Hello,

Currently EV is computed only when moving all-in, but I think this gives a somewhat skewed representation of how the situation really is. I think most people use the EV stats and EV-Allin graph to see how well they are doing taking bad beats and outdraws into account but I want to point out a few shortcomings to the EV calculation and a method to improve it.

For example:

Assume a headsup game with 2 players with 25bb stacks. Hero (on the button) has

AhQco and raises to 3bb, villain on the big blind flat calls with QhTc.

The flop is As4cTd

Villain checks, Hero bets 5, villain calls

Turn is a 9c.

Villain checks, Hero bets 15, villain calls. Both players have a stack left of 2 bb.

River is a Tc giving villain his 2-outer.

Villain bets his last 2 and Hero calls.


Now within holdem manager, since its an all-in on the river when Hero is behind, there is no EV-difference and the EV value for this hand is exactly -25bb. Now intuitively there is something wrong here, for most players this feels like an obvious outdraw, regardless of the meaningless 2 remaining big blinds that went in on the river.

We now propose a more refined method for computing a more accurate representation of EV taking outdrawing, as in our last example, into account. The basic idea is to compute equity for bets on the street on which they were made. So we compute pot equity for each player for the amount of chips that went into the pot for each street. So the EV in our example is now computed as follows:

(Equities were computed using Pokerstove)

Preflop Betting: 6bbs, Hero Equity: 73%, Villian Equity: 27%
Flop Betting: 10bbs, Hero Equity: 91%, Villian Equity: 9%
Turn Betting: 30bbs, Hero Equity: 95%, Villian Equity: 5%
River Betting: 4bbs, Hero Equity: 0%, Villian Equity: 100%

We now multiply the equity per street for Hero with the corresponding betting:
6*0.73 + 10*0.91 + 30*0.95 + 4*0 = 41.98bbs
And for villain:
6*0.27 + 10*0.09 + 30*0.05 + 4*1 = 8.02 bbs

So Hero EV should be 42-25 = 17bbs and villain EV should be 8 - 25 = -17bbs.

As we see, this gives us a far more accurate result how Hero was doing when most of the betting was done. There is also not much of a difference anymore when the final 4 river bbs would have went in on the turn as well. Note that there can also be some examples in which the EV computed by HM is actually an overestimation, for instance due to an outdraw by Hero. When the betting is all-in on the river the outdraw incorrectly is assigned full EV giving an incorrect idea of having played the hand correctly. Obviously, for non-showdown hands, current EV computation should be reserved in cases where villains hand is unknown; EV should then simply remain equal to the amount lost or won in the pot.

I hope that it is clear why this EV computation is better than the one currently implemented. I also hope to see some feedback from other forum posters about what could be wrong using this approach and how we might improve it and maybe someday to see this computation implemented in Hold'em Manager.

Kind Regards,

Immo