Math Help Needed: Calculating "Fair Value" of a bet

[elgreco]

Hello everyone. I was hoping one of you mathematically inclined people would be kind enough point me in the right direction.

I run a weekly NFL Pick’em office pool I got the idea that I could use it to place some good value bets by “buying out” some of the finalists on Monday before the MNF game. More often than not, the winner of the pool is determined by the result of the MNF game. If I could determine what the “Fair value” is for the “Pick’em ticket” each person holds, then I could offer to buy it at a discount.

If two people are tied going into MNF, and each person has a selected a different MNF winner, then determining the value of each position is easy since I can just use the ML numbers that are already established. My plan is to use the ML odds of the big books as a “fair value” price point, and make my offer at a heavy discount to those numbers.

My question is how to properly value a ticket that depends on a Total. If two people go into Monday night tied, and they have picked the same team to win, then the tie will be broken by who guessed the closest total score of the MNF game. Here is an example of my problem:

Pot Value: $400
Ticket A has picked a Total Score of 40.
Ticket B Has Picked a Total Score of 50.
Pinny has the Total at 43

How do I calculate the “Fair Market Price” for tickets A and B? I have played around with determining the % difference between Pinny’s 43 and the actual 45 and running the numbers that way, but since I’m not a math guy, I don’t feel like I am doing it right.

Also, if it does't enormously complicate things, how would I calculate it if a 3rd person were involved? For example: Ticket C has picked a total of 51.

Any help would be appreciated. Thanks!

[LT Profits]

What happens if there's a tie, i.e., number lands on 45 and both guys are off by 5? That aside, you can use the drop-down menu and/or the alternate totals at Pinny and 5 Dimes to find pricing on a lot of the desired numbers.

[elgreco]

If it splits in the middle, then the pot gets split down the middle. For the time being, your 5dimes idea is going to work. Thanks for the tip.

[matekus]

Mark-To-Market Alternative

elgreco,

An alternative approach would be to use a "Mark-To-Market" (m2m) approach [Yao (2007) pp 64-68].
Use m2m = (Stake * (OriginalPrice - CurrentPrice)) / CurrentPrice to calculate the current value (pre-MNF) of each remaining ticket in the pool.

For example, assuming 40 entrants paying $10 for total pool of $400 and two remaining competitors on Monday night, m2m = (10 * (41.00 - 2.00)) / 2.00 = $195 and as long as you offer less than that amount you are in the money!

matekus

[elgreco]

Hey Matekus,

First off, thank you for taking the time to reply. While I appreciate the advice, I really don't think that is the correct approach for this exercise. That seems like it is better suited for a event that is determined randomly... like a coin flip. In my situation, one side could be +220 and the other -180.

[matekus]

Replace Default Current Price

elgreco,

Using your counterexample, you should replace 2.00 (default current price) with the decimal equivalents of +220 and -180 respectively giving you $118 and $254 approximately as the current fair values.

matekus

[elgreco]

Exactly. If you read my post again, I already have that part covered.

What i don't have covered is how to calculate my edge on Totals when I change the Total. If Pinny has the Total at 43, and I assume the probability is 50%, how can I calculate the probabilities if I move the Total to 45?

(For now, I can use LTProfits idea of getting the alternate line odds from 5dimes)

[matekus]

Bookmaker Edge

elgreco,

As the bookmaker, you can determine whatever edge you like relative to the market (Pinnacle).

For example, with competitor A, if the market price is Pinnacle +220 (equivalent to $118 m2m) and A accepts your offer of $100 that gives you an edge of 6.46% (approx). Similarly, for competitor B at Pinnacle 180 (equivalent to $254 m2m) accepting your offer of $225 gives you an edge of 19.50% (approx).

matekus

[elgreco]

You are correct, but that only works when you have a market price. For the question I have been asking, we do not have a market price. We have to create a market price.

We know that Pinny has the total at 42 -108, what are the odds going to be if we move the total to 45, or 52, or 38? The only price we have is for the Total set by Pinny, we do not have a price for the total we created.

[matekus]

Competitors Unable To Adjust Position

elgreco,

Forgive me if I have misunderstood the problem but, given that the competitors are unable to adjust their positions once they have accepted your discounted offer, why does a subsequent Pinnacle line change matter?

matekus

[elgreco]

Ok, I'm going to restate everything in a pure form so that everyone knows what I'm talking about:

Pinny has the Total score at 42 -108. The total that is offered to me is 45, not 42. I need to know what the value of the under is at 45, and what the value of the over is at 45.


If you want to know why my only choice is 45, I have included the 3rd paragraph of my first post below:


My question is how to properly value a ticket that depends on a Total. If two people go into Monday night tied, and they have picked the same team to win, then the tie will be broken by who guessed the closest total score of the MNF game. Here is an example of my problem:

Pot Value: $400
Ticket A has picked a Total Score of 40.
Ticket B Has Picked a Total Score of 50.
Pinny has the Total at 43

How do I calculate the “Fair Market Price” for tickets A and B? I have played around with determining the % difference between Pinny’s 43 and the actual 45 and running the numbers that way, but since I’m not a math guy, I don’t feel like I am doing it right.

[durito]

http://www.sbrforum.com/betting-tools/half-point-calculator/

This will only be accurate when you are close to the actual total. But, I suppose for your purposes it will suffice ok even with things like 50 v 40.