Hypothetical Question
 

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.)

Re: Hypothetical Question
 

$1300/hr at 40 h/hr.

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David that seems like a very difficult question. How about if we start with the heads up case? There at least there is hope. If that proves solvable (and it well might), we can then think about adding players.

Re: Hypothetical Question
 

If everyone folds, you would collect 1200 in blinds per hour. Every 5.5 hours you would pay off aces (not counting the times you will draw out) and every 5.5 hours you would split a pot with someone who has the two other kings.

Unfortunately in the 2/3 structure the small blind will call with most of his hands and big blind will usually call with all of his hands. So it is all about winning chances of kings against 2 more or less random hands.

Re: Hypothetical Question
 

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David that seems like a very difficult question.

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It is only difficult if the fact that the game is normally beatable for $50/hr means there is an idiot trying to crack you from any position but the BB. Otherwise, assuming no collusion then 2 things happen:

1) Someone has AA. They will reraise preflop, and we will lose 4BB total calling down.

This will happen 9/221, so 9 * (-4.75) / 221 = -0.19 BB

2) Someone will call from the BB with an ace or pocket pair and try to spike. The value lost here is marginal, and I'd estimate it at ~0.05 BB, since the implied odds aren't great for them.

So that's -0.24 BB to tack onto the 0.75BB gained from stealing the blinds ~0.51 BB per hand, or ~$1225/hr.

edit- missed the 0.75 BB lost in stolen blinds when AA happens. also forgot other KK, but that's worth ~0.005BB.

Re: Hypothetical Question
 

I have to take issue with your claim that someone trying to spike doesn't have good implied odds. The problem being that we won't know if they spiked or not.

Are we going to fold whenever an ace comes -- and let the PPs bluff us out? Or are we going to call down -- and lose lots of money to Ax?

It's not even clear to me that it would be unprofitable for one of these hands to cold call behind our openraise -- and raise the flop if they like it. AA can do the same.

Re: Hypothetical Question
 

[ QUOTE ]
I have to take issue with your claim that someone trying to spike doesn't have good implied odds. The problem being that we won't know if they spiked or not.

Are we going to fold whenever an ace comes -- and let the PPs bluff us out? Or are we going to call down -- and lose lots of money to Ax?

It's not even clear to me that it would be unprofitable for one of these hands to cold call behind our openraise -- and raise the flop if they like it. AA can do the same.

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As soon as we get raised on a street we just call down (mostly; we mix in a few folds to the raises at the game theory optimal amount). Cool?

Re: Hypothetical Question
 

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big blind will usually call with all of his hands. So it is all about winning chances of kings against 2 more or less random hands.

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You're kidding, right?? He'll call with Ax and pocket pairs and no more.

Re: Hypothetical Question
 

Definitely I agree if we are raised on any street, we should just call down. You don't reraise someone when your cards are face up. Furthermore, frequently on the turn, and always on the river, we should refrain from even *betting*.

The problem is that to answer David's question, we need to know what that "game theory optimal amount" for folding is. And that's very difficult, especially considering that it's board dependent.

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About 80$ an hour. If hey were face up, oppenents with pocket pairs would have all the incentive to play and catch a set. It would depend on how many times people would suck out on you. It would be more but not that much more...

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You're kidding, right?? He'll call with Ax and pocket pairs and no more.

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Why would calling with a pocket pair be any more profitable for the BB than calling with a suited connector? Remember, aces are "outs" for him too.

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I'd be making $500.00/hr.

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I don't think the kings can beat any decent game at all.
At the very least the situation is not nearly
as clear-cut as the first few posters claim it to be.

It's all about the FTP.

If the other players are willing to make 'negative' EV
calls (raises?) preflop to set themselves up for the huge
EV of playing against face-up cards.

Poker is more about uncertainty and deception than cold
odds. And the kings give up way more than they get.

Re: Hypothetical Question
 

[ QUOTE ]
Definitely I agree if we are raised on any street, we should just call down. You don't reraise someone when your cards are face up. Furthermore, frequently on the turn, and always on the river, we should refrain from even *betting*.

The problem is that to answer David's question, we need to know what that "game theory optimal amount" for folding is. And that's very difficult, especially considering that it's board dependent.

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I don't think David was after an exact answer, and the game theory folds aren't going to save us much.

But if you want to work it out, the optimal amount to fold is 1/(1 + Pot), and this works fine on the river, but as you work back each street the 2 K outs have to be mixed in. Eh, goodnight!

Re: Hypothetical Question
 

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?

Re: Hypothetical Question
 

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Why would calling with a pocket pair be any more profitable for the BB than calling with a suited connector? Remember, aces are "outs" for him too.

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Aces are not outs. We aren't folding if an ace comes up (any more than the game theory optimum, that is).

Suited connectors flop draws, which suck in a 2BB pot when they've got no fold equity, or underpairs, which suck full stop.

Re: Hypothetical Question
 

I don't think I suggested collusion, except maybe between
one's preflop self and postflop self. I do believe that
the more players who play correctly against the kings the
worse it will be for the kings, but thats not collusion either.

Re: Hypothetical Question
 

[ QUOTE ]
I don't think I suggested collusion, except maybe between
one's preflop self and postflop self. I do believe that
the more players who play correctly against the kings the
worse it will be for the kings, but thats not collusion either.

[/ QUOTE ]

Ok, sorry, I misread. Anyway, give me an example of a situation where you think it would be profitable apart from AA or Ax/PP in the BB?

Re: Hypothetical Question
 

[ QUOTE ]


1) Someone has AA. They will reraise preflop, and we will lose 4BB total calling down.

This will happen 9/221, so 9 * (-4.75) / 221 = -0.19 BB

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9/221 is not correct for two reasons.

Once Hero has been dealt KK at most two people can be dealt AA. Fixing on one player, the probability that he his dealt AA is (4 choose 2) / (50 choose 2). The sum of these probabilities for 9 people is 9 * (4 choose 2) / (50 choose 2) and is close to the right answer but it's wrong because it double counts the times that two players hold AA. The probability that two particular players hold AA is (4 choose ) / (50 choose 4) and multiply this by (9 choose 2), the number of ways to choose 2 players from 9 players. Hence the probability that our Hero ends up against AA is

9 * (4 choose 2) / (50 choose 2) - (9 choose 2) * (4 choose 4) / (50 choose 4) =.0439.

Re: Hypothetical Question
 

Yeah you're right.. I was just trying to get an approximation down. Anyway, my error seems to amount to an overestimate of about $36.

edit - I've made lots of other assumptions/crude maths too in getting the approximation.

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This would be much more of a social problem than a mathematical one. You would have to spend a lot time disguising your hand (limping preflop, folding the best hand etc.), so that you didn't get your ass kicked at every home game, your funds confiscated from online sites, etc.

similar post

From a purely mathematical sense, just take your figure from PT and multiply by 40 or whatever. If you table hopped enough, people wouldn't catch on, so you could achieve something close to this figure. Also, why are we bothering with limit in the first place?

Re: Hypothetical Question
 

Are you calling everything down, or can I bluff the KK?
Do you fold to 4-flushes and 4 card straights? Fold to an A
on board?

Do you call down someone who reraises you preflop? Will you charge for draws?

Depending on how you handle these situations, which I would
determine rather quickly from whatching you play I think
there are many ways to capitalize on the situation.

Not to mention how hard it would be for the kings to play in multi-way pots.

Re: Hypothetical Question
 

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...you were dealt two face up kings every hand...

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That's gunna be a giveaway no matter how fast you table hop.

Re: Hypothetical Question
 

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[ QUOTE ]
...you were dealt two face up kings every hand...

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That's gunna be a giveaway no matter how fast you table hop.

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I disagree. You would only play a small amount each day, from several accounts. Play one full round on each table. I can't remember what the table WSD stats are like, but you will only be showing your hand perhaps 3-4 times on average (with you folding sometimes). It will look like a mad co-incidence, but by the the 3rd time you show your kings (which is when people will get supsicous) you are nearly at the button.

And then most of the players wont see you again for quite some time....

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you were dealt two face up kings every hand

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I took this to mean they had the picture part facing into the air, like towards people's eyes.

Re: Hypothetical Question
 

I have no idea why everyone is rushing to say how much higher your win rate would be. Your hand is face up!! Maybe they will choose to not give us action pre-flop but they could outplay us perfectly post-flop if they wanted to.

I am not sure exactly how this would play out since we might end up picking up a few small pots here and there but they will be smaller since no one is paying off.

Anyway, my gut says that our win rate would actually drop....that having KK every hand can not possibly overcome the disadvantage of our opponents having perfect information.

I will go with $0/hr.

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LOL oh yeah

Re: Hypothetical Question
 

its interesting and obvious why you chose kings.

i think a few things could happen assuming this is an AVERAGE 20/40 game.

1) players would say to themselves (not the very good ones) "hey, this guys cards are face up, i'll just bluff him" thus you woul dhave to employ a strategy that involves calling down and seeing a showdown very freqently. eventually you'll stop getting bluffed and just pay off AA/Ax on an A high board quite frequently.

2) players may get BOARD folding worse hands and start to play just to try to flop a draw. in scary situations, you'll mostly be check calling, but in back you'll be raising so pl ayers may just be baord of folding every hand to KK so come with worse hands.

3) you will win the blinds very often.

these things combined i think make the game more profitable than $50/hr.so im pretty sure we'll end up with an EV > $50.

thats about all i can come up with at this point.

Barron

Re: Hypothetical Question
 

you're not taking into acct that you are playing HUMANS, not robots.

humans get board. imagine a fish not playing any hands b/c they're worse than KK...eventually boardom will overcome them and either the game will break or they'll start playing worse hands.

Barron

Re: Hypothetical Question
 

[ QUOTE ]
you're not taking into acct that you are playing HUMANS, not robots.

humans get board. imagine a fish not playing any hands b/c they're worse than KK...eventually boardom will overcome them and either the game will break or they'll start playing worse hands.

Barron

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As per usual I am giving my opponents way more credit then they deserve. But what our opponents do is a large part of this. There is an enormous gap between a table of people who fold everything but AA and let us have the blinds and those who play lots of hands and play them well against us.

Re: Hypothetical Question
 

[ QUOTE ]
you're not taking into acct that you are playing HUMANS, not robots.

humans get board. imagine a fish not playing any hands b/c they're worse than KK...eventually boardom will overcome them and either the game will break or they'll start playing worse hands.

Barron

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But the more interesting theoretical exercise is to assume our opponents would play according to the Fundamental Theorem of Poker and use correct bluffing stratgies etc. and then calculate our EV.

Re: Hypothetical Question
 

Between $1200-$1600/hr.

Re: Hypothetical Question
 

[ QUOTE ]
get board.

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boardom

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Wow.

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[ QUOTE ]
get BOARD

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Eliminating the possibility that the first two misspellings were accidental...

Re: Hypothetical Question
 

[ QUOTE ]
[ QUOTE ]
get BOARD

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Eliminating the possibility that the first two misspellings were accidental...

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jeez, can'ta guy just imply that the players were getting wood trying to get at the guy with the kings??

Barron

Re: Hypothetical Question
 

I was thinking about $1500, because I figured you'd win the blinds 75% of the time ($50 x 30) and shouldn't do worse than break even when somebody chooses to compete. But that sounded like such a big number, I was afraid to post. Now that I see your estimate, I've decided to go out on the limb right behind you.

Re: Hypothetical Question
 

I came up w/ an answer of $960 / hr. Here's how:

assumption: The only playable hand outside the blinds is AA. PPs are no good as they can only hope for about 5:1 even with perfect implied odds for the set. Ace-high hands are close, but probably don't impact your bottom line much (aside from forcing you to payoff AA more).

assumption: BB can only play pocket pairs and ace high. Both are clearly profitable. It's unclear whether or not other good drawing hands like T9s could ever be played. Probably not.

estimate: the SB only plays AA. pocket pairs are close and ace-high is almost certainly playable, but I ignored this.

assumption: KK will always payoff no matter what the board. This is a huge assumption, but it makes the math easier. This makes the final estimate a lower bound. KK may be able to do much better by always folding ace-high boards. More on that at the end.

I also ignored any chance of somebody picking up KK. This will happen less than 1% of hands and costs you less than 1 SB.

some math:
probability BB has ace: 16%
probability somebody has AA ~ 4.4%
probability BB has PP which is not AA and not KK 5.4%

So we just do an EV calculation... to do this, I looked at the blinds as already paid and out of our stack, then subtracted those payments at the end. That is, if we win the blinds after posting the big blind ourselves, that's handled below as +1.5 SB in EV, with the 1SB being subtracted at the end.

75% of the time we win the blinds for 1.125 SB / hand
4.4% of the time we lose 8SB to AA (super conservative estimate) = -.35 SB / hand
13% of the time the BB draws to an ace and misses = .325 SB / hand
3% of the time the BB draws to an ace and catches, winning 7SB from us (conservative estimate) = -.21 SB / hand
4.8% of the time the BB draws to a pocket pair and misses = .12 BB / hand
.6% of the time BB draws to pocket pair and flops a set, winning 9 SB from us (pretty conservative) = -.054 BB / hand

Add it all up...

1.125 + .325 + .12 - .35 - .21 - .054 ~= .95 SB / hand

That's $1140 / hr, but we have to pay the blinds ($45 * 4), leaving a net profit of $960 / hr, or .4 BB / hand. This is quite a bit lower than the EV of KK when dealt face down, which makes sense. What's the point? A LOT of your EV comes from your opponents not knowing what you hold.



I think this is a lower bound on the EV of KK face up every hand. Many assumptions might be tweaked to make the hand more profitable. In particular, ace high flops are super scary given the cards your opponents are playing. Also, anyone entering the pot outside the blinds should set off huge warning bells, probably making it right to fold any ace high flop and maybe even some that aren't. In fact, it's conceivable that you could fold preflop if someone entered the pot on your right!

Trying to play this way might make other hands playable / more profitable though, complicating the math.

Thanks for reading,
Eric

Re: Hypothetical Question
 

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.

Re: Hypothetical Question
 

[ QUOTE ]
[ QUOTE ]
[ QUOTE ]
get BOARD

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Eliminating the possibility that the first two misspellings were accidental...

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jeez, can'ta guy just imply that the players were getting wood trying to get at the guy with the kings??

Barron

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To be honest, I think that the misspelling explanation is probably less disturbing than the alternative...

ML4L

Re: Hypothetical Question
 

It seems that if you demonstrate that you're always going to call down, you're going to win the blinds an awful lot.