Monday, September 06, 2010

Another rant on luck (a pointless shout against the void)

It is a subject of some amusement among my friends to chide me on dice beliefs. Many gamers become superstitious about dice, and attempt to convince me that they are unlucky or lucky, and that they have seen strange things.

So, here is an admission. Luck does, of course, exist. Random results are not always ``fair'', in a uniform way. There will be games where most rolls go against you (actually we'd expect that to happen about 50% of the time with two players), and perhaps even a run where this will happen. So yes, one can have bad luck in a particular instance or game. But there is no such thing as someone being intrinsically lucky or unlucky. If someone has had a terrible run of luck, in life and dice, then I would probably call them unlucky, but going forward I wouldn't expect them to be particularly unlucky in the future.

This is the gambler's fallacy, the belief that after a coin has flipped heads 10 times it is now extremely likely that it will flip tails (if anything, from a Bayesian point of view its rather more likely that it will flip heads!).

For those of you who are convinced that you are just unlucky, and can give me countless anecdotes of it, you just aren't. Focusing on dice here, here are the possibilities:

1)You keep using the same dice which are actually biased
2)Your opponents are cheating, either by using biased dice, or tricks
3)You are rolling the dice in such a way that they roll lower
4)You only remember the good times and not the bad
5)You have an inherent universal property called "luck" which inflicts you and causes you to magic dice to bad results.

4, is of course, the most probable situation. If we were to apply occam's razor, we would go with it. Luckily, we're all scientists here, so we can do some experimentation!

1 and 3 can be eliminated together. Get your dice and roll them repeatedly, making sure to record each result, trying to roll as you usually do. Then count up the frequency of the result, and apply something called the chi squared test, where you sum up the squared difference between the number you expect and the number you acheived, and test it against a probability distribution. If you make your sample large enough, and your significance level low enough, you can be pretty certain of seeing whether your dice are biased or not.

If they are not, then 1 and 3 are eliminated. Hoorary! Supposing they are, and we want to fix the problem, we can conduct further experimentation- simply try rolling with some different dice, ideally produced by a different company, and see if your results are different. If they are, its your dice. If not, its your rolling. Both problems have simple solutions. For 1, buy new dice, for 3, buy a dice cup to roll your dice in- that should prevent you from having an unhealthy influence (or, alternatively, use your skills to win at games of dice!)

Number 2 can be tested in much the same way. You will need to meticulously record every single roll your opponent makes, and do so without alerting them that you are doing it. This isn't an easy target, but is vital to ensure that your test is fair and unbiased. If you discover that they are cheating... well the solution isn't easy there, but thats a whole 'nother post.

I've actually cheated a little here. I've yet to eliminate 5. Its a little harder to get rid of. But it can be done. What we need to is make sure that if we are getting bad results, that we eliminate any possible other cause. So we need to roll a range of dice, and we need to roll them using a range of different methods, on a range of different surfaces. We can also start dealing ourselves hands of cards, as we are apparently looking for a universal luck reduction principle here. If all of these lead to a bias, then perhaps the universe is truly against us....

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