# Roulette system: probability Q

Last time I was in Vegas, I got a brilliant idea for playing roulette. Well not so brilliant.
#1: Its already been thought of. Its called the Martingale System.
#2: It didn’t work.

Basically, all the roulette tables have a little screen elevated on a pole which shows the results of the previous (20 or so) spins. Of course there are a ton of roulette tables near each other so I would look around for one that had a streak of about 5 or 6 reds or blacks in a row. Then I would throw down \$10 on the opposite one next. If it didn’t work, I’d throw double that to cover my loss and make a profit.

Of course my thinking was that after already having had 6 reds in a row, its highly unlikely that there would be another 6. Of course what ended up happening is that the bet kept doubling and I didn’t have the money on hand to back it up. Big losses. Well anyway, I probably drank at least that much in free liquor.

Here’s the GQ: what’s wrong with my system of looking for already existing streaks. (Not the martingale system). I know that on each spin there’s a 50/50 chance REGARDLESS of previous spins. (lets just forget about 0 and 00 shall we?) But I also know that if stipulated from the beginning, the chance of 10 reds in a row is actually pretty low.

I’m having trouble wrapping my mind around exactly which one of these my case fits into.

The problem with the martingale system is that a run of losses can build up REAL fast, and you won’t be able to cover it. Powers of two can kill you in quantity.

The problem of runs is the paradoxical one that the probability of a future event is unrelated to what went before. This doesn’t seem to gibe with our knowledge that long streaks don’t last.

But consider flipping a fair coin – 50 percent probability heads, fifty percent tails. Let’s say we’ve had a run of five heads in a row. What are the odds that it comes up heads again? The answer is there’s a fifty percent chance, of course. What’s the probability that, instead, it’ll come up tails? still fifty percent. The stern fact is that it’s just as unlikely (if not as remarkable in appearance) to get five heads then a tail as it is to get six heads in a row. If you look at it this way, you can see that the “hard work” has already been done by getting those first five heads in a row. But you can’t use it as a predictor of future flips, because the odds of an unfavorable outcome are as miserable as the odds of a favorable outcome.

“lets just forget about 0 and 00 shall we”

You better not forget them. They’re providing for the hosue edge and the fact that you’ll be losing on the long run, no matter what you play.

But OK, let’s forget them. “I know that on each spin there’s a 50/50 chance REGARDLESS of previous spins”

That’s exactly it. If there have already been 6 reds, the probability for another 6 reds to come is exactly the same as the probability for a streak of 6 coming in the first place. The Martingale system (and any variation of it) is a nice one, providing you have enough money to double several times in a row if necessary. Then your chances of walking home with more money than you came in are pretty good, but the amount you’ve won is pretty small compared to your initial sum. There is, however, a small chance that you lose, but if you lose you lose heavily.

"But I also know that if stipulated from the beginning, the chance of 10 reds in a row is actually pretty low. "

True, but that doesn’t help you. You’re not interested in the number of reds and blacks within the next ten spins, you’re interested in the result of the very next spin, the one you’re betting, and you just can’t predict this.

The problem with the system is your phrase “stipulated from the beginning”. Sure, the odds of getting a streak of 10 reds are 1/1024, but given 9 reds already, the odds of a 10 streak are 1/2, the odds of an 11 streak are 1/4, etc.

You should do some searches on the “Gambler’s Fallacy”, as I’m sure there are people out there who have explained this much better than I could (and on preview it looks like Schnitte and CalMeacham are among them).

Or, you can think of it this way: Casinos are in business to separate you from your money. They spent money to add those screens to all their roulette tables. Who do you think the screens are meant to help?

Already well explained above, but to look at only 5 or 10 changes, tries, rolls, flips, spins, etc, is also a problem. The house is there for the long-haul, 1,000’s and 1,000’s of rolls, flips, spins so for them the odds will even out (forgetting the 0 and 00), but for you, you have a much, much more reduced window of opportunity. Even if you manage to hang in for 10 or 20 or 50 rounds, and the odds are fantastic against something remaining red or black throughout, it can happen, and then you’re SOL.

From spin to spin, the odds are ~50/50, but to step back and predict the next 4 spins, then you need to get your probability mojo working.

Stick with craps.

Covering the bet could be a problem for someone with a slim bankroll but what kills you is the table limit. For a \$2 game, the table limit is typically \$250. Let’s see what happens with the Martingale system on a losing streak:

1st bet: \$2

2nd bet: \$4

3rd bet: \$8

4th bet: \$16

5th bet: \$32

6th bet: \$64

7th bet: \$128

8th bet \$256 – oops, ran into the limit.

Anyone who has been playing table games for a while can tell you on an even-money bet, a losing streak of eight is not exactly rare and you’d either be stuck with a \$255 loss from the previous seven bets, or dropping \$250 on the table for who knows how long and getting back \$250.

Casinos have been thinking about ways of separating you from your money for a long time, and they’re very good at it.

By the way, the expectation[sup][/sup] of the Martingale system is exactly the same as a single bet, so it’s nothing really special. That said, it’s not a bad idea to use it to keep yourself from going in the hole the way you might if you had no system. You just have to play it consistently, and realize that you’re going to be doing slightly worse than the single bet, due to the table limit / finite funds.
[sup]
[/sup]i.e. if you went to the casino regularly and always played the same way, it’d work out that way. Most people don’t do this, so it’s possible to come out ahead in the short term (though as likely to come out behind).

A couple of notes:

First, there’s the “Grand Martingale” system - double and add one for each loss. That goes \$2, \$5, \$11, \$23, \$47, \$95, \$191, \$383, and you hit the limit anyway. (If the limit were higher reletive to the initial bet, you’d reach it even before the minor Martingale would.)

Second, you can think of the run you want as part of a very long string of plays, say a million, that you’re looking at through a 20-play window. The results over that million plays come out very close to even, so the results in your window don’t really predict the next play. The known results from the screen over the table restrict where you can place the window, but it probably fits several places, and the spin following at each spot will be red or black with 50/50 probability.

True - it’s less than 1 in 1000. But if you’ve seen 9 reds in a row, the chance of ten in a row is now 1/2 (or a bit less if we’re not ignoring the 0 and 00).

The point is that the roulette wheel contains no “Maxwell’s demon” who’s there to say “Whoa - 9 reds in a row! Better make the next one black to keep things right.”

But perhaps the demon is there, but he’s reviweing the entire history of the wheel - millions of spins analyzed in a couple of seconds. His conclusion each time is “Hey, it doesn’t matter - red, black, whatever.”