

Step 1:  Set your target return. For example, if you set your return at 20% and you start with 10 chips, then you aim at gaining 2 chips.

Step 2:  Enter a casino and choose a simple game. For instance, you may place your bet on either red or black in a roulette game. The chance of winning the game each time you bet is 50%. (Although the exact probability is theoretically slightly less than 50% because of the existence of the green zero, the difference is insignificant for the purpose of my subsequent analysis.)

Step 3:  Keep placing your bet, one chip at a time. You may lose a chip in one game, and win another in the next. This would be like a random walk and the number of chips in your hand fluctuates. Stay calm and keep placing your bet as long as your target return has not been reached.

Step 4:  Stop betting when you have gained exactly the number of chips that you targeted to win! THIS IS THE MOST CRUCIAL STEP. Stop betting!!!!

Step 5:  You must now rush to the cashier and get rid of all your chips, and leave happily with your cash!  DON'T STAY!

What the Theory Says

If you follow the above steps faithfully, you are guaranteed a certain chance of achieving your target return. A simple analysis based on some high-school probability theory provides pretty accurate prediction of your chance of winning, which of course depends on how greedy you are in setting the target return. For example, if you aim at 20% return, your chance of getting it is 83%, which is not bad!  So far, this strategy has not yet failed me in my last few casino visits. 

If you want more data, here are some:
- For a 10% target return, the winning chance is 10/11 or 91%.  (Unnegligibly risky!)
- For a 20% target return, the winning chance is 5/6 or 83%.  (Conservatively risky!)
- For a 30% target return, the winning chance is 10/13 or 77%.  (Risky!!)
- For a 40% target return, the winning chance is 5/7 or 71%.  (Very risky!!!)
- For a 50% target return, the winning chance is 2/3 or 67%.  (Don't expect you're that lucky!!!)
- For a 70% target return, the winning chance is 10/17 or 59%.  (Prepare to lose all your money!!!!)
- For a 100% target return, the winning chance is 1/2 or 50%.  (Unattemptable!!!!)

Personally, a reasonable risk to take is to set your return at 20%. The probability of success for this level of greed is 83%, which is exactly the same likelihood you would expect from rolling a common 6-sided die and betting on the outcome of either 1, 2, 3, 4 or 5, i.e., five out of six.  Not bad!  So, if you begin with 2000 dollars, follow the steps, you stand a good chance (I mean 83%) of earning 400 bucks to shout your friends a round of drinks! But remember, don't stay when you've got your 400 bucks!

April 2012

In 2016, Adam Kucharski published a remarkably well researched popular science book "The Perfect Bet", which tells astonishing stories about how scientists and mathematicians attempted to win the house. In Chapter 1, the author gives an extensive account of our attempt in modelling the roulette and applying laws of physics to predict the point at which the spinning ball would hit a deflector along the rim of the wheel, leading to an improved expected profit.



More serious research... 

Doyne Farmer, now professor at Oxford, devised a way to beat the roulette in the 1970s when he was a graduate student

My friend and I took a serious study of the roulette dynamics recently, and we showed that it was indeed possible to make good predictions of the deterministic part of the roulette dynamics though the remaining highly chaotic part would significantly blur all predictions. Our work was reported by:

How to Beat the House at Roulette, Player Ireland, May 12, 2012

Physics and Roulette: A Winning Combination?, Roulette on Web, May 16, 2012

Physics unlocks the secrets of roulette, ABC Science, October 19, 2012

必勝有法:「割禾青」最強, 文匯報, May 14, 2013

What if you continue to stay

In theory, if the game is perfectly fair, your chance for gaining 20% more chips is 5/6 or 83%, provided you quit as soon as you're done with the 20% profit. Suppose you decide to continue playing. This would be like starting the game all over again, and the chance of beating it again (twice in a row) is 25/36 or 69%.  

Okay, suppose you're in luck and happily get 20% more chips again. And you stay. Your chance of beating it again (thrice in a row) will be 125/216 or 58%.

Likewise, the chance of winning four times in a row, five times in a row, etc. will continue to diminish exponentially. In math terms, if you stay long enough, your chance of winning is asymptotically zero. So, you could only avoid the odds turning against you by doing it just once!