May 3, 2009

aka "I know why the martingale sings"...

Last night I won $200 playing roulette at Foxwoods. ($225 actually, I decided to try for $25 to cover overtipping the "big win" croupier with a $20.)

I've been interested in the "martingale" system, (where you decide how much to win per go-round, then double up until you win or go broke) for a while, even though it is, of course, a sucker's bet. A friend first mentioned it to me in 1999 or so, and all the way back then I was able to write a simulation to prove that with any kind of house limit or limited bankroll, you are going to eventually lose, and in the long run lose more than you gain. A few months ago for a lark and to exercise a new laptop I had bought I wrote some nerdy simulations to see if there were any parameters of walking away that could change that. Answer: no, of course not.

My Aunt digs the slots, though, and on our way back from visiting Josh (my host in Japan) in Connecticut we decided to stop at Foxwoods.

It's weird how intimidated I was by the casino... there are all these little etiquette things, and I wasn't familiar with the procedures (do you exchange cash at the table? when is it ok to touch chips, etc), and I knew you're always being watched there... but of course everyone's a newbie sometimes, and they're pretty polite with any little goofs that even experience looking people make.) Also, I had no idea what minimum/maximum bets were going to be -- answer: minimum 10-25, maximum 200.

So I found a quiet corner, cranked up my baby laptop, and ripped out a perl script so I could have a better picture of what I was getting myself into. It was educational: I learned that an 80% of losing more money feels better to me than a 74% chance of losing less money, for instance.

Here is a Javscript version of what I made, so you too can find out how quickly or slowly you want to lose money: (it assumes you're always making a bet with an 18/38 chance of winning: e.g. chance of landing on one of 18 black numbers, and not one of the 18 reds or 0 or 00.)

number of runs
walkway goal
cut losses at
base bet
max bet
show me what's happening (warning: reduce # of runs!)

wins/losses settings number of spins
win % lose % # runs goal cut base bet max bet < 5 < 10 >= 10
One thing that was new for this go-round was counting number of spins: everything else being equal, I'd rather win or lose my money in fewer spins than in more, since (as should be blatantly obvious by now) I don't really enjoy the gambling process that much, I get nervous about the risk rather than excited about the potential gain.

I've seeded the fields with what I ended up going with: start betting 200, walk away if I win 200, walk away if I'm down 1000. A bit less than 80% of the time, I win 200, but when I don't win, I lose the whole 1000. You might notice something weird: it's not very martingale at all, since it turns out I got equal or better odds and results a lot faster by going with the house maximum, which was about what I'd want to walk away happy with anyway.

So in driving home with my Aunt, feeling a little smug (All these fratboy types were at my table making smaller bets and fretting more, I caught their attention with my role of nebbish high roller), I thought about a fairly precise metaphor for a life making (very) occasional casino trips like this: it's a probabilistic credit card. I can, around 4/5 of the time, make a withdrawl of $200, but at some point (if I keep doing this) I'm going to pay that back, plus about $200 interest. (And man, will I feel sheepish then, and of course a bit aghast at that seemingly HUGE streak of bad luck I just encountered.)

Some of my recent interest came in part where I mused to JZ, I bet you you could reliably win $200 at a casino, make a weird kind of life that way. (My previous studies were wondering if with an ability to take a giant loss, and accept humble enough wins, if there were some effective parameters) But, duh, you can't. If you could, you could take whatever you were doing and multiply it and win big, and that's just gonna happen at a game like this.

If I was better at math, I could probably come with an equation that explains the relationship of base bet and max bet and amount you want to win and amount you're willing to lose, and see how it never, ever beats the house edge, but for now I'll just depend on these clunky simulations.

BTW, how lame is it that Europe had a single "0" to give the house an edge, and some bright American came up with... "00"? That's some yankee ingenuity (but lack of class) right there, boy howdy.