So I just came from a “casino night.” The idea of this is it’s sponsored by some organization, you walk in the door, you get 500 points, in the form of casino chips. From this point forward I’ll just pretend they’re dollars.
The history for the past four years of winners is on a website, so you know, based on that data, how much you have to get to to have the max take of the night. For the sake of argument, with pretty good statistical confidence, all one has to do to secure the maximum take is to accumulate about $3000. At the end of the night, the person with the most money wins a prize.
So, to break the system, all it takes is six people to combine their $500, cash out, and they all now have an agreed one in six chance of winning the grand prize. We’ll say for the sake of argument that this prize is of enough value that such scheming would be worthwhile.
Now, the smart thing is that part of the mechanics of the system are that the remaining prizes are distributed by volume-weighted randomness (eg if there are total winnings of $10000 across all players, one has a 3/10 chance of winning a prize). The nice thing about this system is that even if everybody pools their money, they don’t actually do anything to optimize their chance of winning; it is exactly identical to if they just turned in their chips individually. I actually didn’t realize this simple truth until later.
So, four of us played the tables, made about $1500 through some good luck and social engineering, and then threw everything in my cup and I turned in well over $3000. Thus, we won the grand prize. Because the fun was gaming the system, we yielded the grand prize to the second best. Rumors suggest that this person “cheated” as well, but that’s fine. In retrospect, I wish instead we would have elected to give it to the person with the least tickets, randomized if there was a tie, just to stir things up, and point out how the approach is flawed.
Now, it wasn’t as bad as high school, where we had a similar arrangement at the prom and received vouchers for our chips, written in pen, with no sort of checksum or central records — you could just write whatever amount you wanted. And, the volume-weighted random distribution system does a good job of making it hard to game the secondary prizes (Well, mostly. Dealers cheat, go easy on the rules, and despite efforts to statistically detect this, it’s rampant).
So, how do you fix gaming of the grand prize? I think the only way is to also distribute it through volume weighting. But, Sarah pointed out a clever solution to abate some of the trouble — initial chip allocations should be with marked chips. This doesn’t solve the fact that it’s relatively easy to “launder” chips by conservatively playing some blackjack … probability speaking there will be a little money loss, but it would be relatively easy to end up with unmarked chips.
Of course, then you can still convince a group of people, sufficiently large, to each place $100 on a spot on the roulette wheel, and one guy gets roughly $3000 out of it — the threshold to win the grand prize. Now there’s perfectly laundered chips, distributed risk, and a 1 in (small number) of people chance of getting the grand prize.
At the end of the day, this isn’t the point; it’s supposed to be fun, and people are just supposed to play by the rules, but people don’t. Call it what you will, I’ll call it human nature. Our little experiment proved that it could be done, and we declined the reward, because that would have been uncool. Is there any other clever way to “fix” the grand prize system without falling back on the volume weighted distribution model for it as well?