I am also trying to figure out how to compute EHS2, so I will just hijack this thread instead of starting a new one. Hope you excuse. (better to have it in one place, I think)
Quote:
Ok, let's say you want to compute the E[HS2] of your 2 hole cards.
Code:
foreach combination of flop,turn,river
{
reset win,tie,loss
foreach combination of the 2 opponent hole cards
{
update win,tie,loss
}
hs = (win+tie/2)/(win+tie+loss)
hs2 += hs*hs
}
hs2 /= number of iterations
So the 0.9 and 0.1 squared are the square in my code (hs*hs)
Should you really do the 'hs2 /= number of iterations' division? Hasn't that already been done when you divide by (win+tie+loss) ?
Also, if I understand correctly, the above calculation is for 2 players. For more than 2 players, the calculation should take the number of tied players into account. Like this:
Code:
hs = (win+tie/numberOfTiedPlayers)/(win+tie+loss)
Having read this page:
http://www.codingthewheel.com/archives/multiway-ranged-isometric-equity-calculation-in-poker-1/I think the value 'hs' with this formula is also called 'Equity'. (could someone please correct me if I am wrong?)
I have also seen another formula for EHS that is quite different: (source:
http://poker-ai.org/archive/www.pokerai.org/pf3/viewtopica90d.html?f=3&t=2777)
Quote:
EHS = HS + (1-HS) * PPOT - HS * NPOT
Where I believe PPOT is probability HS will increase on River compared to current street (Flop or Turn), NPOT is probability HS will decrease. (could someone please correct me if I am wrong?)
Which formula for EHS is correct, the one shown by vlad2048 or the one above?
If I use the formula above, would this mean: EHS2 = EHS*EHS ?
I have found some definitions that might help in a paper from UAlberta:
http://webdocs.cs.ualberta.ca/~johanson/publications/poker/2013-aamas-kmeans-abstraction/2013-aamas-kmeans-abstraction.pdfQuote:
Hand Strength (HS): In the final round when all public cards have been revealed, a player's hand strength (HS) is the probability that their hand is stronger than a uniform randomly sampled opponent hand.
Expected Hand Strength (EHS): In the earlier rounds, expected hand strength (E[HS]) is the expectation of hand strength over all possible rollouts of the remaining public cards.
Expected Hand Strength Squared (EHS2):A related metric, expected hand strength squared (E[HS2]), computes the expectation of the squared hand strength values, and assigns a relatively higher value to hands with the potential to improve such as flush-draws or straight-draws.
In the definitions above, they say 'stronger than a uniform randomly sampled opponent hand'. But before evaluation and computation of EHS and EHS2, my opponent modeller will put opponents on a hand range, not a uniform randomly sampled hand. How does that change things?
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