Push Lines - Include in probabilities?

[ProlinePlayer]

Do those edges include the probabilities for a push result on one or more games? If not then the edges are much lower than that.

No the edge calculations ignore the push at this point.

There's a post that I think I put in the Theory section which analyzes the effect of pushes on the expected edge. It's not a much as you would think.

That being said, I'm working on and expect to have ready in a few days, an updated version of the ParlayMaker program which does do an exact analysis of the parlay's edge factoring in pushes.

PLP

[sharpasitgets]

That’s not exactly true, this glorious ticket 53V-54V-56V-62V-63V (33% edge), is approximately a 17% loser when one accounts for all the push permutations; which there are 31 of...

[Kaboshed]

Would love to get your thoughts on this PLP. Today I left all but the biggest +1 edge off my plays because I'm really not sure how much of the edge is taken down by the push.

ps how is the NHL tab coming?

[ProlinePlayer]

Would love to get your thoughts on this PLP. Today I left all but the biggest +1 edge off my plays because I'm really not sure how much of the edge is taken down by the push.

ps how is the NHL tab coming?

If sharpasitgets says the problem is that bad then I would fear that it is so. I'm surprised it's that serious but there you go. Should be ready with the update very soon.

PLP

[MattyKGB]

I haven't had much time to look at this but here's something "quick and dirty", someone please check my math:

Suppose you have a 5 game PS parlay with each game having 45% win probability and 25% push probability. This is what a typical medium size edge game might look like.

Win 5: Probability (5!/5!0!0!)x(0.45^5)x(0.25^0)x(0.3^0) = 0.018453 x payout 20
Win 4 push 1: Probability (5!/4!1!0!)x(0.45^4)x(0.25^1)x(0.3^0) = 0.051258 x payout 10
Win 3 push 2: Probability (5!/3!2!0!)x(0.45^3)x(0.25^2)x(0.3^0) = 0.056953 x payout 5
Win 2 push 3: Probability (5!/2!3!0!)x(0.45^2)x(0.25^3)x(0.3^0) = 0.031641 x payout 2
Win 1 push 4: Probability (5!/1!4!0!)x(0.45^1)x(0.25^4)x(0.3^0) = 0.008789 x payout 1.25
Win 0 push 5: Probability (5!/0!5!0!)x(0.45^0)x(0.25^5)x(0.3^0) = 0.000977 x payout 1

Total edge = 24.1644%

Now, suppose you have a 5 game PS parlay with each game having (45% + 0.5 x 25%) = 57.5% win probability and 0% push probability.

Win 5 = Probability (0.575^5) = 0.0628549 x payout 20

Total edge = 25.7098%

And this is the extreme case, with all 5 games on the ticket being push-able.

So unless my math is wrong (very possible, not getting much sleep these days with a 6 week old baby) there really is not a significant impact from the push lines, at least on 5 gamers.

[MattyKGB]

Wait, it gets better...

The variance of the "pushable" 5-gamer is much lower than the variance of the "non-pushable" 5-gamer. Therefore, Kelly betters are able to bet more:

On a 10k bankroll, full Kelly is $251.58 on the "pushable" 5-gamer. EV = 251.58 x 0.241644 = 60.79.
On a 10k bankroll, full Kelly is $135.31 on the "non-pushable" 5-gamer. EV = 135.31 x 0.257098 = 34.79.

So allow me to be contrarian and suggest (IF my math is right, of course) that push lines actually HELP Kelly-betting edge players.

[ProlinePlayer]

Wait, it gets better...

The variance of the "pushable" 5-gamer is much lower than the variance of the "non-pushable" 5-gamer. Therefore, Kelly betters are able to bet more:

On a 10k bankroll, full Kelly is $251.58 on the "pushable" 5-gamer. EV = 251.58 x 0.241644 = 60.79.
On a 10k bankroll, full Kelly is $135.31 on the "non-pushable" 5-gamer. EV = 135.31 x 0.257098 = 34.79.

So allow me to be contrarian and suggest (IF my math is right, of course) that push lines actually HELP Kelly-betting edge players.

Matty I was just wondering if you saw my post on this in the theory section?

I gotta tell you I suspect that there is something not right in the math. (Almost unheard of I know). With 5 games at 25% push probability I believe that the damage has to be higher.

PLP

[BTS]

I haven't had much time to look at this but here's something "quick and dirty", someone please check my math:

Suppose you have a 5 game PS parlay with each game having 45% win probability and 25% push probability. This is what a typical medium size edge game might look like.

Win 5: Probability (5!/5!0!0!)x(0.45^5)x(0.25^0)x(0.3^0) = 0.018453 x payout 20
Win 4 push 1: Probability (5!/4!1!0!)x(0.45^4)x(0.25^1)x(0.3^0) = 0.051258 x payout 10
Win 3 push 2: Probability (5!/3!2!0!)x(0.45^3)x(0.25^2)x(0.3^0) = 0.056953 x payout 5
Win 2 push 3: Probability (5!/2!3!0!)x(0.45^2)x(0.25^3)x(0.3^0) = 0.031641 x payout 2
Win 1 push 4: Probability (5!/1!4!0!)x(0.45^1)x(0.25^4)x(0.3^0) = 0.008789 x payout 1.25
Win 0 push 5: Probability (5!/0!5!0!)x(0.45^0)x(0.25^5)x(0.3^0) = 0.000977 x payout 1

Total edge = 24.1644%

So far so good.

Now, suppose you have a 5 game PS parlay with each game having (45% + 0.5 x 25%) = 57.5% win probability and 0% push probability.

Win 5 = Probability (0.575^5) = 0.0628549 x payout 20

Total edge = 25.7098%

Should the push be evenly distributed here or according to the W/L probability?

Assuming the latter, removing the chance of a push from .45W .3L .25P leaves .6W .4L.

.6^5 = 0.07776 x payout 20 = 1.5552

Total edge 55.52%. Our edge has come down almost 30%.

[MattyKGB]

I think it should be evenly distributed, but I'm too sleep deprived to put together a coherent argument as to why. Anyone else want to give it a shot?

[ProlinePlayer]

I think it should be evenly distributed, but I'm too sleep deprived to put together a coherent argument as to why. Anyone else want to give it a shot?

(45% + 0.5 x 25%) = 57.5%

I calculate this using win/(win+Loss) = .45 / .75 = 60%

PLP