Quote:
Shai,
Sorry for confusion. I should have put a comma after the word mine. I was referring to my hypothetical as opposed to Mike's. Not a "mine bet". My bad.
So, I'm just curious about the ev of the 2 extremes. (we can ignore an arbitrary % of betting rivers. Your Line 2.)
Mike's extreme premise: bet 120$ turn, ship all rivers.
My extreme premise: bet $120 turn, ship all rivers improved to a straight or flush cb all rivers brick rivers.
If you feel like doing also an arbitrary % for shipping rivers too, that's fine. But it's not necessary. I think I'd be able to see a good picture with results of the two extremes. I think this exercise will help me visualize ev better in this scenario. Since obv this arises often.
Thanks buddy,
No problem. For reference, we have J
9
on T
4
8
A
board. Villain has checked and action is on us. Stacks are $350
Line 1: Bet 120 on the turn (we get x/r AI 10% on the turn and always call, and he calls 75% OTT), ship all rivers (he calls 50%).
I did this calculation in post #164 and the result was
Total EV = $156.59
Villain may shove the river some % of the time, but we're assuming he threw away his 2p/sets on turn x/r. It makes a difference of pennies whether he x/r these hands or leads them. I considered including this work but it will just not affect the result significantly at all as we only lose to a river shove when we call with a flush AND it's the A
or 8
(this happens well less than 1% of the time we call). Anyway, I'm leaving some of the work here in case I reexamine it later.
Basically we would add this to the previous equation:
(P(VShoveRiver|calledturn)*(P(HCall|VShoveRiver)*( P(HWin|VShoveRiver)*WinAmt|VShoveRiver - P(HLose|VShoveRiver)*LoseAmt|VShoveRiver) - P(HFold|VShoveRiver)*LoseFoldAmt|VShoveRiver)
Line 2: Bet $120 turn (we get x/r AI 10% on the turn and always call, villain calls OTT 75%), ship all rivers that improved to a straight or flush (villain calls 50%), check behind everything else. We're assuming villain x/r AI with his 2p + sets OTT, so villain should basically never lead shove the river except as a bluff, which for simplicity we assume he never does (it would have close to zero effect on the result unless he bluffs a lot). Also, we're always good when we shove, since villain can't x/c a boat as he got rid of his possible boat hands on the turn.
This line is somewhat complicated so I'm glossing over how I get there, but much of it is similar to post #164
P(CRAI)=.1
P(HWin|CRAI) = .3116
WinAmt|CRAI = 455
P(HLose|CRAI) = .6884
LoseAmt|CRAI = 275
P(VFoldTurn) = .15
WinAmt|VFoldTurn = 180
P(VCallTurn) = .75
P(HChecksRiver) = 30/46
P(HWin|HChecksRiver) = 6/46 (this is reasonable against a station, as he in fact here had just a pair of 8s, so our J's and 9's are often good when he checks)
WinAmt|HChecksRiver = 180 + 120 = 300
P(HLose|HChecksRiver) = 40/46
LoseAmt|HChecksRiver = 120
P(HShoveRiver) = 16/46
P(Vfold|HShoveRiver) = .5
WinAmtVRiverFold|HShoveRiver = 180+120 = 300
P(VCall|HShoveRiver) = .5
P(HWin|HShoveRiver) = 1 (we assume he never checks his boats)
WinAmt|HShoveRiver = 180 + 120 + 155 = 455
Total EV = P(CRAI)*(P(win|CRAI)*WinAmt|CRAI - P(lose|CRAI)*LoseAmt|CRAI) +
P(VFoldTurn)*WinAmt|VFoldTurn +
P(VCallTurn)*(P(HChecksRiver)*(P(HWin|HChecksRiver )*WinAmt|HChecksRiver - P(HLose|HChecksRiver)*LoseAmt|HChecksRiver) +
P(HShoveRiver)*(P(Vfold|HShoveRiver)*WinAmtVRiverF old|HShoveRiver + P(Vcall|HShoveRiver)*P(Hwin|HShoveRiver)*WinAmt|HS hoveRiver))
Total EV = (.1)*(.3116*455 - .6884*255) +
.15*(180) +
.75*(30/46*(6/46*300 - 40/46*120) +
16/46*(.5*300 + .5*1*455))
Total(EV) = $90.20
Assuming I've made no mistakes (pretty sure there aren't any),
checking turn < bet 120 OTT, shove river if we hit < shove turn < bet 120 and shove river
Bet 120 OTT, shove river only if we hit is fairly low variance, though.
Now there's probably some optimal line, shoving X% of rivers. This is impossible to account accurately unless we make a model for every river card though, as villain is unlikely to fold the same amount on, for example, an Ace river as a 2. Unless his river calling range is super inelastic (vaguely possible for a calling station), we'd need to model individual rivers differently.
I could try to solve for X given our assumptions though. I don't think it would be too difficult though it would take a bit of work.
Quote:
The ev of cb all rivers unimproved is -$120 x .70. We miss 70% of time. Right?
Ev of shipping all rivers we improve is $120 + money we make on river (I forget remaining stack sizes).
Combine the 2 and that's are ev given my premise. Right?
Your first sentence is correct and we improve to a straight or flush more like 35% so we'd miss a bit over 65% but you are close. You have the right idea but you forgot to account for the 180 in the pot on the turn. You have to account for the action of multiple streets correctly which can be tricky. There's a reason I multiply the river action by .75, because .1 of the time there's a check-raise and .15 of the time villain folds. We need the probabilities for the actions on each street to sum to 1. And you left out our fold equity.
The check-raise potential on the other hand is not that important. It costs us like $3. I thought of including a river leading possibility as well, but this would be worth even less, possibly pennies. As we add variables the model gets exponentially more complicated. Making it 10% more accurate might take 2-3 times as long to do the calculations.
I need to figure out how to make Mathematica applets for changing multiple variables simultaneously and viewing the output. I knew how in grad school but no longer. Short of that I could make some excel sheets maybe. Hmmm...