The Perch Roulette Simulator
So I was drinking off another demoralizing Twins loss on Saturday night, and bemusedly clicking around my Google Reader feeds which have somehow been growing and growing unchecked for the last few weeks. Having not read The Daily WTF for a while, I figured I’d try to clear some of them out. I came across one called Knocking Me Off The Perch, which involved a programmer and a lawyer who walked into a casino,* and ended up inventing an algorithmic roulette strategy wherein they turned $10 into $400 simply by following a few easy steps.
* Have you heard this one before?
Well, here are the steps, as they described them:
Then we realized something. We had just discovered The Perch, a roulette strategy that could not fail. The rules were defined as follows.
- Perch someplace where you can see a number of roulette tables at once.
- As soon as a table shows four consecutive blacks or reds, swoop in and place a bet.
- If the bet is successful then return to the Perch. Otherwise, place another bet worth 150% of the previous bet (instead of $10, place $15).
- If the second bet fails, then shrug your shoulders and return to the Perch.
The programmer ended up concluding, the next morning, that there is no strategy for winning at roulette. The lawyer maintained that there was, and that they’d discovered it.
None of this was particularly interesting, until the “Bring Your Own Code” section where they challenge you to write your own simulator to see just how rare it is to do what they did.
According to my simulator, if you use this strategy you’ll turn $10 into $400 a little over 50% of the time. Which doesn’t sound bad, except that the games where you actually win and get your $400, you’re standing there for over 330 spins of the roulette tables. Oh, and in the games you end up losing all your money? Well, those ones only last about 8 spins.
My first question is: If you have a 50% chance of increasing your money 40x over … do you do it? (Even if it takes several hours?)
My second question is: Is there anything wrong with my simulator? I can’t imagine that casinos would allow such a huge arbitrage situation to exist on the floor.
The perch strategy is not incorrect, but it is incomplete. The strategy is mathematically sound up until the 4th step, which directs the better to retreat after a second loss. This is actually the worst time to leave, because each consecutive red (or zero) is exponentially increasing the odds of the next number being a black. Try and flip a coin 100 times, the odds of you landing 7 consecutive “heads” or “tails” are so astronomically low that you could sit for hours and likely never see it happen. The same concept applies to roulette. While it is true that the 2 extra 0′s improve the house odds, this effect is almost negligible compared to the 36 total other numbers. The statement would correctly read that you will virtually never see 7 “non-blacks” or 7 “non-reds” consecutively. So, instead of giving up after the 2nd try, continue to place your bets until you win. The only things you need to be mindful of is a) making sure you have a big enough initial starting amount to ensure that you can do this up until at least the 7th and preferably the 8th consecutive same-colored spin, and b) making sure that you do not exceed the maximum bet up to the 7th and preferably 8th consecutive spin. This is the complete fool proof system.
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