Anyone good at probability?

[andicap]

I flunked probability in high school so could use some help.

What are the probabilities that the top two favorites will finish either 1st or 2nd -- assuming one of the spots is already taken. In other hands, I would estimate one of the first two favorites generally has about an 80% chance of finishing at least second. (Estimate, true??).
But if one of the slots is second does that cut that to 40%?

thanks

[tanda]

With 8 horse field and 33% favorite win rate and 20% 2nd favorite win rate:

Favorite first, 2nd favorite out of top two: 23%
Favorite first, 2nd favorite second: 10%
2nd favorite first, favorite out of top two: 12%
2nd favorite first, favorite second: 8%
Other first, favorite second: 17%
Other first, 2nd favorite second: 10%.

In total: 80% chance that one or both will finish in top two.

Disclaimer: this assumes that horses run second in the same proportion that they run first (FALSE) and that the high-odds/low-odds phenomonom of 1-2 finishers does not occur (PROBABLY FALSE) and also includes some calculation methods that are slightly inaccurate (I know how to make the calcualtions more accurate, but do not have the time, plus since the other errors will still exist, it is not worth it).

A database search will give you the empirical answer. This is a rough abstract mathematical answer.

[andicap]

Thanks,
basically I'm trying to caculate whether I can take the lazy road and use the top two favorites with my longshot "keys" for exactas. (unless it's relatively easy to toss one of them ... a weak "E" in a race loaded with pace for example)

[NoDayJob]

Occasionally I play exactas using a back wheel to the 4 lowest odds on the ironman if my top rated horse is outside of them. The chances of 1 of the 4 lowest odds winning or placing is about 90%. -NDJ

[Rick Ransom]

andicap,

First of all, I think your number is low. Here's an estimate I got from a 2317 race survey done by Robert Rowe:

Favorite 1st: 33.6%
Favorite 2nd: 20.7%
2nd Favorite 1st: 21.0%
2nd Favorite 2nd: 18.1%

That adds up to 93.4%! Yeah, it surprised me too.

I'm not sure exactly what you want but this might help. If you assume that first or second is already taken, the probability of a horse taking the other spot is the same as the horse winning a race against all of the other horses excluding the one you specified.

You said you were assuming that one of them had finished second. That would happen 20.7 + 18.1 = 38.8% of the time. I'd calculate the probability of Favorite 2nd and 2nd choice 1st as:

.207 * .210 / (1.0 - .336) = .0655

I'd calculate the probability of 2nd choice 2nd and Favorite 1st as:

.181 * .336 / (1.0 - .210) = .0770

Now, add these and divide by the probability of your assumption of one of them finishing 2nd:

(.0655 + .0770) / .388 = .367

So, my estimate for this scenario is 36.7%. It would be different if you assumed one of them finished first.

Calculating probabilities can be difficult and I've seen cases of experts disagreeing on how a problem should be solved. So others should verify my logic and either agree or tell me why it might be wrong.

All that being said, this all assumes that the events are independent of one another, which is not always true. For example, an early speed horse finishing 2nd may compromise the chances of late runners finishing first. It's probably pretty good as a rough estimate though. I would check it out on some real data though before I put any faith in it.

By the way, what are you going to use this for?

[andicap]

That's why I failed probability...I didn't understand any of your math :)

I'm doing OK picking higher priced horses many of whom finish second. Want to know how often I'll win the exacta if I play

key/chalk, 2nd chalkl
chalk, 2nd chalk/key

of course it depends on how often my horse comes in and I wouldn't do it unless my keys were at least 6-1, preferably higher.

[Rick Ransom]

Oops, correction. Forgot to subtract the duplicates out from the 93.4%. Favorite 1st and 2nd Favorite 2nd occurs .336 * .181 = .06 of the time and 2nd Favorite 1st and Favorite 2nd occurs .210 * .207 = .04 of the time. So that leaves us with about 83% which sounds right. I think the rest of the analysis is correct though.

[Rick Ransom]

andicap,

I see what you're trying to do, but I don't think theoretical probability estimates will help you much. For one thing, longshots finish second more than expected according to their odds. Also, the public bets differently in exactas than in the win pool. Middle odds range horses seem to be the best. Favorites and extreme longshots are overbet. Wheels like NDJ mentioned work pretty well because you're betting more relative to the odds on the 4th choice than you are on the favorite. I think I'd go with 2nd thru 5th choice and throw out the favorite but, of course your win % would go down.

I sympathize with you. The two most annoying things for me is to have my top selection run 2nd and my 2nd selection win. If your top two are good, you might try 1st choice to place and 2nd choice to win as backups for the 1st choice win bet. That would give you more stability without losing much if anything from your overall $ won.

Unfortunately, different selection methods don't always produce the same results though, so you can't really generalize. I've played some selection methods where it was less likely for my 2nd horse to finish 2nd if the top horse won. That's not the case with what I'm currently doing, but it is possible.

[Rick Ransom]

andicap,

Another thing I've thought about doing is a quinella wheel. Similar to front and back wheeling in an exacta but easier to bet. You would win as often as with a place bet but it should give better returns. Has anyone checked this out?

[ceejay]

http://www.turfpedia.com/playing_the_races/quinella_betting.html

Why tracks offer both Exactas and Q's on the same race is beyond me but since some do...

Quinn says that big longshots in Q's with favs are underplayed. I sometimes use his EX/Q double.

I often use his second strategy especailly at tracks with thin pools (BRD comes to mind). No stats to back it up but it seems to work pretty well.

[Rick Ransom]

ceejay,

Interesting. Maybe the Dr. Z fans should be looking in the exotic pools.