Math in Harrington

First of all a happy NEW YEAR everyone !

I know a lot of you have read or are reading Harrington, I have finished part one during the holidays and found it very interesting.

However there's a sample of a hand at page 150 that involved quite a bit of math, it's not so difficult but I don't see me doing that in the short time period you have on-line (not every site has an extra time-option).

I have to admit I was never excellent at math but there's more to poker than that, does stuff like on page 150 come easily to the most of you all or is it just me who finds this difficult ?

give us a clue.. what does he say on page 150?

Thanks Stu. Not all of us have our copies close to hand. Mine are at my house and, unfortunately, I'm not.

Harrington on Hold'em Volume 1?

5/5 in hijack position (2 off button) with $2,130 with $50/$100 blinds. Equal'ish stack except for SB at $550. UTG+2 limped, the rest folded.

You call, and the SB shoves. Everyone else folds.

The SB is identified as a tight player, and the problem asks if you are justified in calling.

Harrington figures out all pairs in his range that have you crushed, and all the overs that you have barely beat.

You do not need to do this math each time. This is a pretty common situation in tournaments. It's an easy call if he has overs (as you have the best of it) and it's a bad call if he has an over pair, as he has you crushed.
Just remember that with small pairs like this 2:1 is fine for calling. At about 1.5 to 1 it gets dicey and you should consider giving it up.

LOL are you looking at his cards? Say you didnt know if he had overcards or an over pair.. In general would this situation be a call or fold?

Personally I think it would be a fold

The more familiar with the math you become away from the table the easier it is to identify the optimal play when situations come up...Honestly I am still trying to get more familiar with math and I think good players are always looking at trends and how to best exploit them.

I don't go through complete calculations in my mind each time I act... I put the villian on a range in my mind and have a rough idea about the math driving my decisions. If it is a close decision I may tank a bit
to do some very short/rough calculation...but usually my decision is more read driven at that point. (I play all cash games live [because I live in Wa])

The point here is that you give yourself a rough guesstimate, and then act according to the available odds.

This becomes easier in time.

The "math" he was referring to assumed that the tight guy would shove with overpairs or 6 possible unpaired hands. If you're up against that range, it's a call. Of course you can't see his cards. But assuming he has unpaired overs or an overpair in that range, it's a nice call.

You win about 20% of the times he has an overpair, you win more than half of the times he has two overs. Since there are a lot more overs you need roughly 1.5 to 1 to make it a +EV call. You're getting 2:1, which is substantially better.

If it was a loose player he could be doing this with "any ace" type hands and it's an insta-call.

Basically Harringon broke it down to 150 different card combinations the guy could have and if you played them all out, and you can expect to win 62 times and lose 88 times.

So yes, you should expect to lost this pot most of the time (88 times out of 150) but since you're getting 2:1 on your money and you're not losing twice as often as you win, it's a +EV call.

In other words, it's like getting $2 if you win and losing $1 if you lose. You lose 88 times for -$88, and win 62 times for +$124 so over the long run you're up $36. (Same principle, not the exact percentages though)

Quick head math.
Your M = Roughly 17.5 (Stack/(BB+SB) Not wonderful, but not bad
His M = Slightly less than 3 - Hail Mary Time
Pot odds = Less than 2:1 (550 to win 900).

Conclusion: Bad bet. Fold.

You fold even against a loose player here? M less than 3 he could do this with a lot of hands.

Also, I believe anyone who thinks the math isnt important... is naive. Its like trying to drive somewhere without a map.

Conclusion, favorable situation. Call.

ZZFLOP was just concerned about all the math it took to come to that conclusion. The math just backed up the conclusion. Once you see that situation, you don't have to figure out the chances of winning with each possible hand combination in his range. You just need to know that you need good enough odds, and you do.

Easy call. Also, if you limp with 55 here, you have to have a plan if someone behind raises. IMO, if you're going to fold to the desperate SB shove, you shouldn't limp behind anyway.

The problem for me is that to have any advantage over his range, he has to be playing atleast thetop 40% of hands. He is a tight player and so I would assume he has waited a bit to get a hand he feels is worth playing.. and that is likely within top 40% (checked this out on pokerstove)

Quote from OP: "The SB is identified as a tight player, and the problem asks if you are justified in calling."

Against a known loose player? I'd probably beat him into the pot. Although the pot odds still suck, I figure the read on a player is also hugely important and chips are chips.