Regarding yesterday's question:
Most people choose option 2. It seems more plausible because it has two greens, and we know the dice is more likely to turn up green. However, if you look carefully, you can see that sequence 1 is actually contained within sequence 2. Sequence 2 is just sequence 1 with an extra G added at the beginning. This means that is 2 wins, 1 must win also. Sequence 1 is strictly better than sequence 2, and you should bet on it.
The general lesson to learn is that each bit of information in a prediction makes the prediction less likely, no matter how plausible it seems. The combination of A and B is always less likely to happen than A alone, no matter how much the combination might 'make more sense' than A alone.
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