This is for ranking the 169 starting hands. Based on a simulation I have win, loss, ties for each hand.
Not sure how to credit the ties.
Lets say one hand is 40 (win), 40 (loss), 10 (tie)
And another hand is 45, 40, 5
And another hand is 40, 45, 5
My thought is to treat a tie as 1/2
So would have
45
47.5
42.5
Does that seem like a proper criteria for ranking?
Is there a better criteria for ranking?
In an ICM with chip lost more valuable than a chip won I may want the 40, 40, 10.
Ranking these hands based on their EV seems perfectly reasonable to me.
Personally, to list from strongest to weakest, I would just sort by Win% (descending) and then Loss% (ascending), so your hands above would be ranked the same way you arrived at with your "0.5 points for a Tie" approach:
/----------------------------\
| Rank | Win% | Loss% | Tie% |
|------+------+-------+------|
| 1 | 45 | 40 | 5 |
| 2 | 40 | 40 | 10 |
| 3 | 40 | 45 | 5 |
\----------------------------/
Note that in this case, the Tie% is actually irrelevant as if two hands have the same Win% and Loss%, they must by definition have the same Tie%.
This just represents the EV of the hands though, you could equally arrive at the same result by scoring each hand as:
1(Chance of Winning) + 0.5(Chance of Tie)
so for example your 45% Win, 40% Loss, 5% Tie hand has 47.5% equity/EV in the pot:
1(0.45) + 0.5(0.05) = 0.45 + 0.025 = 0.475 (47.5%)
Which gives the same rankings a different way (and is the approach you proposed):
/-------------------------------------\
| Rank | Win% | Loss% | Tie% | Score% |
|------+------+-------+------+--------|
| 1 | 45 | 40 | 5 | 47.5 |
| 2 | 40 | 40 | 10 | 45.0 |
| 3 | 40 | 45 | 5 | 42.5 |
\-------------------------------------/
If you wanted to somehow skew the results so that chips lost have a greater negative impact than chips won have a positive impact, then this would take some more consideration and surely would need to depend upon specific situations, tournament payouts and such to be meaningful rather than arbitrary?
