Hypothetical Question

[elindauer]

Hi sparks,

Do some sanity checking next time. $1620 is the max possible if you win the blinds every time, so $1550, after recognizing that you'll see aces a couple times an hour and plan to call down... is way too high.

A couple quick glaring ommisions:

- you have to pay the blinds. Subtract $180 / hr.
- Ax can call profitably from the blinds.

good luck.
eric

You are right about AXo in the Big Blind.

You are getting 3.5 + 1 + 4 + 2 = 10.5:1 effective odds to flop an Ace and not have KK redraw to trips. That is enough to call. That's enough for pocket pairs to call too.

In the small blind you are getting 10.5:1.5 = 7:1 to flop an ace and KK not to hit his redraw, which is also enough, though close.

Also you are right about KK. I should neglect that outcome along with 2 AA's.

I stand corrected.

-v

[LearnedfromTV]

I don't know the answer but there is something big I have not seen mentioned yet.

It is NOT legitimate to ignore the non blind hands, even if you assume your opponents will refuse to play when they do not have the (implied) odds to call preflop.

To take the simplest case, you have KK UTG, raise, and it is folded to the button. The button's thinking is as follows:

If I call, the SB is getting 11:3 to call and see a three- or four-way flop. If I call and the SB calls, the BB is getting 7:1 on a four-way. If I call and the SB blind folds, the BB is getting 11:2 on a three-way.

My call widens the range of hands with which the SB and BB can call. The fact that I can influence them to call by calling myself widens the range of hands with which I can profitably call, given the implied odds of hitting my hand in a multi-way pot in position against a preflop raiser who I can play perfectly against, including optimal bluffing.

Now back the same reasoning up to the cutoff.

The first coldcall starts a schooling effect that makes this quite a bit more complicated than the headsup v BB analyses would indicate.

Edit:

Another example: Faceup KK on the button. UTG open limps with 88, UTG + 1 calls with AJ, MP1 anticipates a six way pot and calls with 87s, etc. There are a ton of way that three players could be dealt hands from the set of hands that can profitable play for two bets six way with a faceup KK included. The faceup KK actually gives good multiway hands extra incentive to call because they can (almost) guarantee that they only have to put in two bets. The only exception being when someone picks up AA.

Given the presence of other players playing postflop against each other and the faceup KK, proper strategy for the KK postflop would be much more complicated than proper headsup strategy.

Generally speaking I think this is still a very profitable spot but you would win a great deal more in position. You may even be even money or negative in EP. A wild guess is that the overall EV is much closer to the 100-200 range than that 1000 range.

[tpir90036]

[ QUOTE ]
I'm not familiar with the example, but claim AA in no limit is always profitable. Move in preflop. Perhaps you meant pot-limit with deep stacks?

[/ QUOTE ]
In the example the person with AA is not aware his opponent knows he has AA every hand. Pot-limit with deep stacks could play out the same way I imagine.

[mmbt0ne]

</font><blockquote><font class="small">En réponse à:</font><hr />
Wow, intuitively I'd think it's a LOT closer to $0 than $1500, and I'm not even 100% sure that it's a positive number (though I think it marginally is). One of us is way off.

[/ QUOTE ]

You're going to be able to steal the blinds a lot. Like, a lot a lot. Also, there are going to be times when people play you with a draw, and they don't hit. I have no idea what the number is, but this is interesting so I'll try to calculate something, sometime.

[elindauer]

Great point Learned. I actually tried to work this in but found it pretty complicated, as you point out. Here are some thoughts I had:

- the players are probably reasonably tight (&gt; 1 BB / hour win rate normally), and DS specifies that they won't collude (your type of "collusion" is a little different, granted), so there won't be either accidental schooling or preplanned schooling going on.

- most hands are well short of having the right odds to call. Pocket pairs for example are looking at 10.5:2 to call, so the extra induced calls have to contribute another 5 SB at least to break even. This is unlikely, especially when you consider the type of hand that might be induced to call, which, I think, is the suited connector. Now if you get action postflop with your set, they are drawing for flushes and straights to beat you, and it's almost impossible for many bets to go in on any street, as the KK is definitely shutting down.


So if you still can't call with pocket pairs, and ace high was already just break even, can this effect cause a hand like 98s to cold call behind you? I haven't done the math, but I suspect the answer is still no. If I'm right, calling light hoping to generate a schooling effect is proably just going to leave you high and dry playing KK heads up. Players will quickly be forced to abandon the strategy.

-Eric

[LearnedfromTV]

I think you are right that the multiway pot doesn't happen a lot. But I think it happen more than you think, mainly because:

I think you underestimate the value of playing a three or four way pot with a pocket pair or an ace given that your hand is hidden and KK's isn't and you can bluff. A basic strategy for KK is to payoff all bets, which means hitting a set guarantees you a small bet on the flop and 3 big bets, getting a raise in on the turn or river. Even if KK knows you have an A or a pp, any flop can potentially be one where you outflopped him. If he starts folding to aggression to save bets you can bluff to gain them back (and then some).

The other thing to consider is that if it is a game you can beat for $50/hour, someone in the field isn't playing perfectly. Given the right distribution of hands, one or two bad calls can encourage several correct calls. Even if the first calls is profitable for KK, the sum of the calls probably isn't given how hard it will be for KK to play correctly postflop in a multiway pot.

Also in multiway pots, the bluffs that are run at KK can be two-bet bluffs. Say it is three way: SB has AJ spades, BB has QJ. Flop QT2 two spades. CHeck to KK, KK bets, SB semibluff checkraises, BB three bets. If KK decides he is ahead he still has to dodge sixteen outs, and some percentage of the time he faces these bets SB was bluffing but BB flopped a set.

All of this is just rough musing, but the one thing I'm sure of is that the calculation is made very complicated by the multiway possibility, and it isn't irrelevant.

[LearnedfromTV]

Three more things:

1. Given that two cards are known, the odds of flopping an ace or set are slightly higher than they would be otherwise.

2. Assuming KK folds sometimes, playing correctly against it includes bluffing sometimes. EVERY bluff is a semibluff. Two or three outs for the turn to back up a flop bluff isn't insignificant, especially when KK never knows if a card beat him. Or a bad case for KK: Ax suited flops a 12 out draw, a pocket pair bluffs, the draw calls, KK calls. Now KK has to dodge 14 on the turn, plus backdoor straight outs could show up, etc.

3. Folding isn't the only way KK can be ahead and give up flop EV. The mismatch of information will make it easy for draws to draw correctly, because KK can't just raise evey time the board is suited and someone bets. Most of the time the bet is a hand that outflopped KK.

[ QUOTE ]
In a typical ten handed 30-60 game where you normally make $50 an hour, what would your win rate be if you were dealt two face up kings every hand and your opponents didn't collude? (Assume 40 hands per hour.)

[/ QUOTE ]

Why would anyone who is serious about poker care about the answer to this question?

Hi Elindauer,

I should have read your post before I created mine.

Reading through the math, everything looks fine except
I get 15% (184/1225) for the probability BB has an Ace but not AA instead of 16%.

It turns out that the case when the SB has Ax has a large impact because you turn a blind stealing situation into a small win.

13% of the time the SB draws to an ace and misses = .31SB
3% of the time the SB draws to an aces and hits = -.21SB

Then 59% of the time you steal the blinds = .885SB, and:

.885 + .325 + .31 + .12 - .35 - .21 - .21 - .054 ~= .82 SB / hand

That comes to about $800/hr, down about $150/hr from when the SB was ignored.

I liked your analysis a lot, thanks.

-v