straight win vs pick3+

[reno cool]

Lets say we have a track with a 20% takeout on all types of wagers.

Now this of course means that the average player will get back 80% of all money bet. Lets assume there's a handicapper who bets a win ticket every race. He is better than average and his expected return is 90%. Still a loser but much better than average.

What happens if this handicapper bets his picks only when he's able to play a pick 3 or more with them?

a. he becomes a winner since he only pays the vig once and his advantage over the public becomes cumulative.

b. still at -10% expected

c. something else is involved

[Ganchrow]

Correct me if I'm wrong (and I don't claim any real knowledge of the mechanics of horse racing) but isn't a pick-3 just a parlay?

If so, then like a parlay, a pick-3 of multiple -EV bets will only serve to further decrease your expectation.

[reno cool]

A typical sports parlay with money lines lets say, has 3 games each with vig built in multiplied. So there would be no difference in expectancy, as I understand.
In the case of a pick-3, It is a one time bet that gets taxed only once.

avg bettor: .125^3 =.00195----chance of winning 1 race to the 3rd power.

assume payoff of 409 to 1 will give 80% payback.

handicapper hits .1406^3=.00278 at same payoff 409 to 1 =113.7% payback.

the 14.06% to 12.5% is the 9-8 ratio of a simple win % difference between the 90% ret player and the 80% ret player.

Does this seem a fair way of looking at it?

[Ganchrow]

A typical sports parlay with money lines lets say, has 3 games each with vig built in multiplied. So there would be no difference in expectancy, as I understand.

This is incorrect.

Just think about in the case of N bets all at decimal odds d and win probability p, such that on each bet EV < 0.

Because EV(single) = p * d - 1, EV(single) < 0 implies p * d < 1.

True parlay odds on the N-bet parlay would be d^N with win probability p^N.

Hence EV(N-bet parlay) = (p*d)^N - 1.

Because by assumption p * d < 1, we then have (p*d)^N < p*d implying EV(N-bet parlay) < EV(single).

avg bettor: .125^3 =.00195----chance of winning 1 race to the 3rd power.

assume payoff of 409 to 1 will give 80% payback.
handicapper hits .1406^3=.00278 at same payoff 409 to 1 =113.7% payback.

the 14.06% to 12.5% is the 9-8 ratio of a simple win % difference between the 90% ret player and the 80% ret player.

Does this seem a fair way of looking at it?

Anyway, unless I'm misunderstanding the workings of a pick-3, the same logic as above would apply, but just to spell it out:

If an average bettor (meaning EV = -20%) wagers on a race with a win probability of 12.5% (we're ignoring varied payouts for win/place/show) then this would imply he's getting odds of 5.4/1 (80%/12.5% - 1 = 5.4).

Parlay 3 of these bets (again simplifying by ignoring win/place/show) and he'll see a payout of about 261.1/1 with a win probability of 0.195%, for an EV of -0.488.

Note that that oayout odds on the parlay are not 409 to 1 -- this would imply a house edge of "only" 410^1/3 * 0.125 ≈ -7.14% per single which violates your initial assumption of a uniform 20% house take.

The "talented" handicapper facing a track takeout of only 10% will see his bets at odds of 5.4/1 with win probability 90%/(1+5.4) ≈ 14.06%.

Parlay three of these bets and he'll win with probability of about 14.06%^3 ≈ 0.278%.

At payout odds of 261.1 this corresponds to an EV of about 262.1 * 0.278% - 1 ≈ -27.1%.

IMPORTANT EDIT: A quick Google just told me that apparently pick3's generally have their own associated betting pools. This renders the above analysis useless (in re: pick3s, at least -- parlay analysis remains accurate) insofar as pick3s may not simply be treated as parlays.

I told you I didn't know anything about the mechanics of horse betting.

[reno cool]

In a race there's lets say 8 horses or dogs. If everyone was to bet blindly the avg chance of hitting is 1 in 512. with 20% hold that corresponds to a payoff of 410. A pick 3 is a parimutial pool where the takeout of 20% is taken from the whole pool, not each leg individually.

I believe what you're showing is someone who would take his winnings and bet them all in the next race, and so on. (exposing his bets to more takeout)

[Ganchrow]

Yes. You might have missed my above edits. I had been erroneously conflating a pick3 with a parlay.

My mistake.

If the pick-3 betting pool accurately reflected the same zero-vig probabilities as the single race betting pools (and I have absolutely no idea whatsoever if this assumption actually holds in practice) then your breakeven rate would indeed be lower.

Thinking of it in terms of parlays:

The breakeven on a single bet at -110 (that's vig of 4.55%) is 52.381%.

If a 2-team parlay only charged you total vig of 4.55% as well (implying payout odds of about +281.8) then your breakeven rate would drop to 51.177%.

If a 3-team parlay only charged you vig of 4.55% as well (implying payout odds of about +663.6) then your breakeven rate would drop to 50.781%.

If an N-team parlay only charged you vig of 4.55% as well (implying decimal payout odds of about (1-4.55%)*2^N) then your breakeven rate would drop to 50%/(1-4.55%)^(1/N).

So as N approached infinity, the (1/N) exponent would approach 0, the (1-4.55%)^(1/N) term would approach 1, and breakeven would approach 50%. (Kelly be damned.)

[reno cool]

So I think we kind of agree on this.

Although I make some oversimplifications as you say, it appears that if you're a pretty good handicapper, and you insist on betting to win and avoiding exotics (such as p3 and maybe even tri or super) you're making things harder on yourself.

Of course most serious players don't have a selection in every race. Plus you have to worry about your own bet affecting the pool and so forth.

Man, I wish I would of thought about this more 15 years ago.