VCG: Yes, that *and* Green 0.

Sinnick: OK, so here's the crackpot probability theory. Actually, I believe you are right and that it is ridiculous for dice to know what was thrown before. I'm actually going to simplify even further and use the coin toss, and we will assume that it is a perfectly balanced coin, tossed perfectly so that it is always a 50/50 chance of heads or tails coming up each time - the actual probability of this is as near to nothing as makes no odds, but why let reality get in the way of mad probability theory?

You toss a shiny, newly minted penny. It comes up heads. It was a 50/50 chance, no doubt. You toss it again, and you're quite right that the coin doesn't know or give a flying crap what happened before. It's an independent event with a whole new 50/50 chance. It comes up tails. Everybody is happy. Apart from the people bored to shit with this and still reading.

You toss the coin ten times. It comes up 6 heads, 4 tails. That's life. Stuff happens. But, I instinctively know three things in the real world: one is that the coin might be slightly biased towards coming up heads, or the tosser could be deliberately or accidentally tossing in a way which favours heads. Fnar. I know, because I taught myself a technique to be able to toss a coin so that the call while it was in the air would always be right (or wrong if you want it that way), providing I used the display-the-result-on-the-back-of-my-hand technique. Can't do it if you let the coin fall to the floor.

Well done, you're paying attention because you've clocked, what there was a third thing instinctively known. Well, the first two things are biases which affect the outcome. But if I judge that neither of these things are actually in play, then I instinctively know to call tails on the 11th toss. I believe there is a very slight chance in favour of it coming up tails rather than heads.

If you toss the same coin 100 times, it might come up 51 heads, 49 tails. If you toss it 1,000 times it might come up 500 heads, 500 tails. What we know for sure through experimentation, though, is that the more times you toss a coin, the balance of heads versus tails **tends** towards 50/50. If that is true, then if you've tossed a coin ten times and it has come up heads 10 times, and we're happy there's no jiggerypokery going on, then there is an inescapable increasing chance of tails being next each time you keep tossing. At least until such time as the number of heads and tails has evened out again. The coin doesn't know that, but the universe does?

So there has been this coin being tossed for a long while. You don't know how long when you rock up. You see it go heads five times in a row. What do you bet it will be next? My theory says don't bet. You don't know. To you, it looks like tails should be slightly favoured. But it isn't necessarily. It could be that since the tossing started long before you arrived, tails is ahead overall, and heads should be the marginally favoured call. You just don't know that. You can only witness the bit you witness and you think the probability is relative to you and your experience. But the universe it still balancing out all probabilities of everything, all of it tending to the expected outcomes over a very long arc of time.

So you turn up to a casino which has been there for twenty years. Has someone recorded all of the outcomes of every spin on every wheel at every table? Probably not. Have a bit of fun. Expect to lose. It's designed that way. Even for the 50/50s like red or black. Ever so slightly, so that some folks just don't notice. Even in a fair casino. If it's a casino which trains its employees in the dark arts, then you lost the moment you walked in. But if you're up and you like having money more than losing it, walk out with a bounce in your step and never go back there or anywhere else. Probability says you'll lose it next time. But, of course, that's not a certainty.

Death. Taxes. You won't be able to train a badger to juggle lampposts in the next 30 seconds.