Monday 20 April 2009

What Are the Chances?

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Given that I've been practically living at work this past week, you can probably guess what's on my mind. Seeing as it's bad customer service to tell people that their "systems" are complete crap, and I'd probably get fired for it, I guess I'll have to complain here instead. I've picked up on a couple of "systems" that people seem to have for beating roulette, and the most common ones seem to involve red/black or the two out of three dozens bet.

The first one is the idea that if you see someone spin a long line of numbers that are one colour (say black), then a red is sure to come up next (see: Gambler's fallacy)! That happened last night, when I had a streak of seven black numbers on my board. So I had a guy start to bet on red. Unfortunately for him, I spun a few more black numbers and then a zero, and then two more black numbers, and by that time, he had run out of money. It's true that the chance of getting a hundred billion numbers of one colour is low (1/2^hundred billion), but on any one spin, the chance of getting either colour is the same (48.6%, or 47.3% on a double-zero wheel). Work-Paul says that if anything, you should bet the streak, rather than trying to bet the opposite colour, although I'm of the opinion that both are bad lines of thinking.

Although, there are the people who have the idea that they can bet red/black, and if they lose, they just bet again and double their last bet, and keep doing that until they win, so eventually they will win, winning back their loses, as well as their original bet. Eg. You bet $5 on red, but lose. So you bet $10 on red, and win, getting you $10, leaving you with a total of $20, minus the $15 (5 + 10) that you bet, you made a profit of $5. It does work in theory, but if you think about it, you have two things working against you. First is the table maximum. You can only bet up to a certain amount, and while even on the cheapest table the max is $1000 for red/black, you might be really unlucky. The second thing is, the bets get out of control really quickly. The second thing is, the bets get out of control really quickly. I should really have just linked the wiki article (Martingale Betting System), thanks Julian and YC for reminding me what his name was.


No. Losses in a Row Current Bet Cumulative Amount
155
21015
32035
44075
580155
6160315
7320635
86401275
912802555
1025605115

So if you'd be risking over $300 if you were unlucky and happened to get 5 losses in a row (which I have seen - I managed to spin three zeroes in a row once - and zero in roulette is neither odd, even, red, nor black), and even after only 8 losses in a row, you've already hit the table maximum if you're going to try and win your money back. All to make a measly $5, which if you really had $5115 to risk, you'd have to be asking yourself why you're going to so much trouble for $5.

The second bad line of thinking is the two dozens/columns idea. If you bet red/black, odd/even/1-18/19-36, your chances are just under 50% of winning, but some people have the idea that if you bet two out of the three dozens/columns, your chances of winning are better than that (which is true), and so it's kinda like you're beating the system! For the non-roulette players, you can bet on three different dozens, 1-12/13-24/25-36, or on three columns (imagine the board divided into three columns) and if any of those numbers comes up, you win back twice what you bet (and you keep your bet).

So say you bet $5 on both the first and second dozens, if any numbers between 1 and 24 come up, you win $10 (double your bet), but you lose $5 (since at least one of your bets will have lost), leaving you with a total of $15 (10 + 5, the bet that won) minus the $5 you lost, meaning you won $5. However, if any numbers between 25 and 36 comes up, or a zero, then you lose $10.

Your chances of winning $5 are 24/37 (on a single zero wheel) = 0.65
Your chances of losing $10 are 13/37 (on a single zero wheel) = 0.35

Your expected return = (0.65 x $5) + (0.35 x -$10) = -$0.25

Chances are you will lose your money, so why do people keep insisting that this is a sure way to win?! T_T I guess if you're only playing for a few spins, then this is one of the better odds you can get on the table, but it's not a good idea long term.

To be honest, after a month of working there, I've only seen one winning system:

...you've got to ask yourself one question: Do [you] feel lucky? Well, do ya, punk?


2 comments:

YC said...

I guess casinos are predicated on people being idiots. The martingale just doesn't work, especially in a game like roulette where for each bet the expected value is negative. Multiple bets will only increase the negative expected outcome. But I guess some people just like the thrill. Personally I can understand people who go to a casino to lose money (a fun pastime) or who play games against other people and not against the house (poker), but I don't understand how people who bet seriously on roulette prevent themselves from dying of sheer stupidity.

Luke said...

If you're going to put all that thought into it and get all analytical about it, you probably wouldn't bet, at least not where it's you against the house, at all.