I'm looking at yoooou Barney! |
Now, if you do seriously study for the Price is Right, there are two places where your game can loose clout. First is getting George to tell you to come on down. Second is the Big Wheel, because no matter how hard you study, it's a completely random process and there's no way to "guarantee" a win. However, you can maximize your chances of winning.
Assume you don't spin first. Then there is a bid that your spin must beat, and there is little choice on the contestant's part. Thus, we assume that you spin first. Now we need to figure out what number you should try to get above in order to maximize your chances of winning.
Since the wheel has values from 5 to 100, there are 20 spots for the wheel to stop. The goal is to get closest to 100 from one or two spins without going over. If your final total is a 50, then either person spinning after you can beat that score to knock you out (to simplify things, let's ignore ties for now). For each person, they can either spin above a 50 (10/20) OR they can spin below a 50 and then spin a number which will not put them over. I will consider each individual spin in order to correctly get the probabilities: if your first spin is a 5, then you have to get at least a 50, but not 100 (or 1/20*10/20). If your first spin is a 10, you have to get between a 45 and a 90 (or 1/20*10/20). If your first spin is a 45, then you have to spin between a 10 and a 55 (or 1/20*10/20).
This means that if you stay at a 50, then your chances of the first person beating you is (10/20+9*1/20*10/20=29/40), or almost 3/4. The chances of either person beating you (roughly speaking) is 3/4+1/4*3/4, or 15/16. We need a better number if want to get into the Showcase Showdown.
Continued in Paaaaaaart twwwwwwwo....