hellersorr Wrote:
-------------------------------------------------------
> Okay, I have a question, except I don't really
> know how to ASK the question.
>
> The question has to do with a five-horse parlay in
> which only five horses are played (one in each
> race) vs. a Pic-5 in which WAY more than five
> horses are played. I mean: Nobody but the insane
> plays a five-horse parlay.
>
> What are your mathematical thoughts on this?
> (Assuming you can see where I'm trying to go.)


Try not to let the reference to parlays confuse you.

The only reason parlays are used to estimate Pick 5 payouts (and other horizontal wagers) is because it’s the easiest way to determine each horse’s associated win probabilities, which is ultimately how you calculate the win probability of a multirace bet and its associated payout.

It has nothing to do with the actual betting of a parlay. You’d never want to bet a parlay anyway because you’re getting hit with the takeout five times instead of once in a Pick 5. This means, depending on the track-specific takeout, a Pick 5 is going to pay on the order of twice what the parlay pays, and it’s part of the reason why the Pick 5 and the other horizontals are such great bets (along with the fact that your edge is multiplicative).

[u][b]Why We Use Parlays to Estimate Multirace Exotic Payouts[/b][/u]

Let’s say we want to estimate the payout on a $.50 Pick 5 at Gulfstream (win takeout = 17%, Pick 5 takeout = 15%). And let’s say, for the sake of simplicity, that the winner of each leg paid exactly $8.00.

One way to calculate what a Pick 5 should pay is to first figure out what the associated win probabilities are, then multiply the five win probabilities together, and then adjust for the Pick 5 takeout.

So if the winner of each leg paid $8.00, the odds of each horse were 3-1 and the associated win probabilities were 1/(3+1) = 25%.
Backing out the win takeout, the true win probability of each horse was = 0.25*0.83 = 20.75%.
So the probability of hitting the Pick 5 sequence of those five horses = 0.2075^5 = 0.0385%.
Adjusting for the Pick 5 takeout, the probability = 0.000385/0.85 = 0.045%.
Which equates to odds of (1/0.00045)+1 = 2,210-1.
Hence the estimated $.50 Pick 5 payout = $1,105.

That’s a whole lot of work to calculate a Pick 5 payout. Fortunately there’s a much easier way to do it, which is where the concept of a parlay comes in. Since the $2 win payouts are readily available (unlike the associated win probabilities), we can just multiply the five win payouts together and then adjust for the difference in takeouts.

We first compute the $0.50 raw win parlay: ($8.00^5)/(2^4)/4 = $512
Then we just adjust for the difference in takeout: $512*(1-0.15)/(1-0.17)^5 = $1,105
Same result, but much, much easier to compute.

The underlying assumption of course, is that horses are bet in the same proportion in the multirace bets as they are in the win pools. In theory this is true if the markets are efficient. It turns out to be true in practice as well, at least over the long run, although day-to-day actual results can and will vary from the theoretical estimate.

[u][b]The Power of Multirace Exotic Bets[/b][/u]

As to the question about playing a myriad of combinations in a Pick 5, that's perfectly all right and desirable. Ideally you want to play any and all positive-expectation combinations, as determined by your fair odds line. This is where the other advantage of multirace bets – the fact that your edge is multiplicative – also comes into play.

Unlike win wagers, where each horse you bet needs to be an overlay in order to show a profit, not every horse in a Pick 5 combination need be an overlay. All that matters is that the overall combination is an overlay (ie. has a positive expectation). In fact, you could actually put together a ticket where [i]none[/i] of the horses are overlays in and of themselves in the win pool and still have a positive expectation on the overall Pick 5 combination.

For instance, let’s say you're a decent handicapper, not great, but good enough to cut the track take down to say, -4%. Now suppose you’ve identified five horses in a Pick 5 sequence that you deem to be partial overlays, but none of them are worth a bet on their own because they don’t quite overcome the track take.

For simplicity, let’s say you've identified a horse in each leg whose fair odds you think are 3-2 but that is going off at 7-5.
Your edge on each such horse = (final odds+1)/(fair odds+1)-1 = 2.4/2.5 - 1 = -0.04 = -4%.
Because you’re still looking at a negative expectation, albeit much less than the track take, none of these horses are playable in the win pool. But let's look at this in a Pick 5 at Gulfstream again.

The $0.50 raw win parlay on this series of horses = ($4.80^5)/(2^4)/4 = $39.80.
But because of the difference in takeout rates and the fact that you only get hit with the takeout once, the Pick 5 should pay $39.80*(1-0.15)/(1-0.17)^5 = $85.90.
The $0.50 raw win parlay based on your fair odds = ($5.00^5)/(2^4)/4 = $48.83 (this is your break-even point).
The result is, instead of the -18.5% negative expectation you’re facing in the win pool ($39.80/$48.83-1), you now have a +76% [i]positive[/i] expectation in the Pick 5 pool ($85.90/$48.83-1).

Because your edge is multiplicative, and because you only get hit with the takeout once, you can play many, many combinations in the multirace exotics, many of which contain horses that are even underlays in the win pool, and still make money. You just need to try to make sure you’re only betting combinations that have an overall positive expectation when you string the individual horses together.

This is exactly how the computer guys are crushing the game. You do [i]not[/i] have to be the best handicapper in the world. You don't even have to find horses that are positive expectation bets on their own. What you do have to be able to do is identify horses that at least have enough value to significantly reduce the track take, and then use the advantageous takeout structure of exotic wagers to turn the tables in your favor.

The beauty of the multirace exotics is that you really only need one overlay to generate a pretty high ROI.

For example, consider a Pick 5 where you have one +25% overlay along with four efficiently priced horses (where you expect to lose the track take). You’re overall expectation is 1.25*(.83)^4*(1-0.15)/(1-0.17)^5 = 1.28 = +28% ROI.

You can even throw in an underlay or two (where you expect to lose more than the track take) with a modest overlay or two and generate a significant ROI: 1.25*1.1*.90*.85*.70*(1-0.15)/(1-0.17)^5 = 1.589 = +59% ROI.

If you happen to get a bunch of mild overlays of say +5% to come in, you would generate an ROI of 1.05^5*(1-0.15)/(1-0.17)^5 = 2.926 = +192.6% ROI, or almost three times your investment.

And if you were lucky enough to string together a bunch of +25% overlays in the same sequence, your ROI would be a whopping 1.25^5*(1-0.15)/(1-0.17)^5 = 6.585 = +585.5% ROI.

You're unlikely to get all your biggest overlays home in the same sequence of course, but this shows the power of the multiplicative effect of your edge and of the advantageous takeout structure of multirace exotics when combined with just some modest handicapping skill. Those large ROIs will of course be diluted by all your other losing Pick 5 combinations, but as long as you're playing only positive expectation bets, your long run ROI should trend towards your average expectation.

With such large ROIs, you can play a lot of combinations and still show a healthy profit. In fact, it’s preferable to play more rather than less combinations since it will increase your win rate, an important consideration when dealing with low-probability wagers that put your bankroll on a rollercoaster ride. You just need to make sure you’re emphasizing your overlays and/or partial overlays and minimizing your underlays so that the combinations you’re playing all have a positive expectation (ROI).