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Originally Posted by SentToStud
Here's a question for you (or anyone else) I really don't know the answer to:
In a 19% takeout pick 4 pool (Keeneland Fall) , what would you say the equivalent per race takeout to be?
Does it go like this: (1+x) * (1+x) * (1+x) * (1+x) = 1.19, solve for x. ??
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I’ve been meaning to think about this, so I’ll give it a shot. I believe you have to start with some assumptions. I like to start with simple assumptions.
Let’s say you have a Pick 4, and you like a horse in each race. Each of your horses has 25% of the pool bet on it, and each of these 4 horses actually has a 25% chance to win the race.
You have 2 choices. You can bet $2 on the first horse and if it wins you parlay the amount you collect into a bet on the 2nd race. And so on, with the 3rd and 4th races. OR, you can bet a $2 Pick 4.
Let’s further assume that these 4 horses have been bet “correctly” in the Pick 4 pool. Because each horse has a (1/4) chance to win its race, the odds of winning the Pick 4 are (1/4)^4 = 0.39%. So the 4 horses you like have 0.39% of the Pick 4 pool. With 19% takeout, a $2 payoff would be $414.
So the question is, what kind of win-bet takeout would give you a $414 payoff on a 4-race parlay? The answer is 5.1%. I got that by stepping through the 4 races. With 5.1% takeout, the $2 payoff from the first race is $7.59 (I’m ignoring breakage, for this) Take that $7.59 and bet the 2nd race, and the payoff is $28.80. The payoff on the 3rd race would be 109.29. And on the 4th race, $414. (same as a Pick 4 with 19% takeout)
There’s probably a simple way to express that, but it’s not jumping out at me. It’s not the formula S2S suggested. That formula yields 4.4% for “x”.
I’m pretty sure that it doesn’t matter in my calc that the odds are the same for each race. But it does matter that the odds in the Pick 4 pool are in line with the odds of each race.
There are numerous caveats. It doesn’t really make sense to talk about the “effective takeout”, unless you were going to bet all 4 races anyway. That is, if you would normally pass 1 or more of the races, then you are not getting the same benefit from the Pick 4.
The biggest caveat is that it’s entirely possible I’ve made an error in my math or my procedure above. I'm very open to corrections or a more general solution.
--Dunbar