Party 3/6 turn decision

[BottlesOf]

We're talking about just one street, as if the card misses on the turn, we definitely won't have the odds to go to the river.

There are 47 cards that could fall on the turn. 2 of them give us a set. So 45 cards don't helps us, and 2 do. 45:2 = 22.5:1

[irisheyes]

[ QUOTE ]
I'm going to attempt my first real +/- EV analysis on this and report back.

[/ QUOTE ]

Ok, I agree with Rob's analysis. There are four scenarios:

1. Hero calls, CO calls, UTG+1 calls (24.33 SB)
2a. Hero calls, CO raises, UTG+1 folds, MP1 calls, Hero calls (26.33SB)
2b. Hero calls, CO raises, UTG+1 calls, MP1 calls, Hero calls (28.33SB)
3. Hero calls, CO raises, UTG+1 folds, MP1 3-bets, Hero folds (-1 EV)

Rob assigned the following probabilities to these scenarios:

1. p(0.3) Everyone calls
2a. p(0.0) CO raises, UTG+1 folds, everyone else calls
2b. p(0.5) CO raises, everyone calls
3. p(0.2) CO raises, UTG+1 (who cares), MP1 3-bets, Hero folds

Final pot size estimates are 33SB for scenario #1 and 40SB in scenarios 2a/2b.

Scenario 1

i. Everyone calls, turn is a 2 p(0.04)
ii. Everyone calls, turn is not a 2 p(0.96)

(0.04*33)+(0.96*-1) = +0.36 SB EV

This is what everyone is seeing and thinking the call is +EV.


Scenario 2

i. CO raises/Everyone calls, turn is a 2 p(0.04)
ii. CO raises/Everyone calls, turn is not a 2 p(0.96)

In (ii) you lose 2 small bets for a shot at a larger 40SB pot.

(0.04*40)+(0.96*-2) = -0.32 SB EV


Scenario 3

i. You simply lose 1SB because of the 3-bet = -1 SB EV.


Final Analysis

1. p(0.3) + 0.36 SB
2. p(0.5) - 0.32 SB
3. p(0.2) - 1.00 SB

The call is -0.25 SB EV


Even if you tweak the numbers and make it p(0.5) for #1, p(0.4) #2, and p(0.1) [this would be a very passive table] it's still -0.05 SB EV. Clearly not an 'easy call', but probably not worth a half-hour's analysis one way or the other [img]/images/graemlins/smile.gif[/img].


But what about the Flush Threat?

Each of your three opponents on the flop has p(0.25) to be suited (3-1). The odds that the suited cards they hold are spades or clubs is p(0.5). 3*(0.25)*(0.5) = p(0.375). If your miracle card on the turn is the 2[img]/images/graemlins/club.gif[/img], you now have a 37.5% chance of being up against a flush draw. If the card is 2[img]/images/graemlins/diamond.gif[/img], you have a 18.75% chance of being up against a flush draw. Averaging out the turn, there is a 28.1% chance you are up against a flush draw. There would be 9 clubs and 8 spades left to complete these flushes. 17 outs if the 2[img]/images/graemlins/club.gif[/img] fell, and only 8 outs if the 2[img]/images/graemlins/diamond.gif[/img] fell. Average this to 12.5 outs for flushes.

However, if the turn card was 2[img]/images/graemlins/club.gif[/img], 3 of a flush draw's potential outs give you a full boat (T[img]/images/graemlins/spade.gif[/img], 6[img]/images/graemlins/club.gif[/img], and 3[img]/images/graemlins/club.gif[/img]). This would be great for you. T[img]/images/graemlins/spade.gif[/img] is the only flush-completing out you have if the 2[img]/images/graemlins/diamond.gif[/img] was your turn card. Average this to 2 outs of the 12.5, so let's reduce the flush draw's outs to 10.5 on the river. 10.5 outs / 46 cards = p(0.228)

The flush redraw will happen approximately p(0.281)*p(0.228) = p(0.064) or 6.4% of the time. In that event you will lose at least 6 additional SB (7.5 with the flop call), and -7.5 SB * p(0.06) = -0.48 SB EV.

Summary

I think based on the preflop action it is an even higher likelihood that your opponents are suited, but given a purely random distribution the flush redraw on the river costs you another 0.48 SB. If your table was filled with passive players and there was only a 20% chance of a raise or 3-bet on the flop, given the presence of the 2 spades your call has got to be -EV.

Whew... brain hurts, please insert Guinness.

[irisheyes]

Bad form to reply to my own post, but just in case anyone cares, I did not intend the summary to be read as that you should subtract 0.48 SB from the flop EV. It is turn EV that is impacted by the flush redraw.

Basically scenario #1 is +EV 0.26 SB instead of +EV 0.36 and scenario #2 is -EV 0.44 instead of -0.32.

With the flush redraw, Net EV is reduced to -0.34 SB from -0.25 SB using my above post and Rob's probability estimates.