Program to calculate exotic odds?

[Koko]

Does anyone have or know of a program to calculate odds on exotic bets using win odds as the input. To clarify, if I want to know the odds of a superfecta combination by inputting the win odds of each slot, example,
I provide the win odds of the various contenders

1st slot 6/1
2nd slot 4/1
3rd slot 19/1
4th slot 23/1

The program would then spit out the odds of this combination hitting. Has anyone written such a program, know of a freeware program of this sort or a commercially available program? I appreciate your assistance.

[cj]

1/(Odds + 1) = Win %

First, the 6-1 has a 1 in 7 chance of winning, or 14.29%.

Now the second horse, at 4-1, had a 1 in 5 chance of winning, or 20%. But in this case, the first horse has already won, so he has a 20 in 85.71 (100% - 14.29%) chance to beat the rest of the field, or 23.33%.

So far, the chances of having the first two are .1429 * .2333 = 0.0333, or 3.33 percent.

Your third horse is 19-1 or 1 in 20, or 5%. Assuming the two above have run 1-2, you now give this horse has a 5 / 62.38 (100 - 14.29 - 23.33) chance of beating the rest. That is 8.02%, or .0802. Multiply this by the 3.33% (.0333) above to get .0027, or 0.27% of hitting 1-2-3.

Your final horse is 24-1 (I changed it to do it in my head), or 1 in 25, or 4%. You now give this horse 4 / 54.36 (100 - 14.29 - 23.33 - 8.02) chance of beating the rest. That is 7.36%, or .0736. Multiply this by .0027 above, and you get .0002, or 0.02% chance of hitting this super.

So, in the above, fair odds would be as follows, remembering fair odds are 1 / W% - 1

Exacta: 1 / .0333 - 1 = 29 to 1, or a $60 fair payoff
Trifecta: 1 / .0027 - 1 = 369 to 1, or $740 fair payoff
Superfecta: 1 / .0002 - 1 = 4999 to 1, or $10,000 payoff

I hope I didn't screw up the math, but that is the gyst of it. It wouldn't be hard to program. If you built in takeout, the payoffs would be even bigger. I just used your odds as the actual chance of winning.

Disclaimer: If you already knew how to do it, my fingers are pissed at me.

[Big Bill]

Koko,

If you can get your hands on a book written by the late Dick Mitchell called, "Thoroughbred Handicapping as an Investment", you will find a chapter on the subject. I believe it covers what cj was describing in his post. That chapter also included a simple program written in BASIC that enables you to enter toteboard odds and the size of your wager and the output is the fair price an exacta must pay to be a fair bet. I put that program in a handheld computer (PC-3) and used it at Beu a few times. I've never been much of an exotics player, so it wasn't used much!

Big Bill

[Koko]

Thank you Bill, and C.J., your post was not in vain, thank you as well.

[bigal]

I have seen other posts on using the Harville formula to compute Exacta/trifecta payouts and decided to test it. My database has thousands of records from the Texas/Louisiana/Ark tracks, so I decided to test it. It works to a large extent on exactas. Trifiectas offer much more variance and may not be valid for this method. I used 1028 races from 8 tracks run in 2004. All had 10 runners and eliminated any problems with small fields.

Compute:
- final odds probabilites for all horses Example: 2:1=1/3=.333: 6:1=1/6=.1667: 10:1=1/11=.909, etc

- add them all up. That is the total prob. including track takeout (1.17 to 1.24). Reject any races outside the range because something is wrong.

- Divide w/p/s horse probabilities by this number to get rid of track takeout.

- Exacta probability(Harville): win prob X (place prob/(1-win prob)

- I used 1.618 / (exacta probability) to predict the exacta payoff

If underpredicts on high probability exactas, and overpredicts on low probability exactas. At the lowest end of the scale it jumps off the board.
I think this is due to longshot players boxing the bottom 3 or 4 horses.

Any sharp math/stat guys out there that want to take a shot at curve fitting? I can supply the data.

Bigal