The poker room at the Lodge was the last place I expected to have a mathematical discussion, although in retrospect it makes sense as at least some players play on probabilities versus bingo.
The question was if a person has 400 entries in a 10,000 entry raffle with 10 prizes being drawn what are his chances of drawing at least 1 prize. My contention was that it was 40%, the dealer I was discussing this with claimed it was much lower. The correct answer did not strike me until I was about half way down the hill on my way home. The calculation should be based on the probability of not drawing any of the prizes and this is a fairly straightforward calculation (with a scientific calculator) of 0.96^10 or 96% to the 10th power which turns out to be 33.52%. The exact calculation which includes the effect of reducing the number of entries in the raffle with each draw improves his chances to 33.53%.
I realized that my original logic of 4% multiplied by 10 had to be wrong when another dealer stated that having 1000 entries did not guarantee a prize, yet I could not connect the dots until I realized the hypothesis that needed to be tested. While 33.5% is close to 40% and not much lower, it did confirm the gambler’s fallacy of a sure thing.
The rest of the night was entertaining with a full room thanks to the drawing and a water pipe breaking at Colorado Central Station. I held my own in the 2-5 game and then got snapped off one too many times in the 5-5 game for a net loss on the night. It had been a while since I had played cards and it was nice to get out. At least I was able to redeem my vouchers for $5 and a “free” hat.
On the upside that may have been my last smoking visit as the casino exemption expires December 31, 2007 and the New Year will usher in all non-smoking casinos.