Push Lines - Include in probabilities?

[MattyKGB]

I would consider that a 2% edge. However, this hypothetical is not a push example. All possible outcomes are settled.

See, that's my point. The difference between the "push" example and the "$100.01" example is miniscule and irrelevant - a penny on a $100 bet. So why is one a 33% edge and the other a 2% edge?

[sharpasitgets]

I struggled with this concept as well for a while. I think of a push as an ignored trial in an experiment.

Say we flipped a coin 100 times and 25 of those trials fell off of our experimental table and therefore we considered them as “push” flips.
Now our valid sample size is 75 trials not 100. Therefore when we express probabilities of heads or tails, I would express it as percentage of valid trials.
So in your first example, I would argue when this event occurs we are only interested in 3 of the results. In your second example we consider all 100.

[MattyKGB]

Your interpretation confuses a neutral result with a non-result. They are not the same thing. Regardless of how you visualize it (as an ignored trial, etc), you have two situations that are virtually identical but you are assigning a 33% edge to one and a 2% edge to the other...that to me is a sign of a flaw in the logic.

[Dilbert]

Let's change the example a little.

Suppose you pay $100 for a proposition with a 2% chance of returning $200, a 1% chance of returning $0 and a 97% chance of returning $100.01. Now what's your edge?

The edge is 1.0097%.

[MattyKGB]

Let's change the example a little.

Suppose you pay $100 for a proposition with a 2% chance of returning $200, a 1% chance of returning $0 and a 97% chance of returning $100.01. Now what's your edge?

The edge is 1.0097%.

Agreed.

[Dilbert]

Consider a single bet that has 2% chance of an even money win, 1% chance of loss and 97% chance of push.

Would you say the edge on this bet is +1% or +33%? I'd say it's +1%.

I don't think that the method here is a matter of right or wrong but more a case of preference of several legitimate ways of doing this.

But in your example, if I was playing this and would win 2 out of 3 settled bets at even money, I would consider that I had a very large edge. Not a marginal 1% edge.

PLP

All outcomes need to be used in the calculation of edge and all pushes can be ignored in the calculation of the kelly fraction. The edge would be 1%. The kelly fraction would be 1/3.

[MattyKGB]

Consider a single bet that has 2% chance of an even money win, 1% chance of loss and 97% chance of push.

Would you say the edge on this bet is +1% or +33%? I'd say it's +1%.

I don't think that the method here is a matter of right or wrong but more a case of preference of several legitimate ways of doing this.

But in your example, if I was playing this and would win 2 out of 3 settled bets at even money, I would consider that I had a very large edge. Not a marginal 1% edge.

PLP

All outcomes need to be used in the calculation of edge and all pushes can be ignored in the calculation of the kelly fraction. The edge would be 1%. The kelly fraction would be 1/3.

I wasn't sure about your Kelly claim so I ran the numbers myself and obviously, you're absolutely right. It's almost like you've been doing this for a while

[ProlinePlayer]

The point in the end is that it really doesn't matter how the ev is calculated. As Dilbert points out either method will result in the same wager being made.

I do not disagree with either side here. Over the years I have at times done it one way and at other times done it the other. Both work just fine.

PLP

[ProlinePlayer]

I've been doing a lot of work on the ParlayMaker routines this week and my time there has given me some new insights into this issue.

Throw out the push results (the ones that fell off the table ), is that ok? Although, as I said earlier, for most things there is no real difference in the end, I now agree that one does need to factor in all the outcomes, pushes included. Surprise surprise !! Matty and Dilbert are right. Converting the results to win/loss just is not the right approach.

Going back to Matty's 1-2 and 97% push example. If this game is being bet straight up then there is no difference with either approach as Kelly would give the same bet sizes. But the error occurs if we include this game in a parlay. Let's say a 3-teamer in which the other 2 plays are -5% ev. Throwing out the pushes would give us a +ev play. But that is not what is really going on. What actually happens is that 97% of the time this game is not going to cover the -ev of the other 2 plays. If all results are included we quickly see that this is not a playable 3-teamer.

When Sharpasitgets mentioned the huge drop in ev I assumed the cause was the drop in payouts levels. But it really may have been more a case of over stating the edge to start with because of the pushes.

PLP

[MattyKGB]

When Sharpasitgets mentioned the huge drop in ev I assumed the cause was the drop in payouts levels. But it really may have been more a case of over stating the edge to start with because of the pushes.

I haven't reproduced Sharp's calculations but I think this is likely the case.

As long as you continue to list the push probabilities on your site, that's good enough for me because all I'm going to do is take the win prob + 0.5 x the push prob and pretend that that's the win prob. It's not perfect but as you correctly stated earlier there is no single number that would be perfect, and I showed earlier in this thread that that's a pretty good approximation at least in the case of 5-teamers (which make up the majority of my plays and probably most other edge players' plays as well).

Thanks,
-M