Limit Holdem Hypothetical Question

[timmer]

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?

[superchoatie]

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.

[knife420]

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

[TomBrooks]

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.

[Lester B]

[ 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.

[Poliorcetes]

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?

[jackaaron]

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.

[KingJtheStandard]

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

[big show]

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.

[Poliorcetes]

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