From another thread: I got curious, and implemented a quick simulation of this free throw contest idea. Player 1 is an 0.60 free throw shooter, and he competes against 5 other players who are all 0.50 shooters. In a straight 50-shot playoff, Player 1 wins nearly 60% of the matches. If we eliminate the lowest scorer after every ten shots, Player 1 still wins 57% of the time. This is closer than I expected. It's tough to draw any conclusions from the analogy, but it is clear that it is similar to EBJ in some ways and dissimilar in others. The main difference is that free throws are independent events, while blackjack hands are correlated due to the shared dealer hand.
netball I thought the free-throw contest was a good analogy but don't know enough about basketball to feel comfortable commenting on it. Ken, when you said you were suprised how close the simulation was, what did you mean? Did you mean you thought there would be more or less of a difference? How far off the mark was your best guess? Cheers Simon
After reading about your simulation, I wasn't all that surprised about the answer you got. The only times that the format would make a difference is when the good shooter gets eliminated just before he was about to go on a big run. In general, in a free-throw shooting contest, if you are in last place at any point, it's quite hard to catch up. Not true in EBJ, where you can increase your variance when it suits you to come back with a big bet from behind. Perhaps a better model would be a contest where the baskets are worth a variable amount of points, and you are trying to finish #1 or #2. For Example: EBJ: 11111223<ELIM>22222334<ELIM>333333446<ELIM>44558 TBJT: 1111111111/1111111111/2222233458 My guess is that in this simulation, TBJT would be a worse bet for the 60% shooter than the EBJ contest, but I'm too far removed from my programming past to test it.
