Hello,

Decission point is a turnbet: Villain bets the turn, his betting-range consists of 50% value-hands against which we have x% equity and 50% bluff-hands against which we have y% equity.

We call, villain now bets the river again, this time he never bets his bluff-range again, so his riverbet consists of a 100% Valuehands. Is our EV for the river now (assuming we have calculated our EV for calling the turnbet separately):

1) EV(Rivercall): ((Riverbet)*0.x - (riverbet)*(1-0.x))*0.5

OR

2) EV(Rivercall): ((Riverbet)*0.x - (riverbet)*(1-0.x))*1



This is really confusing me right now. I know whenever we call the riverbet, we are always (and therefore a 100%) up against his value-range, however I think that if this scenario happened a 100 times, we couldnt be paying off his riverbet more than 50 times, because the other 50 times he checks back his bluff-range. Can someone help me understand this?

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.

The decision point apparently IS the turn. I would say getting EVturn +EVriver is quite unconventional. And, you have to include the possibility of villain checking. Here is how I would do it assuming hero calls turn and river bets and if V checks so does hero and win % = 50. Also, you are assuming that river card does not change equities.

EV turn call =0.5* ((100+50+125)*0.1 – (50+125)*0.9) + 0.5*0.35*((100+50+125)*0.85 – (125+50)*0.15) + 0.5*.65*(150/2) …… (last term is check/check)

EV = -4.3, so turn call is slightly negative.

Thanks, I'll use your formula then One more question though:

The blue part tells us our EV when we are up against his bluff-range, right? The probability of winning (100+50+125) and losing (125+50) here is 0.5*0.35. Isnt there some EV missing, considering that on the turn he bets a 100% of his 50% bluff-range? Wouldnt it have to be:

0.5*((100+50)*0.85 - 50*0.15) for the turn and 0.5*0.35*(125*0.85 - 125*0.15) for the river?

Hero doesn’t win (or lose) anything on the turn. Payoffs are made on the river. If V bluffed turn and river(Prob = 0.50*0.35), hero wins( Pot + Turn Bet +River Bet) 85% of the time and loses his turn and river calls 15% of the time.

Thanks, good to know. Sorry I keep coming with questions I just cant answere them myself :/ If you dont mind: How would your equation of:


change if, lets say, we had 85% equity against villains bluff-range on the turn, but when he bets the river, we then only have 70% equity against his bluff-range(because he may have improved some of the time)?

The equity on the river is all that counts- same idea as for payoffs.

okay, big thanks!

argh, one last thing ( I'm certain): How would


change, if we only called the riverbet 75% of the time?

Let X represents the EV terms with villain betting on the river, then the modified EV with a 75% river call is

EV = 0.75*X - 0.25*50 + 0.5*0.65 *75

The middle term is hero folding on the river and losing the $50 he called on the turn.

As a check, the frequencies of actions are:

V bets value, hero calls: 0.75*0.5 = 0.375
V bluffs, hero calls: 0.75*0.5*0.35 =0.13125
V bets, hero folds: 0.25 * (0.5+0.5*0.35) = 0.16875
V checks, hero checks : 0.5*0.65 =0.325
Sum= 1.0


So far, you proposed an analysis involving 7 estimates, (villain value/bluff ratio, hero river call frequency, value and bluff equities, etc.) I doubt that having the right EV equation with so many estimates (7) will help much to improve your play. I would suggest dealing with simpler problems first.

If you have another question about this, hopefully someone else will answer to provide another perspective and perhaps verify or refute my equations and/or what I suggested.

TYVM!