Rags To Riches - What will her odds be?

[SentToStud]

Originally Posted by Dunbar

I like the "auction" approach, STS!

Here's an example that shows you can't do the calc like you did it above. Say we have 3 horses, except I'm going to identify them by the cards J, Q, and K. After shuffling, you will pick them 1 at a time for win and place.

What is the chance a J will “finish” either 1st or 2nd? Common sense says that the J has 2/3 chance of finishing 1st or 2nd in a 3-card "race". Same for Q or K.

What’s the chance that J and Q BOTH finish in the top 2? By your methodology, it would be 2/3 * 2/3 = 44.4%. But it’s easy to show that 44.4% is wrong. There are only 3 possible pairs that can hold the top 2 places: JQ, JK, and QK. Each of those 3 pairs must have the same chance, namely 1/3 chance. So the chance of J AND Q finishing in the top 2 spots is 33.3%, not 44.4%. Similarly, your ".8 x .5 = .4" is an over-estimate of the combined chance of both horses finishing in the top 3. So, given your 80%/50% assumptions for Curlin and Hard Spun, the bet is even better for you than you thought.

--Dunbar

I follow. What if I said I thought it was 80% and 50% after accounting for the fact that they might both run in the $? I think that's the difference. In any event, I enjoyed and appreciate your responses.

There's a few of us from high school who have been doing this reverse auction stuff for years, mostly conducted during Thanksgiving/Christmas and usually related to people surviving through the following year. I have a pretty big exposure on Ted Kennedy this year. One of the other guys has him checking out at 14-1.