Hypothetical Question

[David Sklansky]

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.)

[ALL1N]

$1300/hr at 40 h/hr.

[catlover]

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.

[ALL1N]

[ QUOTE ]
David that seems like a very difficult question.

[/ QUOTE ]

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.

[catlover]

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.

[ALL1N]

[ 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.

[/ QUOTE ]

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?

[jason_t]

[ 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

[/ QUOTE ]

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.

[ALL1N]

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.

[Eric P]

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

[Shandrax]

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.