Calculating exacta fair values
 

According to Dick Mitchell's books, using your own fair value odds line, the way to calculate fair value for an exacta is as follows:

Amount of the exacta x odds on first horse x odds on 2nd horse +1

Since Youbet displays exacta probables based on $1 exactas, the amount of the exacta can be eliminated for an ultra simple calculation of odds on first horse x odds on second horse +1.

Therefore, for a $1 exacta, a 5-1 horse on top of a 6-1 horse in the exacta would be:

5(6+1) which is 5x7 = a fair value payoff for a $1 exacta of $35.

However, in RECREATIONAL HANDICAPPING, James Quinn's exacta chart, which lists exacta combinations at 15-20% overlays, lists this same $1 exacta as being $77 at a 15-20% overlay.

$35 fair value for that $1 exacta according to Mitchell and $77 value at 15-20% overlay according to Quinn's chart is a massive discrepancy.

Any ideas on what the cause of this seemingly huge discrepancy might be? Is Mitchell's formula correct or am I missing something here?

barry meadows chart which i got from the best of thouroughbred handicapping has that same exacta at $104 for $2 bet this is meadows chart i believe and is an acceptable overlaid price.this is the chart i use for all my exacta plays...mitchell does have some good ideas though... i like the mitchell matrix... and the fact he advocates not betting lots of combos and insists on enouhg of an overlay to cover losing exacta combos

Meadow's chart sounds right based on Mitchell's $35 fair value for a $1 exacta, so it sounds like they are in agreement.

Mitchell's $1 fair value for exacta: $35
Meadow's fair overlay prices for same $1 exacta: $52

That's exactly a 50% overlay, so I'm guessing Meadow's fair value was also $35 and he recommends a minimum 50% overlay, which is what I play as well: only combinations that are 50% or more overlayed. At Quinn's 15-20%, and I believe Mitchell's recommendation is 20% or 25%, both would require one SERIOUSLY accurate oddsline with very little room for error.... I GREATLY prefer the 50% mark.

In one of Mitchell's earlier books, his formulas also involved taking into consideration the track take when computing fair exacta values; perhaps that's why Quinn's values are so much higher. Since the exacta probables are actual payouts there is obviously no need to adjust for track take. Was there in the past? That's one I never understood when reading Mitchell's earlier book, since exacta probables as long as I've been playing have been actual payouts AFTER the track take has been removed from the equation.

the main thing is that the formulas you mentioned suck at determining exacta fair value. They are just fun shortcuts. Field size and pool distribution run amok with general shortcuts.

If you want an accurate formula, instead of being lazy and using the win odds of the two horses, you have to estimate what hit percentage that exacta has of occurring.

Once you have done the work, there are two things you can do.
You can divide 1 by the estimated hit percentage to find a fair payout for $1 exacta. EXAMPLE = 1/ 3%estimated hit percentage = $33.34

The other thing you can do is multiply the estimated hit percentage by a low estimate of the $1 exacta probable. This will tell you how much of an overlay you have. Example = 3%estimated hit percentage x $32 = 0.96 or a 4% underlay.

Mitchell and Track Take out on Exactas
 

I think what you are referring to here is Mitchell's ALTERNATE method of determining exacta fair pay. Instead of using your own fair odds line, he commented that the public was a good handicapper, and to compute fair value based on tote board odds the formula would be amount bet x odds on top horse x odds + 1 on bottom horse divided by track payout squared. the reason for this is the tote board odds total much more than the 100% to account for track takeout.\duck

meadows chart is so much easier and guarantees that you get an overlay ...even if late monies come in on your combo 50% is a nice cushion....i read both of mitchells books "common senses handicapping"was excellent ..."common sense betting" i found the math portion of it to be very boring and hard toget thru but his advice on structuring the exotic bets and betting to win was excellent.....

I believe Youbet's tote displays payouts on $2.00 exactas, at least they do for Socal tracks.

I agree fmwolf
 

Meadow's charts are great. Mitchell's exacta formula is very simple and conforms to Meadow's method EXACTLY.

Yes, Mitchell's math is tough in spots, but math is an important part of this game in my opinion.
duck

I really don't know what you are complaining about here, Robert. The Mitchell formulas and the Meadow approach yield exactly the same results and those results ARE IN FACT the mathematical fair odds of a combo hitting, assuming the odds used are correct. AND THEY YIELD EXACTLY THE SAME RESULTS AS YOUR APPROACH.

Yes, exactas can be affected by the pace of the race and all sorts of other things, but those considerations are to be taken into account when making a final betting line with odds for each contender.

So I don't understand why you say the formulas suck. They are correct formulas, BASED ON THE ASSIGNED ODDS OF EACH HORSE WINNING. Those assigned odds should consider the other things that concern you, pace, whether the horse is a hanger or has seconditis, etc., etc.

so it looks to me like it is apples to apples, and there is no reason to say these formulas suck, because they don't. How any particular handicapper assigns odds, however, MAY INDEED SUCK.

But correct math does NOT suck.

Just my opinion.

duck

Having no dog whatsoever in this fight, as they say, I can confirm that YouBet posts $2 exacta prices, not $1.

having the chart or a hand held computer just makes it so much easier at crunch time to make a wagering decision.....to stop and hand calculate or recalculate exacta odds is a pain...i just look at the chart and the track matrix and see if i have a bet....easy

Exacta Fair Pay
 

I do the same thing, fmolf. But it is nice to know the reasoniong behind what I am doing. And I don't understand Robert's problem with the formula. Indeed, he seems to not want you to use a chart either.
duck

I think you both are right. The formulas are right if the odds are right. That's the key. If you believe the public, then the odds of the winning horse are right by definition, but the question is whether the odds to win of the underneath horse can be translated using an easy formula (Harville I believe) to get the probability of placing. Most would say that this isn't correct. The odds of coming in second are not the same as the odds of winning given that a certain horse has won the race. Pace, style, etc make this a questionable proposition.

Also, if you are going to use the formula, don't forget to adjust for track takeout. You are taking it out twice from the two win horses, so you need to adjust that and then takeout the (usually higher) takeout of the exacta.

Exacta Fair value and track takeout
 

If you are using your own betting line, that line should add up to 100% and represents what you think is fair pay AFTER the track takeout. That is the formula we have been discussing, with the same result reached with several different mathematical approaches.

BUT, if you are using the tote board odds to represent your opinion of each horse's chances, those odds total far more than 100% to take into account track takeout. And the formula takes into account the effect of track takeout by becoming this: amount bet x odds on Horse A x odds +1 on Horse B DIVIDED BY the track PAYOUT squared after takeout. So, if a track pays out 76% on exacta and takes out 24%, then the track payout squared would be .76 x .76 or .5776 being the divisor.

That formula, witho that divisor accounts for the track takeout. You now have what is fair pay for the quoted TOTE BOARD odds on this exacta combination, and are free to add any premium or cushion you are comfortable with to make it an overlay. If no overlay, no bet.

duck

Absolutely true, so the win odds are not a terrific barometer...the exacta pools always reflect horses that are chronic losers who finish 2nd a lot...conversely there are, for example, layed out class horses that if ready have a solid win chance but are bet at a lesser ratio in the 2nd position considering they may not be ready.