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Arena of Death
Some time ago I was playtesting a game called Arena of Death which I was writing. This was a boardgame in which each player controls a team of gladiators fighting with guns and swords in an arena full of bits of cover, rather like a paintball arena.

For each character, there is a chip which is put into a cup. Over the course of a round, chips are drawn blindly one at a time from the cup. Each time a chip is drawn, the character represented by that chip does an action. Then another chip is drawn. Another character gets to act. This goes on until the cup is empty. Then all characters have acted. Then the chips are put back into the cup and a new turn begins.

This guarantees that in a turn, all the characters get to act once, in a random order - right? Does it my arse!

During the playtest game which I played with the Baron von Scott, the problem was that we kept drawing our own chips. My two characters were represented by blue and green chips, the Baron's by red and yellow chips. In theory it didn't matter who drew a chip, because it was completely random which chip came out - if all four chips were in the cup, there was no reason why I should pick out my own chip rather than my opponent's. But I did so, repeatedly, and the Baron drew his own. This happened almost every time. It went beyond a joke until we were both completely pissed off by it. It reached a stage where we knew that if I picked the chip it would be one of mine, and if the Baron picked it would be one of his. This meant that the order of play became more predictable, which was damaging to the gameplay (random order of actions is important to make the game work properly).

After the game I worked out that at least 80% - if not 90% - of the time, we were picking our own chips out. And we must have made the best part of a hundred picks. This is clearly beyond the realms of probability. Some supernatural force was at work during this game.