Limit Holdem Hypothetical Question
 

Playing nine handed where you are excellent and the others are all equal and OK skillwise, such that your EV is normally one big bet an hour. You now see one the the two cards of the player on your right, every time. You play your optimimum strategy and will not be detected. What's your new hourly rate?

Re: Limit Holdem Hypothetical Question
 

I would rather see a card from the player on my left. I'm not sure I can quantify my new hourly rate(I'm thinking negligible) but I'm sure you have an answer.

Re: Limit Holdem Hypothetical Question
 

My first thought was, "Zero. I'd get caught and tossed long before the first hour was up."

I'm not a theoretician or math whiz, so maybe my next thought is naive/infantile: You're gaining an advantage on 1 of 8 opponents (12.5%). Assume you aren't playing in more than 25 or so % of the hands and he isn't either. Don't you have to factor in how many of the same hands you'd play in?

Unless your play is affected by the knowledge of his card how would the BB average change?

Then, IMO, it seems the unknown card could skew everything.

Re: Limit Holdem Hypothetical Question
 

[ QUOTE ]
I'm not a theoretician or math whiz, so maybe my next thought is naive/infantile: You're gaining an advantage on 1 of 8 opponents (12.5%). Assume you aren't playing in more than 25 or so % of the hands and he isn't either. Don't you have to factor in how many of the same hands you'd play in?


[/ QUOTE ]

You are not only gaining an advantage on him since you will have one more card to eliminate from your odds calculations and one more card to eliminate from all other opponents hands. But I'm no where near the math whiz to quantify this into BB/hr

Re: Limit Holdem Hypothetical Question
 

Im gonna take a shot at this one DS. Alright, your advantage over every player is .125 of a BB/hr. So you have a big advantage over the player to your left. Im gonna say your advantage increases over him to .5/hr because you know half his hand. That makes your new hourly rate 1.375 BB/hr.

Re: Limit Holdem Hypothetical Question
 

What about factoring in the fact that you can now eliminate outs from other players (and yourself). Just speculation, I would think it would change the number but perhaps that's already factored in [img]/images/graemlins/smile.gif[/img]

Re: Limit Holdem Hypothetical Question
 

Theoretically, it should at least double was my first instinct...

*edit, I now see you were talking about only seeing 1 card, I misread it and thought we could see both hole cards of the opponent on our right.

Re: Limit Holdem Hypothetical Question
 

It's hard for me to construct a situation in which seeing one card would make you call or raise preflop when you otherwise would have folded. Seeing the card <u>would</u> make you fold some marginal hands you might otherwise play, for example if you would usually fold a pair of Queens or lower if you saw the player on your right a matching card. You might fold something Ax, if x is less than a Queen and calls with an Ace. Suited cards are less valuable if he has a match to the suit.

So a few times an hour you'll fold a marginal hand that might have cost you an average of small fraction of a BB. Similarly, you might pick up a little equity by knowing an out is gone for you or another player. Both of these effects together are probably on the order of 0.2 or 0.3 BB/hour.

The big advantage is when you and the player on your right are heads up in the pot. For example, if you see a heart in his hand and the board has three spades, you don't have to worry about a flush. Your top pair is far more powerful if you know he has at least one lower card, since he cannot then have a higher pair, and he's less likely to pick one up.

I think this is where the big advantage lies. This might be only one hand per hour, but it could earn you 3 BB or more.

Re: Limit Holdem Hypothetical Question
 

how often would seeing that one card allow you to:

-alter your play to be more profitable than it would have normally been?

-correctly estimate long run odds so that your expectation increases by that slight increase in accuracy?

-outplay others at the table?

and...........

-what is the size of those advantages?

at first glance it looks to be small compared to 3bb but larger as a % of the initial win rate. probably around 20%-50% of 1bb/hr extra at best.

Barron

Re: Limit Holdem Hypothetical Question
 

One consideration to account for is how often you can isolate the player on your right with a raise. You no longer have to continuation bet those times when you know he has paired and you haven't, and you can simply take a free card and fold the turn. That's a significant advantage, depending on how often you end HU against this opponent. If he open raises in early position and you see a 9, then you essentially know his precise hand. It seems that you can 3-bet him pretty lightly, as low as JTo, assuming that the other opponents don't get involved in hands where there has been an EP raise and reraise without very premium hands.

As another example, suppose he open raises in middle position and you know his hand range here is 88-AA, AJ-AK, ATs, KQs. You see a T in his hand. You can now profitably 3-bet AJo behind him, which you normally would have mucked.

In situations where he has a wide range (blind steals), you can always 3-bet his steals, even OOP in the SB, because you can profitably apply pressure on him every time his known card does not pair, while you can simply check/fold when it pairs (and you didn't hit plus don't have outs to continue).

My estimate is that you would gain approximately half a big bet per hour with this information.

Re: Limit Holdem Hypothetical Question
 

the hourly rate increase could vary greatly, if would depend on more the style of the player on my right than on the fact that i can see one card, if he is just a tight OK player as you put it, i might be able to save a few bets as the session goes on, but my winrate will not drastically jump, but if it is an aggresive player like myself the fact that i can see one card will be bumping my winrate for the session drastically as long as the player is willing to stay in the game im bumping my winrate 1-2 bets an hour. A typically good aggressive player could be subjected to isolation and forced to pay out in this situation, while the weak tight just ok opponent on your right will just make you fold the hands u would have folded to begin with

Re: Limit Holdem Hypothetical Question
 

I think this is going to make you change a decision now and then and you could save or make one or two BBs on occassion. If this only happens once per hour, that's pretty easily at least one BB/hour. That's a 100% increase on your regular winrate. I think this is conservative, and 2 or more added BB/hour might be possible.

Re: Limit Holdem Hypothetical Question
 

[ QUOTE ]
Playing nine handed where you are excellent and the others are all equal and OK skillwise, such that your EV is normally one big bet an hour. You now see one the the two cards of the player on your right, every time. You play your optimimum strategy and will not be detected. What's your new hourly rate?

[/ QUOTE ]

I am going to take a stab at this based on a couple of assumptions.

For simplicity's sake, lets assume by 'ok skillwise', he plays 25% of the hands he's dealt including the blinds. Lets say he plays adaquately postflop.

To simplify, lets say I play 20% of the hands I am dealt, and my postflop skills are superb, and everyone at the table knows how good I am.

I will also forgo the variable of the dealer position, and assume all hands are played the same; ala 7-stud.

for the 75% of the time he is not in the hand, you are playing a 51 card deck, knowing one card does not exist. Knowing the identity of that one card when your opponent is out is of little value.

Say we're dealt 50 hands an hour. At 20%, we're playing 10 hands per hour. That means we are making .1 BB per hand we choose to play.

Lets assume knowing that a particular card is OUT of play will never influence whether to play a hand we normally wouldn't choose to play.

But, knowing a particular card is out of play will influence us to fold a hand we'd otherwise play about 5% of the time.

So 80% of the time, we're folding anyway, so it means nothing to our winrate. Of the 20% of the time we'd normally play, 5%, or one hand every other hour, we'll fold a hand because we'd be correct to do so. so if we are gaining .1 BB for every time we play a hand, we gain <font color="green"> .05 BB <font color="black"> extra for folding that hand we'd normally have played.

Of the 10 hands an hour we play, he is in for 25% of them, or 2.5 hands we'll play together. The 7.5 other hands per hour we play are not influenced by this information.

If the known folded card is of mid to lower value, it is unlikely that any of the opponents are holding hands that are likely to be improved by the dead card, since they are known to be 'ok skillwise'. We'll say this is 66% of the time, with 5% variable.

Of the 34% of the time the known card is of higher value, the card will be of value to the opponent probably about 10% of the time.

So 10% of the 7.5 times we will gain. We will gain roughly 2% equity knowing that card is out of the deck. Which, is of rather low EV.

When we're in the hand together, we have a 5% edge because our hand selection is better since we are a better player. Other than that lets assume half the time we will win at showdown and half the time we lose at showdown.

Of the 50% of the time we are destined to lose, 25% of the time we will see it coming, allowing us to limit our losses in those hands. We'll say we lose half as much as we normally would have. So for 2.5 hands, If X is what we win normally, and Y is what we lose normally:

(X-Y) + (Y*.125) (1.05) = Our added EV for knowing one of his hole cards, including our edge because we are a better player. <font color="green">.13 bb </font> gained.

Being an excellent player knowing this information should increase our EV to about 1.2 BB/ HR.

Re: Limit Holdem Hypothetical Question
 

I like the way you break this down, but i think you need to adjust more for the number of hands it would be optimum to play, both when the transparent villain enters the pot. Would you not be looking to isolate with almost any hand because you can get away cheaply on the flop half the time, and outplay him the other half even with junk?

Is it not these situations that need closer scrutiny?

Re: Limit Holdem Hypothetical Question
 

If this poor mope shows you his cards more than twice, tell him. He needs all the help he can get already!

Re: Limit Holdem Hypothetical Question
 

Not much of an increase. How often does that information matter to how you play your hand. You have 83 off soot, you see he has a 2 in his hand PF, it's not like you raise.
Mr. Sklansky I believed you touched on this in one of your books on paying for information.
I leave it for others to elaborate.

Re: Limit Holdem Hypothetical Question
 

This might not be even close to right, but...could you break it down mathematically based on this concept...

When I have (some range), I won't play when he has x. Or, when I have (some range), I will play when he has (some range).

Of course, the rest of the table will make a difference to your play as well, however, with this new information, you would make a slight adjustment.

Re: Limit Holdem Hypothetical Question
 

If i see he has a 2 in his hand, and he limps first in, then yes, i raise with 8/3o.

Re: Limit Holdem Hypothetical Question
 

In what situation. He limps UG? You are going to raise? He limps in the cutoff and the big blind never folds, you are going to raise? My point is there are very few situations in which the information is helpful.
You can come up with a perfect situation in which this information is valuable, but it won't come up very often. It is like worrying what to do when it is folded around to you on the button and you have AA. [img]/images/graemlins/club.gif[/img]

Re: Limit Holdem Hypothetical Question
 

did we figure in or establish how many hands per hour we are getting? and any change we might get considering the information?

Does this figure include the number of correct over calls or non calling wagers we might be making?

Re: Limit Holdem Hypothetical Question
 

I think we can play many more hands per hour, because we want to be in the pot with most of our legitimate hands, and whenever we can isolate the man on our right.

Let's say we hold AJo, and we see villian enter with an exposed card lower than a jack. I think we raise every time here, because we have a good chance of dominating our villian.

If our villian opens the betting, we're in great shape because of our informational advantage. If everyone folds around including our villian, we get the blinds plus our villian's money, which is 2.5 BB. If this situation (everyone folds) happens once every 2.5 hours, we've doubled our hourly rate from 1 to 2 BB. This effect might be even more noticable if our villian raises. Let's say villain is in Early position and we see a 9 of hearts, and he raises. We can reraise with QTo and put villian on a very small range of hands. Since we know he's solid, he either has 99, or A9s (hearts).

Because we know villian is a good player we really almost know BOTH of his cards. (he's not playing 93o, K9o etc. from early or middle position). Thus we're in a position to isolate him with reraises and take down some large pots.

We may also be able to isolate him with lousy hands profitably. Let's say we hold Q3o, and we see the villain has the 9 of hearts. When Villian opens we raise. Now if villian calls, and the flop comes with no 9 and no Ace but overcards to the 9, we can probably bluff him off the hand. if a Q falls we can value bet.

Whenever the table allows us to isolate the villian I think we're going to average several big bets. We're never going to pay off our Villian but he's frequently going to lose to us.

Because of hand selection I think we can treat it as if 2 cards are out of the deck when villian raises or calls from early or middle position.

I'd say we make our 1 BB per hour on our legitimate hands, plus we can enter half the time villain enters (whenever we have at least one overcard to villains card) and we probably average at least 2 or 3 BB on our plays against villain. Since the table is solid yet doesn't catch on to the situation, I think we're isolating villain 50% of the time (4 BB EV?), getting everyone to fold 25% of the time (2.5BB EV) and getting into a screwed up situation 25% of the time (-2BB). This totals out to 2.25BB per tricky play.

So, maybe we have 1.1 BB per hour now on our regular hands, and we're also playing half of the time when villain opens the betting (let's say he plays 4 hands per hour and opens twice). Thus we're getting 2.25BB additional per hour from our sneaky plays.

3.35 BB per hour.

Re: Limit Holdem Hypothetical Question
 

this seems huge. holdem is about isolation and who better than someone right on your right. I'm raising almost 100% of the hands he limps with even if I see an ace. Half of his hand his transparent and if he is at all decent the other card can only be a few choices. I'd 3 bet him with many weaker holdings if he opens and isolate him whenever I have a legit chance to get it HU. This has got to be a bonus of more than 1bb/hr.

Re: Limit Holdem Hypothetical Question
 

i think the isolation factor is certainly the largest to be considered here.

i dont give you more than an extra .5BB an hr tho.

1.5BB

Re: Limit Holdem Hypothetical Question
 

I think there are more things going on here than most people are considering. The knowledge of another player’s card can be an advantage in several ways. The fact that this player is one your right is optimal, as you get to play after him 89% of the time.

First, there are some advantages to knowing the card even when Mr. Right folds.

1) As someone pointed out, the deck is one card smaller, which gives you a small statistical advantage. That by itself is small, probably less than 0.1BB/hr

2) But remember that is not just removing a random card – it is a specific card. Lets say Mr. Right folds a 7 [img]/images/graemlins/heart.gif[/img]. If the flop then comes with two 7’s, or 5-6-8 rainbow, or 3 hearts, your have a huge advantage on the table because you know that the 7H is out of play. I expect the known folded card would affect the flop about 30% of the time.

3) If you hold the same number Mr. Right folds, it helps you to know that your hand is weaker against your remaining opponents. How strong does your KQ-offsuit look against 2 limpers when Mr. Right folds a King? You can expect his card to match one or both of yours (and therefore weaken your hand) about 6% of the time. We need to remember that money NOT lost is the same thing as money gained.

4) A final effect on the other players would be a change in your image. Since you are playing your optimal game, you will start winning more/losing less. This may affect your table image and result in a change in the way that they play you. This by itself may cause another player to be hesitant to face you and may result in more lay downs against you. It is hard to put a value on this, but if it happens only once every other hour, you can see a gain from it.


Of course, when Mr. Right is in the pot, you have a huge advantage and can greatly increase your odds of winning more or losing less money.

5) First, and most obvious, you know one of the cards he is playing. Many people have discussed this already. You can get a pretty good idea of how his cards stack up to yours through the whole hand. This is the biggest advantage and will probably affect about 25% of the hands. Sometimes it will make you more likely to enter and hope to win more, sometimes it will keep you from entering and, therefore, lose less. Again, not losing money counts as a positive gain for you.

6) Your domination of Mr. Right will continue, even when you are not in the hand. You will learn his playing style and be privy to his betting styles, slow-plays, and bluffs. Within a few hours, you will likely have a good idea of what his second card is simply by the way he plays the hands. In other words, you could make the correct move on Mr. Right over 80% of the time. You may as well be playing with his chips.

7) Unfortunately, there can be a small, long-term disadvantage. Your complete domination of Mr. Right may cause him to nearly cease playing with you. While this has an advantage by itself, it will not be as valuable to have Mr. Right folding almost every time you enter a pot. He will probably not stick around for long, but you never know. If he figures it is short-term bad luck, he may lose his mortgage to you.

The effect of all of this is kind of hard to put a precise number on. You will almost certainly play more hands with your added advantage. Lets say you increase from playing 10 hands/hr up to 12. I would put the advantages as follows:

1) 0.1BB
2) 0.5BB
3) 0.2BB
4) 0.1BB
5) and 6) 4.0BB
7) –0.5BB (negative)

For a total estimated effect of about 4.4 BB per hour.

This may even be a low estimate, but it is hard to put an exact number on hypothetical situations.

Re: Limit Holdem Hypothetical Question
 

So Mr. Sklansky,

What say you?

TBk

Re: Limit Holdem Hypothetical Question
 

[ QUOTE ]

7) Unfortunately, there can be a small, long-term disadvantage. Your complete domination of Mr. Right may cause him to nearly cease playing with you. While this has an advantage by itself, it will not be as valuable to have Mr. Right folding almost every time you enter a pot. He will probably not stick around for long, but you never know. If he figures it is short-term bad luck, he may lose his mortgage to you.


[/ QUOTE ]

What your saying here I agree with totally, however since it was stated that "you will go undetected" I think we are supposed to ignore this point. And treat this like the poor sap never catches on that hes been paying you off all night and never getting payed off by you.