Pick 6 Ticket Structure -- Crist

[chickenhead]

Until I started playing them more often I didn't really realize how important the consos are. Assuming you are hitting consos fairly regularly, playing isn't really that taxing to a bankroll.

I am still trying to figure out whether I'm in the "always a bridesmaid, never a bride" phase...or whether I'm actually doing really well. I have been in a position to do really well, just haven't hit yet.

TLG -- what is your average size play? In the $4-500 range? I know it will vary, but the preponderance of your plays.

[rrbauer]

The whole problem with having a P6 winning that is loaded with favorites is that when it happens it belies the fact that it's a rare occurrence and it rewards plays that will very seldom be rewarded over the long run. So looking at the results from the example being used and saying "Wow that's nice that all of those people got a nice return for their small investment" is little more than a charitible comment. The situation falls more squarely into the category of bad plays that win.

[the little guy]

Originally Posted by chickenhead

Until I started playing them more often I didn't really realize how important the consos are. Assuming you are hitting consos fairly regularly, playing isn't really that taxing to a bankroll.

I am still trying to figure out whether I'm in the "always a bridesmaid, never a bride" phase...or whether I'm actually doing really well. I have been in a position to do really well, just haven't hit yet.

TLG -- what is your average size play? In the $4-500 range? I know it will vary, but the preponderance of your plays.

I actually don't play that often these days but I would say $400-500 is about right. It's not a lot of coverage but it's within my comfort zone. I have only hit a couple this year ( though I haven't played many ) and both were for plays about $200. One paid $2200 and the other just under 10 grand.

[Light]

Real life experience:

For what it's worth,ToeToe came over to see me unexpectedly yesterday to play the Pk6 at GGF. I wasn't in the mood to handicap and gave him ($4) for 10% of his ticket. He went to the track,I stayed home. All the horses he mentioned won except I know he played a"miss 1,miss 2" type of ticket structure. I think he had 4 singles. It payed 5k for 6 and $63 for 5. I thought,I could get back $500 for my $4 investment. He called me and said he got 5 out of 6 4x. He said it would have cost him another $20,to cover all his horses.

This is why I don't like the "miss 1,miss 2" etc. strategy.Maybe it can work at times,but most of the time,this is the result I see from it.

[the little guy]

Originally Posted by Light

Real life experience:

For what it's worth,ToeToe came over to see me unexpectedly yesterday to play the Pk6 at GGF. I wasn't in the mood to handicap and gave him ($4) for 10% of his ticket. He went to the track,I stayed home. All the horses he mentioned won except I know he played a"miss 1,miss 2" type of ticket structure. I think he had 4 singles. It payed 5k for 6 and $63 for 5. I thought,I could get back $500 for my $4 investment. He called me and said he got 5 out of 6 4x. He said it would have cost him another $20,to cover all his horses.

This is why I don't like the "miss 1,miss 2" etc. strategy.Maybe it can work at times,but most of the time,this is the result I see from it.

So, let me get this straight, you gave him $4 for 10% of his play, so he was playing for $40. It would have cost him $20 more dollars to go from making multiple tickets to one ticket supposedly covering all horses. So, he would have had to increase his play by 50%. That sounds pretty substantial to me.

What if he was playing for $1200?

[Light]

Yeah, for $1200 better cut down the ticket. But most of us mortals dont bet like that.

[the little guy]

You miss the point....obviously $40 was the comfortable play for him. He knew what he could have done for $60 but chose to bet the $40...which is fine.

Your comfort zone was obviously $4, which is fine, as you could have talked things out with him and given him $24 for 40% of the play but didn't.

[Light]

Actually the reason I only gave him $4 was because he had 4 singles. When I play pk6's I like 2 singles max.How many people can hit with 4 singles in one day. He hit them all. He missed the race where he had multiples and the Baze horse at 3/5.

[classhandicapper]

Originally Posted by classhandicapper

I've discussed the mathematics of comparing parlays to multi-race bets. It's a silly and often misleading idea. I can demonstrate why if desired.

I think it's worth reviewing a typical Parlay vs. Multi-Race payoff so we understand what's actually going on and why the parlay invariably pays so much less.

Here's a comparison of a $2 parlay and $2 Pick3 on 3 "even money" shots.

I am using "even money" shots and a Pick 3 to keep it simple, but it could just as easily be a Pic 6 and any odds you want.

I am using 15% and 25% "takes" to approximate the fact that most multi-race bets have a higher take, but it could easily be others.

I am assuming the horses are bet in the win pool so that you would lose the "take" if you played the horses to win. I am also asuming are bet in the same proportion in the mult-race bet. (this is for demonstration purposes)

Here's the Parlay:

1. 3 even money horses parlayed

2. Each horse has approximately a 42.5% chance of winning.

(.425 * $4.00 = 1.70 ROI for a 15% loss)

3. The parlay will pay $16, for a profit of $14 on a $2 parlay if you hit it.

4. You will hit the parlay 7.676% of the time (.425 * .425 * .425)

5. 7.676% * $16 payoff = a 1.228 ROI on your original $2 parlay bet. That's a loss of "38.6%" instead of the 15% take.

*The reason the loss is much higher than the 15% take is that you aren't actually betting $2 in a parlay. You are betting $2, then if you win you are betting $4, then if you win you are betting $8 etc..... All those bets are subject to the 15% take. * However, you did lose 15% on everything you bet.

Now for the Pick 3:

1. Same 3 even money horses bet in a pick 3.

2. Each has a 42.5% chance of winning.

3. The Pick-3 pools are bet in proportion to the win pools

4. Calculate the payoff as if the take on the first race is 25%, but the take on the 2nd and 3rd races is zero. This approximates a Pick 3.

Payoff #1 = $3.53 instead of $4.00.

Payoff #2 and #3 = $4.71 instead of $4.00

$2 bet returns $3.53.
$3.53 bet returns $8.31
$8.31 bet returns $19.57

Conclusion:

1. The pick 3 payoff is much higher than the parlay. $19.57 vs. $16.00

2. The Pick 3 ROI is 1.50 per $2 bet or a 25% loss which is equal to the Pick 3 take. (7.676% * $19.57 = a ROI of 1.50 on a $2 which is 25% loss)

When books say there is great value in multi-race bets because the payoffs are much higher than the parlay, they are often at least partially misunderstanding why. The parlay payoff is the result of getting taxed 3 times on amounts "greater than $2" when you hit. The losses are compounded.

The fact that the Pick3/4/6 invariably pays more than the parlay tells you nothing about what your ROI will be on that kind of multi-race bet.

You still have to bet combinations that are good value or you will lose 25% of everything you bet EVEN WHEN THE PAYOFF IS HIGHER THAN THE PARLAY!!!!

[chickenhead]

Now if we're not all totally worn out from class's example, I have just a little bit more math here that I think proves beyond any reasonable doubt that a heirarchical ticket structure is better than a flat structure.

First premise:

Barry Meadow recently posted here the win percentage of the various public choices:
1) 33%
2) 21%
3) 15%
4) 11%
5) 8%

we will assume that your personal rankings performs to these percentages.

Second Premise:

We'll be looking at the ticket structure:
All A's
All A's with one B
All A's with 2 B's
All A's with 1 C

We can see from the above table that if we're using a heirarchical structure and group our top two ranks as A's, our third and fourth ranks as B's, and our
fifth rank as C our probability of hitting in that category for any given race would be:

A: 54%
B: 26%
C: 8%

That sounds like a pretty nice ticket.

A pick 6 ticket with the above structure would cost $3200 (2 A's, 2B's, and 1 C in every race). The expected win percentage (the sum of the prob of each ticket hitting) is 20.47%

In case anyone wants to check a few, here are the probabilities on each ticket:

AAAAAA 0.024794911
BAAAAA 0.011938291
ABAAAA 0.011938291
AABAAA 0.011938291
AAABAA 0.011938291
AAAABA 0.011938291
AAAAAB 0.011938291
BBAAAA 0.005748066
BABAAA 0.005748066
BAABAA 0.005748066
BAAABA 0.005748066
BAAAAB 0.005748066
ABBAAA 0.005748066
ABABAA 0.005748066
ABAABA 0.005748066
ABAAAB 0.005748066
AABBAA 0.005748066
AABABA 0.005748066
AABAAB 0.005748066
AAABBA 0.005748066
AAABAB 0.005748066
AAAABB 0.005748066
CAAAAA 0.00367332
ACAAAA 0.00367332
AACAAA 0.00367332
AAACAA 0.00367332
AAAACA 0.00367332
AAAAAC 0.00367332

OK, so there is our heirarchical ticket. $3200, 20.47% chance of winning.

Now lets compare it to a flat ticket of roughly the same cost. Well, I want to use the same number of horses per leg for this example, which doesn't work out to a whole number -- but that is fine for our purposes.

We'll use 3.5 horses per leg, which gives you a $3,677 ticket. So we're actually spending a little more on the flat ticket. What is it's probability of hitting?

Let's see, we have .33+.21+.15+ (1/2)(.11) = .745 or 74.5% chance of hitting each leg.

If you didn't follow that, since we're using 3.5 horses, we add the probability of our top 3 picks plus one half the probability of our fourth rank.

So if our probability of each leg is .745, our probability of hitting 6 in a row is .745^6, or 17.10%

To put the two tickets side by side:

Heirarchical: $3200, 20.47%
Flat: $3677, 17.10%

That adds up. Even by spending more money on a flat ticket, you will see a lower hit rate. But that doesn't make sense, or does it? Of course it does, because the heirarchical ticket is playing more combinations with a higher probability -- the distribution is skewed towards them.

If anyone cares to challenge the math go ahead, or even the assumptions underlying the example -- but I think it's pretty rock solid. I really don't think it is reasonable to think you can outperform a smartly structered ticket with a flat ticket -- the mathematics say otherwise.

A flat ticket is simply putting too much money into low % combinations as compared to the structured ticket.

[Indulto]

Originally Posted by chickenhead

... We'll be looking at the ticket structure:
All A's
All A's with one B
All A's with 2 B's
All A's with 1 C

We can see from the above table that if we're using a heirarchical structure and group our top two ranks as A's, our third and fourth ranks as B's, and our
fifth rank as C ...

... A pick 6 ticket with the above structure would cost $3200 (2 A's, 2B's, and 1 C in every race). The expected win percentage (the sum of the prob of each ticket hitting) is 20.47%

...

AAAAAA 0.024794911
BAAAAA 0.011938291
ABAAAA 0.011938291
AABAAA 0.011938291
AAABAA 0.011938291
AAAABA 0.011938291
AAAAAB 0.011938291
BBAAAA 0.005748066
BABAAA 0.005748066
BAABAA 0.005748066
BAAABA 0.005748066
BAAAAB 0.005748066
ABBAAA 0.005748066
ABABAA 0.005748066
ABAABA 0.005748066
ABAAAB 0.005748066
AABBAA 0.005748066
AABABA 0.005748066
AABAAB 0.005748066
AAABBA 0.005748066
AAABAB 0.005748066
AAAABB 0.005748066
CAAAAA 0.00367332
ACAAAA 0.00367332
AACAAA 0.00367332
AAACAA 0.00367332
AAAACA 0.00367332
AAAAAC 0.00367332

C-HD,
I may be up too late, having a Senior Moment, or just have lost too many brain cells, but I would appreciate your detailing how you calculated the $3200 cost for the ticket(s) implementing your proposed play.

Thanx.

[chickenhead]

Originally Posted by Indulto

C-HD,
I may be up too late, having a Senior Moment, or just have lost too many brain cells, but I would appreciate your detailing how you calculated the $3200 cost for the ticket(s) implementing your proposed play.

Thanx.

Sure. Remember we have 2 A's, 2 B's, and 1 C horse in each race. Below are the tickets -- and the number of combinations on each ticket. Since we have the same number of A's and B's in each race, all of our tickets with A's and or B's have 64 combos each (2x2x2x2x2x2), and our set of tickets with the 1 C are 2x2x2x2x2x1.

AAAAAA 64
BAAAAA 64
ABAAAA 64
AABAAA 64
AAABAA 64
AAAABA 64
AAAAAB 64
BBAAAA 64
BABAAA 64
BAABAA 64
BAAABA 64
BAAAAB 64
ABBAAA 64
ABABAA 64
ABAABA 64
ABAAAB 64
AABBAA 64
AABABA 64
AABAAB 64
AAABBA 64
AAABAB 64
AAAABB 64
CAAAAA 32
ACAAAA 32
AACAAA 32
AAACAA 32
AAAACA 32
AAAAAC 32

[classhandicapper]

Chicken,

Thanks, that was good, but now I have a headache too.

The structure I am contemplating is similar, but it's based on value and not win percentage.

I'm going to make it a pick 3 just to keep it very simple. Let's say I have several contenders (C) in each race, but in each race I have only one that is likely good off at good value. Call it "V".

I not am attemping to cover the highest probability of cashing. I am attempting to ensure that every ticket I bet is good value. By insisting that there be at least 2 value horses on each ticket, I am sacrificing win probability, but excluding combinations that probably have a negative ROI expectation and perhaps allowing myself to add in a few other positive ROI tickets for the same money.

V V V

V V C

V C V

C V V

IMHO, (and I have little to no experience with pick 6s), my approach is better for multi-race bets if you are trying to ensure long term profits and not just trying to hit the damn thing.

However, on a carryover day, the number of combinations that have a positive expected ROI explodes higher because of all the extra money. So then, I think your approach would be much superior because value is secondary to actually hitting it.

Does that make some sense?

[chickenhead]

I think it's pretty hard to know what your ROI is going to be on these bets as a whole. And you will never have enough data to prove that you haven't just been lucky (or unlucky).

With that said, I think the problem, at least in pick 6's, of trying to put too fine a point on it and only play select value combos is that your projected win %, the number of these bets that you expect to win going in quickly gets to be microscopic..like much less than 1%. Just on the natural order of things you could go many years between hits. It's clearly a case, at least to me, where I'd be willing to trade ROI for a higher hit rate, but where exactly that happy medium is I don't know.

For things like pick 3's, where the pool is way more efficient and we talking orders of magnitudes less combinations, I think demanding more value is the way to go.

[LemonSoupKid]

Does anyone have insight or new thoughts on playing the pick 6 now that withholding has changed and/or the pick 5 is an improved, value play?

Thanks