Re: Hypothetical Question
 

[ QUOTE ]
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 will go with $0/hr.

[/ QUOTE ]

To outplay us, they have to make us fold the winner. We can thwart this strategy by never folding. It's very difficult to draw out on KK, and it happens rarely enough that it's unprofitable to call preflop with virtually everything even if you know (or perhaps, especially if you know) that your opponent would payoff all the way.

For example, a pocket pair. You're only going to flop a set 1 time in 8.5. Even if you can raise the turn and get paid off for 7SB postflop, that only gives you 10.5:2 (5:1) odds to draw for the set. You're 7.5:1 to flop a set and you still might lose sometimes when you do... so you have to fold. Calling is a losing play.

Ace-high? You'll flop an ace less than 1 time in 5, about 4:1 against. Again, you're getting only 5:1 to play preflop, so you can call, but you aren't exactly breaking the bank with your profits from this hand, especially since an ace-high flop is the only one the KK may fold. Even if you figure an ace high flop just results in KK check-calling (assuming you have position!) and gets you 5SB, then you're getting only 8.5:2 preflop and make almost nothing with this hand.

If you can only play AA profitably, you aren't going to have many opportunities to outplay your opponent, whether you know his cards or not.

good luck.
eric

Re: Hypothetical Question
 

I would turn this around and ask what hands you are prepared to call face up Kings with? then work out the probability that any of the opponents will call (so that you don't just pick up the blinds) and that when they do call what the probability is that they hit their hand on the flop to be worthwhile continuing calling/raising the kings bets.

There is no way the EV of having kings every hand is close to 0 even when face up.

Re: Hypothetical Question
 

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

[/ QUOTE ]

I agree, this is a very good point.

-Diplomat

Re: Hypothetical Question
 

[ QUOTE ]
I would turn this around and ask what hands you are prepared to call face up Kings with?

[/ QUOTE ]

Let me think about this for a while.

Re: Hypothetical Question
 

Zero because it would be a table of one.

-f

Re: Hypothetical Question
 

[ QUOTE ]
Zero because it would be a table of one.

-f

[/ QUOTE ]

Actually, several people in this thread have claimed KK face up is $0 and might even be negative. If a few more agree we might be able to get this game going.

-eric

follow up question
 

What is the weakest hand you can play profitably face up under the given conditions?

good luck.
eric

Re: Hypothetical Question
 

I think your point re: not folding ever has some merit... but "outplaying" encompasses a lot more than just making us fold winners. It has come to mean "bluff someone out" on here I guess... but that is not exactly what I meant. Jason_t said what I was thinking in a better way, relating it to the FTOP.

Re: Hypothetical Question
 

[ QUOTE ]
I think your point re: not folding ever has some merit... but "outplaying" encompasses a lot more than just making us fold winners. It has come to mean "bluff someone out" on here I guess... but that is not exactly what I meant. Jason_t said what I was thinking in a better way, relating it to the FTOP.

[/ QUOTE ]

The fact that your opponents will play perfectly does not mean that you will not make any money. FTOP is written the way it is on the assumption that you are going to get the same cards as your opponents. If you get the same cards yes, the person that plays closest to perfect wins. In this thuogh, the cards are not evenly distributed. You are being deal a group 1 hand every time!

You won't turn a profit above the true value of your cards, but KK is simply so much better than your opponent's random holdings that you will turn a huge profit. Of course, if you played your hand perfectly, you'd make even more, probably 50% more profit.

Anyways, I've done a bunch of math in this thread to how kings at about $1000 / hr. You'll have to give some non-qualitative arguments if you want your claim of break-even to be convincing.

good luck.
eric

Re: Hypothetical Question
 

If this is the canterbury 30/60 game, Im pretty sure most of the hands would still be multiway capped preflop anyways. Im thinking youd make like $10,000 per hour [img]/images/graemlins/smile.gif[/img]

edit to say its probably closer to $20k/hr if Jimmy or Dennis is in the game.

Re: Hypothetical Question
 

$1458.20/hr.

Lawrence

Re: Hypothetical Question
 

FWIW, after reading some of your explanations and thinking about it some more, I realized my thinking was flawed before. I'm still not sure it's $1500 profitable, but it certainly is a profitbale game (over $500/hr I'd think).

In a no limit situation, this situation could certainly be -$EV if the stacks were deep enough, but I guess that's a different question altogether.

I also ignored the "typical game" disclaimer initially and assumed that your opponents would be playing optimally against you. That made a big difference as well, as Barron brought up some excellent points regarding that aspect of the question.

Re: Hypothetical Question
 

[ QUOTE ]
$1458.20/hr.

Lawrence

[/ QUOTE ]

If everyone folds every hand, you only make $1620, and you'll run into aces nearly twice an hour. This estimate is too high.

-Eric

Re: Hypothetical Question
 

My claim was based on a number that I made up because I didn't think it would be as high as people were saying. At no point did I ever think my claim would be convincing... nor is there any math on earth that would make it so.

I was thinking along the lines of the pocket aces situation that Matt Matros talks about in his book where you could be dealt them every hand and be -EV if your opponent knew you had them. That was a no-limit scenario though and is not really applicable here.

good luck.
tpir

Re: Hypothetical Question
 

Assume:

1. The blind structure is a $15 SB and a $30 BB.
2. You raise with your KK preflop every hand.
3. If you are called you will employ a strategy of betting every street unless you are raised, wherupon you will check/call down.

Then

1. The only hands that are correct to call you when not in the blinds are AA and KK.
Reason: The hand is only getting 7:4 immediate pot odds to flop a winner or a draw worth continuing with.

2. The only hands that are correct to call you out of the Small Blind are AA and KK
Reason: The hand is only getting 7:3 immediate pot odds to flop a winner or a draw worth continuing with.

3. The only hands that are correct to call you out of the big blind are AA, KK, and AXs.
Reason:
The 3rd conclusion requires a little explanation. The big blind is getting 3.5:1 immediate pot odds. If he has an Ace in his hand, he cannot call your bet on the flop if the flop doesn't have an ace. This means that AXo doesn't have the proper odds (4:1) to call just to hit an ace (or possibly flop a straight or trips with its kicker) on the flop. AXs on the other hand, DOES have proper odds to call.

So, if they employ any strategy other than calling with AXs, AA, KK from the BB and AA,KK from any other position, you will GAIN over them employing just the above stretegy.

This means we can reach a lower bound on your earn by computing how much you'll make from your opponents employing the above strategy.

Stealing the blinds for a round will gain you:
1.5 SB * 8 + 1 SB + 0.5 SB = 13.5 SB.
ROUGHLY once every 2.5 rounds (9 players * 25 hands = 225 hands dealt) someone will be dealt AA, whence you will lose a maximum of 18 SB with your strategy.
I will neglect the case you run into 2 AA's and the case you run into both AA and KK.
You will also run into KK roughly once ever 2.5 rounds, whence you will usually split the blinds.

Roughly once every 3 rounds(46/1326 ~ 1/29), someone will be dealt AXs in the big blind, but I will assume that you will break even with in this case, since their call is marginal.

So my rough estimate to a conservative lower bound on your earn per hour is:

[13.5SB * 2 rounds +
1.35SB * 2 hands -
18SB (lose to AA) +
0.75SB (chop with KK) +
0SB (BB has AXs once every 3 rounds, fudging it to 2.5)
= roughly 12.5 SB won every 2.5 rounds.

In one hour there are 4 rounds =>

Win rate = (4/2.5) * 12.5 ~ 20 SB/hr =

10 BB/hr or $600/hr

If players play badly, you can make much more than this. But in a game where you're not quite making 1 BB / hr straight up, you would expect most people to properly respect your KK.

Also, no one would play with you if you got KK face up every hand. This is purely a hypothetical example of theoretical value. So arguments factoring boredom of your opponents, etc. into the analysis don't make much sense to me. If you are going to assume you can get a 10 handed game going where you get KK every hand, you might as well assume everyone keeps forgetting that you had KK the previous hand and that your exposure of the current hand happened accidentally.

-v

Re: Hypothetical Question
 

I've replied twice, and you've deleted twice. Now I'm just going to say... wrong. You figure out why!

-Eric

Re: Hypothetical Question
 

Here are some points for you to consider:

You should look at implied odds, not immediate odds, when deciding what hands are playable against the KK. Ax is definitely playable from either blind and probably outside the blinds as well, although somewhat marginal there.

You'll chop with KK much less often than you'll lose to AA.

You're doing a lot of rounding in your final EV calculation that is going to throw off your answer somewhat.

You're basically on the right track though I think, you just need to be more precise about how often the different events occur.

good luck.
Eric

Re: Hypothetical Question
 

Here are my thoughts, which are along the lines of Eilindauer's.

According to the fundamental theorem of poker, your opponents will always be gaining against you, and you will always be losing; but, this is far outweighed by the power of your holding.

(1) With K's face up, you should raise every time preflop (very important).

(2) Always bet, never re-raise, and always call down (this could be modified, but this strategy keeps it simple)

Only AA has equity against you, and one of your 9 opponents will have it a little more than twice an hour, say 3 times. So 37 times an hour you win the blinds ($50) and 3 times an hour you lose 90 + 30 + 90 + 90 = $300. (when in position, you call, when first to act, you bet and call a raise, so the average is 90 on the turn and river)

You'll be making 1850 - 300 = $1550.

Once your opponents see that they can't bluff you, they will stop calling with anything but AA. Or, they will go broke.

Sparks

edit: should probably be 120 on the turn and river since your opponents will quickly learn to c/r you with AA.

Re: Hypothetical Question
 

[ QUOTE ]
I was thinking along the lines of the pocket aces situation that Matt Matros talks about in his book where you could be dealt them every hand and be -EV if your opponent knew you had them. That was a no-limit scenario though and is not really applicable here.

[/ 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?

Either way... yeah... thinking along these extreme lines far overstates the impact that your opponent's knowledge of your cards is going to have. You'll make much less money than KK face down... but you'll still make a ton of money.

-Eric

Re: Hypothetical Question
 

i must be getting good because my first answer was "an awful lot" and then i went straight to your answer and saw i was right. so now i dont even need to look at all the other answers ill just wait until sklansky posts his in about a month.

Re: Hypothetical Question
 

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

Re: Hypothetical Question
 

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

Re: Hypothetical Question
 

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.

Re: Hypothetical Question
 

[ 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.

Re: Hypothetical Question
 

</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.

Re: Hypothetical Question
 

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

Re: Hypothetical Question
 

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.

Re: Hypothetical Question
 

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.

Re: Hypothetical Question
 

[ 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?

Re: Hypothetical 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

Re: Hypothetical Question
 

[ QUOTE ]
[ 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.

[/ QUOTE ]

that's wrong as well. folded to SB who makes a raise small in comparison to both blinds stacks, at that point SB's hand is revealed to be AA (both players know the BB knows). with what range of hands can the BB profitably call? DS says all hands.

Re: Hypothetical Question
 

[ QUOTE ]
[ QUOTE ]
[ 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.

[/ QUOTE ]

that's wrong as well. folded to SB who makes a raise small in comparison to both blinds stacks, at that point SB's hand is revealed to be AA (both players know the BB knows). with what range of hands can the BB profitably call? DS says all hands.

[/ QUOTE ]

And he's right. Although I heard about this as a problem given by Chris Ferguson a few years ago at an rgp convention. The idea is that the implied odds of outflopping combined with the opportunity to three-barrel bluff, two-barrel bluff/semi-bluff, and one-barrel bluff/semi-bluff each with optimal frequency make it impossible for AA to profit.

The reason Sklansky had to use KK instead of AA for a limit example is the opponent can't make pot-size bluffs so correct bluffing frequency is much lower. I.E. AA is correct to just call down. I'm not convinced KK is.

Re: Hypothetical Question
 

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


[/ QUOTE ]

Ahh yes. Note that the blinds are 20 and 30. Also, I'm not so sure that Ax is profitable. Even with Ax suited, it only wins 1/3 of the time when going to showdown.

Revised formula for win rate:

(37 x 50) - (3.7 x 50) = 1665
3 x (90 + 60 + 120 +120) = 1170

So if you play like a robot, always bet, call, and don't re-raise, you'll make 1665 - 1170 = 495/hour. The above equation assumes the worst case scenario when you're in the blind and get three bet PF for $90. In reality your profit would be a little higher than $495.

Sparks

Re: Hypothetical Question
 

[ QUOTE ]
. Ax is definitely playable from either blind and probably outside the blinds as well, although somewhat marginal there.

[/ QUOTE ]

Are you assuming a raise every time PF from KK? If not, you should be, I think.

Sparks

Re: Hypothetical Question
 

[ QUOTE ]
[ 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?

[/ QUOTE ]

Ha. Good question. I find it interesting for two reasons:

1. I think the first step to understanding poker well is seening how the game would be played with perfect information. This question is a bit more complicated than that base case, but still provides some intersting math and discussion about bluffing frequency etc.

2. It's interesting to compare your expected win when your cards are known to the average win of KK when dealt face down. It helps put a real number on the value of deception.


I can see that it's a somewhat theoretical concept though that might not interest you. I'm sure you could be a great poker player and never think about things like this.

my 2 cents.
Eric

Re: Hypothetical Question
 

[ QUOTE ]
[ QUOTE ]
. Ax is definitely playable from either blind and probably outside the blinds as well, although somewhat marginal there.

[/ QUOTE ]

Are you assuming a raise every time PF from KK? If not, you should be, I think.

Sparks

[/ QUOTE ]

Huh? Of course I'm assuming KK raises. If there was no raise, we wouldn't be having a discussion about what hands were playable from the big blind! [img]/images/graemlins/smile.gif[/img]

-Eric

Re: Hypothetical Question
 

[ QUOTE ]
I'm not so sure that Ax is profitable. Even with Ax suited, it only wins 1/3 of the time when going to showdown.

[/ QUOTE ]

Hi Sparks,

You don't have to show it down just because you called the flop. Ax is definitely playable from the blinds if KK will call down an ace-high board.

good luck.
eric

Re: Hypothetical Question
 

I think that your opponents don't know you have pocket kings for the sake of this example

Re: Hypothetical Question
 

I am right in thinking that if someone chose to play sub-par hands with some potential against you, hoping others would enter the pot with them, that the KK would be worse off if several pots go four or five way?

And players will be "colluding" in an honest non-colluding way against you still, in multiway pots. You can probably see why in a three-way, more bets are going to go in between two-pair (having the KK beaten of course) and a straight.

Lars

Re: Hypothetical Question
 

I am right in thinking that if someone chose to play sub-par hands with some potential against you, hoping others would enter the pot with them, that the KK would be worse off if several pots go four or five way?

And players will be "colluding" in an honest non-colluding way against you still, in multiway pots. You can probably see why in a three-way, more bets are going to go in between two-pair (having the KK beaten of course) and a straight, as long as the KK is still in there paying off bets too.

Lars