Lloyd Christmas said:
No problem.
Each half point is worth about 8 cents. So if it's 2 points off market, that's 4 half points. 8 x 4= 32. So if +4 is (-100), +6 is (-132).
132/232= 56.9. So +6 is going to win 56.9% of the time. We'll forget about pushes right now for simplicity.
If you are betting $100
56.9 x 100 = +5690
43.1 times you would lose 110. 43.1 x 110 = 4741
5690-4741= 949 that you would make over 100 games. Divide that by 100 and you have $9.49 in equity for each wager.
If you look up the push percentages for 4, 5, and 6, you get 4.16, 4.37, and 3.48
If you were betting $1000 on each side (which would be a $100 risk)
4.16 times you will push one, and win the other for +1000
3.48 times you will push one, and win the other for +1000
4.37 times you will win both for +2000
88 times you will lose one and win the other for -100
You then need to multiply the push percentages by the amount listed with it
For example, you would multiply 4.16 by 1000= +4160
3.48 x 1000= 3480
4.37 x 2000= 8740
You then add all those together to get 16,380
Then multiply the -100 by 88 for -8,800.
16,380-8,800= 7580.
7580/100= 75.80 in equity on the middle.
Lloyd, digging this thread up (I bookmarked it years ago)...thinking some things out, would love your feedback
I am trying to understand the best way to measure edge. Is equity best? In the above, you refer to equity which is equivalent to expected value in dollars. The alternative way I am considering is what I'll call return on risk (ROR) -- "equity" / risk. By risk, I mean amount risked or maximum loss possible.
As I write this out, I'm thinking equity is a better measure of edge than ROR. Why? ROR will not change as you increase/decrease the amount risked, while equity is sensitive to the amount risked.
In the example, the straight bet that wins 56.9% of the time has a ROR of ~8.6%. The middle has a ROR of ~75.8%.
Meanwhile, equity depends on how much you risk. If you risk only 100 on both sides of the middle, your equity comes out to be 7.58; less than the 9.49 equity of the straight $100 bet.
In sum, while ROR normalizes edge as a percentage, equity is a better measure because it varies with the actual dollar amounts at stake.
Now, I think I need to consider how variance should influence amount risked (if it should at all).