Mathematics of Small PPs UTG (or early)

[waynethetrain]

I've been reading a lot of the former discussion on playing small PPs from UTG (and early) position. Some of the mathematics seems to indicate that you have to make up "X" number of SBs for all your limps when you win for it to be +EV. The assumption is generally 12% probability of hitting your set and 75% or more pot equity when you do.

I have to question these assumptions.

Either I am misunderstanding the mathematics or everyone else is overlooking something. I will hit my set about 12% of the time. 75% pot equity seems like a reasonable assumption based on my own results and millions of hand simulations I have done with TTH. However, I believe people aren't giving enough weight to the losses incurred when you do hit and don't win.

You are almost always playing to the river. So that's a minimum of SB, SB, BB, BB = 3BBs lost. However, it is likely to cost you much more than that because you will certainly look for an opportunity to raise with you set. Furthermore, among the hands where your set lost, it is extremely likely that you were re-raised by a flush or straight. So it cost you even more than usual.

I know some of the best players here insist that limping with small PPs from UTG is correct on generally loose/passive tables. However, based on my observation of average pot sizes on most of the loose tables I play on, I don't have nearly as much confidence as others that these are profitable plays unless the tables are extremely loose (which IMO is much rarer than almost anyone here seems willing to admit). I can't see how you can make up all these losses with a win without the PP occasionally holding up on its own (which is very rare on a very loose table in which you would tend to fold non sets)

I am far from expert and don't even play the small PPs from UTG yet. I'm still having a tough time winning with the mid pairs from middle position /images/graemlins/grin.gif, but I think it is worth revisiting this topic again unless someone has a sample size that is huge.

Most of the large sample stats I have seen on playing small PPs early indicate that they are losers for the "average" micro limit player. Now that doesn't mean they are losers for the average 2+2 player, but it seems so obvious that if you do decide to play them, it should be easy to do so even for a novice. Once you see the flop and know whether you have your set or not there is not much of decision very often. So I don't see where all the 2+2 added value is coming from relative to the average low limit playing that is losing money with these hands. They are easy to play once you decide to do so.

[DeadManJay]

You're going to hit a set on the flop about 1 time in 9. You will win with those sets at least 75% of the time so lets say that you will win with your set 3 times out of the 36 times and lose a set 1 time in the 36 times you see the flop with a small PP. So you've lost around 17BB there? The time you hit and lose you will lose around 4-6BB? We can round that number up to ~24BB total lost in 33 hands. We only need to win ~8BB each time we win with our sets to break even, anything more is EV+

Warning! this is just an attempt at math by a not so intelligent person /images/graemlins/grin.gif

EDIT: These numbers don't include the times that your PP will be good at SD, or the times that it is checked through and you hit your set on later streets. I think you could safely bumb a BB off of my numbers and still be safe just winning 7BB.

[jrz1972]

[ QUOTE ]
Furthermore, among the hands where your set lost, it is extremely likely that you were re-raised by a flush or straight. So it cost you even more than usual.

[/ QUOTE ]

Yes, sometimes you will make your set and lose to a straight, a flush, or the dreaded set-over-set. It happens.

However, sometimes you will fill up and win a ton of money off somebody overplaying his flush. Sometimes you will be the guy with the bigger set and you'll win a huge pot off the smaller set. Recently, I've two hands in which I held XX, the flop came down XYY and I was able to cap both expensive streets against a player holding Y-rag.

These sorts of hands don't happen all that often, but in the micros, you get paid off like there's no tomorrow when they do.

I put small pockets in the same general category as AXs. It's more or less a break-even hand at best except for the occasional huge pot you drag once every several thousand hands. It's those big pots that make these hands good plays.

[aron]

Another aspect is flops getting checked through and you hit a set on the turn.
This won't happen that often but it does in some tiny way improve the number of times you make your PP a set.
And of course on those occasions the final pot will be smaller than otherwise.

-aron

[Carmine]

Also take into consideration the times you miss your set but still go on to win the pot. This will balance out the times you make the set but lose at showdown. Also if you are not at a loose enough table then you just don't play em up front.

[DeadManJay]

The more I think of this the more 7BB makes sense to me. It's recommended that you have ~5 callers PF for this to be a call. 5 callers PF give 2.5BB. If 4 stay around on the flop you're up to 4.5. 2 callers on the turn puts us at 6.5 and 1 caller on the river would come out to 7.5. This is a very rough guess, but I believe this is the reasoning behind wanting so many callers PF.

[kenberman]

[ QUOTE ]
Now that doesn't mean they are losers for the average 2+2 player, but it seems so obvious that if you do decide to play them, it should be easy to do so even for a novice. Once you see the flop and know whether you have your set or not there is not much of decision very often. So I don't see where all the 2+2 added value is coming from relative to the average low limit playing that is losing money with these hands. They are easy to play once you decide to do so.

[/ QUOTE ]

I agree with most of this. The key is knowing when to fold, which is the problem most bad players have. PP's look pretty to lots of people, and they have trouble folding them to 1, 2, or even 3 overcards. like many other things in poker, it's the discipline that's key.

[waynethetrain]

[ QUOTE ]
We only need to win ~8BB each time we win with our sets to break even, anything more is EV+


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This seems like a reasonable estimate.

I believe that estimate is a tough target though. 8BBs is $16 at $1 - $2 (where I play). That's a fairly large "average pot" to hope for on the winning flopped sets relative to the norm for $1 - $2 (when you add my contribution). You really have to hope for not only 4-5 limpers, but multiple players seeing the turn etc...

I'm going to continue tracking my results with the mid pocket pairs UTG before I expand into the low ones. I suspect there isn't enough evidence to encourage everyone to make this play except under extremely loose conditions (that I rarely if ever see).

[parappa]

In general I agree with you. Mho is that people who are saying "you should generally limp UTG with 22" are really saying "you should generally be playing at tables where it is correct to limp UTG with 22." The two statements are completely different. This is entirely game-dependent. I defy anyone to get on 1/2 waiting lists at random, sit down at a table with 2 rocks, 3 tags, a fish and 4 unknowns and make a profit from small pairs or Axs UTG.

[waynethetrain]

I think it's extremely difficult to find a table that makes those hands playable even if you are scouting for them. I rarely find one that stays that loose for more than an orbit or two. The player turnover is too fast.

[GrunchCan]

[ QUOTE ]
Mho is that people who are saying "you should generally limp UTG with 22" are really saying "you should generally be playing at tables where it is correct to limp UTG with 22."

[/ QUOTE ]

Bingo.