Thursday, August 2, 2012

On Coins

Here's a thought experiment I can't remember where I heard it. Imagine you have a coin. How many (unbroken) flips of it turning up heads would it take for you to consider the coin not a fair coin? I'm sure someone out there can do math or something to find a statistical answer. But, go from your gut.

How many times do you need to lose before you think a game is rigged? It's kind of a tolerance test; they have them for pain. The marshmallow test, for example, is another kind of tolerance test. That tests how much self control the kid has; this is testing how much trust you have. Would your threshold change if the person proctoring the flips was someone you trusted? How much?

I've been thinking about this off and on again for a few months. A few flips in a row of heads could be a natural fair coin. A string, of say, HHHHHH, is theoretically possible, if unlikely. As the string gets longer, it gets less and less probable, but not -- technically -- impossible.

Some people are comfortable pulling the trigger sooner. I doubt, in real life, there is anyone who would say they could never make that choice since the improbable scenario in front of them was technically possible, therefore it must be proven the coin is unfair through a hard proof as opposed to an indirect proof (such as a 1,000 unbroken string of heads).

How certain do you need to be before taking action, such as always betting heads or walking away from a cheating coin?

Now, let's reverse this. How long of a string of losses would you take before you decided the coin was unfair? Assume that you are free to change your bet from heads to tails each flip, yet each time you are wrong. How long would it take you to assume you were being cheated and not just unlucky? More importantly: Would you ever reach that threshold, or would you walk away before you hit that point? Would that threshold change if you were making penny bets as opposed to dollar bets?

The problem with this, though, is I've poisoned the well. You know you will always lose the next bet from the rules of the game. Now, you could try and do man-on-the-street style interviews to test it with people who don't know they are about to be cheated. You can't really take their money though, since, you know, you are going to cheat them. That changes things again; they can only gain, never lose. You offer them up a dime each win, and tell them they can only lose from their winnings, but never go negative. How long would people keep going?

Just some thoughts; thinking about it now might help you know how to deal with future events. Or it might not, it may just be frustrating because you can't come up with a good answer. Even with math. So, keep on trying! Or just watch corgi cam. Your choice.



Don't cheat people at games of chance. Also, direct link to the corgi cam YouTube page.

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