Limit Holdem Hypothetical Question

[David Sklansky]

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?

[Banks2334]

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.

[Nut4Dawgs]

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.

[nomadtla]

[ 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

[Blunderfull1]

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.

[Artsemis]

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]

[Lash]

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.

[AaronBrown]

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.

[DcifrThs]

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

[sweetjazz]

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.