Oh Noe! A vet posts an AA hand...and it has maths 4 u 2 do

[shuinthehouse]

If you bet I don't think he can raise without the A or K of spades, so you can safely fold. He has to be worried about you having A or K of spades since you 3 bet PF and donked into his PF cap on a 3 spade board.

PF isn't AQs in his range also? Seems as or more likely to cap with that 5 way than with JJ.

edit: sorry, missed point 4 adding AQs to his range, still seems as or more likely than JJ to me.

[britspin]

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1. Given his range, what are teh odds he has a spade?

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Levelling or something? Odds are 50% obv. [img]/images/graemlins/confused.gif[/img]



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Doesn't the fact that his AA hand has to include a spade change that? Supposes it also affects his AK range too.

I dunno maffs tho. Will hav to show workings.

[TimovieMan]

@ fretelöo:

What else do you propose we do in this situation? Villain knows what we’re about, and must assume after the flop our hand is likely QQ+ (and even more likely KK+). He’s in the same situation as we are, but he’s in position and thus has the advantage.

If we check, and he bets, is he bluffing or is he value betting? We don’t know, so we must call down. –EV
If we check, and he checks behind, is he slowplaying, or does he not have a spade? Coinflip river decision. Likely –EV.
If we bet, and he raises, we can clearly fold our hands. What’s he gonna raise on this board? Only the A. We can fold. -1 BB (if he musters up the nerve to bluff-raise us, kudos to him)
If we bet and he calls, does he have a spade that’s not the nuts, or is he unsure about us having a spade? Again we don’t know. Coinflip river decision. Likely –EV.

Whatever we do, it’s not going to be good on this board…

Hence the requested math, obviously. [img]/images/graemlins/tongue.gif[/img]

[36CampusAve]

:grunch:

Ok, here we go:

1. Odds he has spade is 14/27 = 51.9%.

2. Calling down reasonable? YES – big mistake not to
Scenario 1 – Villain Bet / Bet
a) has spade = -2BB*0.519 = -1.038BB
b) no spade = +15BB*0.481 = +7.215BB
EV = +6.177BB
Scenario 2 – Villain Bet / Check (50% of time)
a) has spade = -2BB*0.519 = -1.038BB
b) no spade but QQ/JJ = +14BB*0.11 = +1.55BB
c) no spade = +15BB*0.37 = +5.55BB
EV = +6.062BB
So, you lose out on ~6BB by not calling down.

3. Is b/f better than c/c?
No, I can’t see b/f giving a better EV than 6BB.

4. Wider range?
Odds he has spade go to 18/35 = 51.4%...so no real change here
EV on scenario 1 above doesn’t change and scenario 2 EV goes down a little but not enough to change anything.

[img]/images/graemlins/crazy.gif[/img] [img]/images/graemlins/confused.gif[/img]

[maverickai]

Question 1
Total hands he can hold:
AA
1 possible hand
1 spades hand

KK
6 possible hands
3 spades hands

QQ
6 possible hands
3 spades hands

JJ
6 possible hands
3 spades hands

AK
8 possible hands
4 spades hands

Therefore odds is (1+3+3+3+4)/(1+6+6+6+8)
= 51.8% he has a spade.
I will round up to 52%

Question 2
Let's assume villian bets out on turn and river, and HERO calls.

Total EV of calling down = ((0.48*15)+(0.52*-2))
= 6.16BB

EV of turn and river call down bets = ((0.48*2)+(0.52*-2))
= -0.08BB

Pot's too big to ignore. Calling is still +EV, so reasonable to call down.

Question 3

Assuming villian will call when he holds no flush, and he will raise if he has a flush.
EV of HERO's turn bet/fold = ((0.48*1)+(0.52*-1))
= -0.04BB

EV of HERO's turn check/call = ((0.48*1)+(0.52*-1))
= -0.04BB

Same EV for both decision. I'd go for check/call, you get to see the river, and you don't forfeit the huge pot.

Question 4

So that adds hands like:
TT
6 possible hands
3 spades hands

AQs
2 possible hands
1 spades hands

The odds he's holding onto spades becomes = (1+3+3+3+4+3+1)/(1+6+6+6+8+6+2)
= 51.4%

Well... not much difference if he's range is widened.

So teacher, is my math correct??? [img]/images/graemlins/confused.gif[/img]

[fretelöo]

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@ fretelöo:

What else do you propose we do in this situation? Villain knows what we’re about, and must assume after the flop our hand is likely QQ+ (and even more likely KK+). He’s in the same situation as we are, but he’s in position and thus has the advantage.

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True. But that doesn't make it right to choose the one line that gives us clearly the worst of all worlds for the price of 1BB and the relieve that we avoided a sticky situation. This hand is so insanely read-dependend that it's almose completely useless to post it without ~50 hands to go before so we can establish some sort of feel. In a vacuum (and stats/some remarks about hand ranges is a vacuum), you can simply choose between making a clearly -ev play or a probably -ev play. Clarkmeistering is clearly -ev because there's simply no chance in the world that a thinking player isn't playing correctly against us on this board.

Checking and seeing what he does at least gives us hopes for doing something +ev.

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Whatever we do, it’s not going to be good on this board…

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Exactly. But why should we make it worse?

[NigelSmith]

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AK
8 possible hands
4 spades hands

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Not too hot on this myself, but I *think* that's one short for the A[img]/images/graemlins/heart.gif[/img]K[img]/images/graemlins/spade.gif[/img]...

Making it 55.5555555555 (etc) he has a spade.

Similarly for AQs when you expand his hand range.

[fretelöo]

[ QUOTE ]
[ QUOTE ]
[ QUOTE ]
1. Given his range, what are teh odds he has a spade?

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Levelling or something? Odds are 50% obv. [img]/images/graemlins/confused.gif[/img]



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Doesn't the fact that his AA hand has to include a spade change that? Supposes it also affects his AK range too.

I dunno maffs tho. Will hav to show workings.

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Yup, a bit too rash there. Point is that for every hand that's unaffected by the board or our hand, the % is 50% (TT-KK/KQ etc.). For the other AA and AK/AQ, things change a bit to the worse: 5 of the remaining 8 AK combos have a spade (A[img]/images/graemlins/spade.gif[/img] K:any:, A[img]/images/graemlins/heart.gif[/img] K[img]/images/graemlins/spade.gif[/img]), same for AQ. However, that only changes 50% to 62%. So if you include QQ etc. where it's exactly 50%, for all practical purposes of "live decision making" 50% is still good enough.

[Bona]

*grunch*

There are 14 cards, 5 of which are spades, in the range you put him on. He holds 2 of those cards. So it appears to me he has a spade about 70% of the time. There is no other hand in his range that beats us so we win 3 of 10 times.

If we assume villain will bet when we check and we check/call down we are putting up 2 to win 15. So in ten trials we win 45 and lose 14 bets. Nice work when we can get it. Call down looks good. If we are wrong and he checks it through. I don't hate that either.

Bet/fold would only be better if we think villain will fold WHEN HOLDING A SPADE more often than he would bet into our check without a spade. I can't calculate that but I somehow I doubt it is the best play. Maybe when I read the other responses I will find out I am wrong about that. Anyway it is read dependent and reads are only so accurate at best.

Adding cards to his range does change the odds incrementally but I don't think it reaches the level of changing our play. The pot is too large for that.

The river card can change the outcome of this hand and never to our benefit. On the other hand there are several cards that can beat us. Even though that is an argument for betting, I make this, overall, a must call, can't bet situation. Not real close IMO.

Now I will read the responses of the real poker players and learn something [img]/images/graemlins/grin.gif[/img].

EDITED TO ADD: Looks like I miscounted. There are 4 spades in his range not 5 so odds are about 55% not 70%. Improves our call down odds. In ten trials we win ~67.5 BB and lose ~11 BB. Even better.

[36CampusAve]

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Not too hot on this myself, but I *think* that's one short for the A[img]/images/graemlins/heart.gif[/img]K[img]/images/graemlins/spade.gif[/img]...


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You are right I missed this in my calcs too. Wont change EV much...too lazy to recalc.