Quote:
Originally Posted by statmanhal
I don’t follow you at all. You first said the decision point is the turn but then stated hero calls the turn. You then talk about EV_river, so I assume you are interested in what to do on the river.
The EV of any decision is basically; P(win)*$Win - P(lose)*$Lose.
$Win has to include the pot amount which does not appear in your equations. You represented the river P(win) as x but you defined x as the turn win probability – assuming I didn’t misinterpret something, you can’t use x for the river without modifying it as necessary for the river card unless you want to assume it has no effect on x.
If you want the EV of your call or check action on the river (no fold), if x and y are valid for the river, and if you call when villain bets and check when V checks (??),
EV_river = EV_V bets.Hcalls + EV_Vchks.Hchks
=0.5*((Pot +Vbet)*x - (1-x)*Vbet) + 0.5*Pot*y
Note this did not include any analysis of the turn decision, since you assumed V bets turn and H called.
Frankly, I doubt if I’m answering your question.
Hello,
I left out the part of the equation for the turn, because I was more interested in how to calculate the EV for the river, because on the river, betting frequencies had changed and because of this I'm uncertain how that changes the probabilities. Sorry if the lack of information caused confusion.
Please allow me to give a new exmaple, starting from the decission point on the turn and using numbers, to avoid any further confusion:
On the turn, the Pot is 100$, we check, vil now bets 50$. When he bets 50$ on the turn, his range consists of 50% value-hands against which we have 10% Equity, and
50% bluff-hands, against which we have 85% equity. We call.
On the river the pot is 200$. We check, villain bets 125$. We now assume that he bets his value-hands 100% of the time, and we still have 10% equity against that range. However this time he only bets his "bluff-range"
35% of the time, against which we win 85% of the time(he may have improved on the river). If he doesnt bet his bluff-range, he checks it back. What is our total EV?
My guess:
EV(turn): ((100$+50$)*0.1 - 50$*0.9)*0.5 + ((100$+50$)*0.85 - 50$*0.15)*0.5
+
EV(river): (125$*0.1 - 125$*0.9)*0.5 + (125$*0.85 -125$*0.15)
*0.5*0.35
My problem is that I'm really uncertain about the river frequencies, because I'm not sure IF the fact that his
bluffing-range got smaller, increases his other range (I actually dont think so, but I'm not certain).
Also I'm not a 100% certain, if the part with the river EV misses some additional EV from the times he's checking back the remaining part of his bluff-range, but I think that EV should be included in the turn equation already.