Optimal maths poker isn't natural or intuitive for many and the math is only one aspect of poker. The requisite to fold for equity rather than chase for excitement is also unnatural psychologically.
Sometimes I miss my Limit Hold'em and as I learn other games I find that I struggle to win at it now. I used to win at $5/$10 consistently (when the games were much softer) and have played up to $20/$40 occassionally. But Adam's suspended blog got me thinking when I watched his hands play out. It reminded me how frustrating the game can be if you don't have the confidence in your own actions and focus on getting it in good.
Today, there appears not to be much wrong with Adam's play. He has recently posted about a new LAG approach though which inherently incurs more variance and attracts action so you will take more bad beats. That aside, I read a snippet last night in "Small Stakes Hold'em" by Ed Miller (I recommend it). The maths seemed so wrong that I was going to check it out. Turns out (no surprise with Sklansky and Malmuth at the helm) that it was spot on.
Using PokerStove Monte Carlo simulation(www.pokerstove.com), with 5 opponents willing to take a flop with 40% of their hands {44+,A2s+,K2s+,Q5s+,J7s+,T7s+,97s+}, which doesn't seem to be unreasonable looking at what reaches showdown with Adam.
The book states that with AA you should be jamming on a dry board with almost 50% equity, but with TT in this spot you should be calling because your equity is closer to 21%. I was amazed! I extended the simulation to see the spectrum. The inter-pair gap gets greater with higher pairs, for the record -
AA thru 22 is 42.3%, 33.2%, 27.5%, 23.6%, 20.4%, 18%, 16.5%, 15.3%, 15.7%, 14.9%, 14.2%, 13.9%.
My interpretation is something that I've experienced and posted about before. When playing against 5 loose opponents willing to get to showdown with marginal hands and draws:
- QQ thru 99 are really middle pairs; (Adam inspired this insight)
- 88 is the cut-off where you are becoming a dog.
- 77 thru 22 are set mining hands with implied odds - flop or stop.
BRAINTEASER : I've run the simulator a few times ... why does it always deliver the pre-flop equity for 77 to be 15.3% while 66 is 15.7%, at first glance an anomaly?
TRUST IN MATHS? Even if you "knew" all the other players starting range was 40% (and the maths above), would you ever prefer 66 preflop over 77?
1 year ago
4 comments:
I'm guessing that your simulation prefers 66 to 77 because the hand ranges you are simulating against include more sevens (T7, J7, Q7) than sixes, and therefore 66 has a better chance to spike a set.
I'm not certain that I understand clearly what the Miller book is claiming there. What do you mean by a "dry board"? Are we talking about a flop of undercards? I would expect TT to have considerably better than 21% equity on an undercard board. Preflop, it could well have a very poor equity against players willing to call a raise with hands like Ax, Kx, Qx.
Are your stove calculations preflop equity against those specific hand ranges?
One important point about middle pairs against overcards, is that a pair like TT has value unimproved, whereas overcards need to hit the board to win. What this means is that even though KJ vs TT is a theoretical coinflip, TT has a big advantage in practice since KJ might be forced to fold on boards before it can hit a winning card on the turn or river. Pokerstove cannot represent this practical difference.
No wonder you're a winner, and apologies to the original authors. The flaw was my paraphrasing as the book section was about playing overpairs - in which 22 is a greatly flawed extrapolation obviously.
My simulation was indeed preflop equity against those ranges. I ran it with a 972r flop and the results were similar, but not as large of a % edge as preflop for AA thru TT.
And I knew the 77 wouldn't stump you for more than a millisecond. And yes, I've folded many a hand that I couldn't continue with that would have been statistically in front because of board texture.
Yesterday OMGClay was on a podcast talking about a hand that he would fold in PLO with vulnerable flop nuts because there just isn't any Turn card that he can be happy about as the board was so draw heavy.
A thought that I have just had is how much poker players remember about hands.
I still remember vividly a K9 hand in Dublin that I played in 2003. And a FH in Sydney from earlier that year when I found out that heads up there is no cap on re-raising the river. Needless to say my 2nd nut lost both times.
But a memory that preceded both those was an old pro in Crown Casino, Melbourne when I was the nittiest player at the table. It would have been my 2nd or 3rd time at a casino. I never lost much, if at all as an Ultra-nit.
This particular hand, I went to showdown with a strong hand that I can't remember, but was beaten by the pros 25o. Another pro to my left laughed "always the top or the bottom". I knew what he meant, but have only in recent months added it to my game all these years later.
In NLH, occassionally hitting that hand amongst newbies is a goldmine. Especially if the A completes the wheel.
I handle pocket pairs at live 20/40 in a way that seems to be in line with what you're saying here:
I will open raise pocket 7s or better from UTG. I will limp the smaller pairs. As I move closer to the button, though, things change.
From the button or one off, any pair is a raise to open. From a few spots right though, if nobody has entered the pot i actually fold the smallest pairs, as they are not strong enough to raise and aren't likely to see a multiway pot.
Thanks Jesse, your last comment on MP play when everyone before you folds is something that I hadn't really thought of ... cheers.
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