Rush

I really ought not to play on the second Tuesday of the month (ok, yesterday was the third Tuesday of the month, but it was my second Tuesday, after returning from LV).

I absolutely dropped my bollocks, to the extent that I got as far as opening up Pokertracker to start doing some research. Then I thought "fuck, I'm tired, and I have no idea where to start. I'm going to bed".

Clearly either I have got worse or my opponents have got better, and there are serious leaks somewhere. I suspect that at UB (where my results have got worse month by month since December, culminating in a minus $400 for April) I've shifted from +0.7BB an hour to something like minus 0.5BB. So it's a matter of finding one-point-five BB an hour somewhere to get that back.

At the moment, it looks to me to be top-pair-top-kicker territory. Opponents simply aren't semi-bluff raising me enough on the turn. The result is that my three-bet gets either picked off as a four-bet (do I cry-call to the end, do I fold?) or flat-called and then I call the river, and lose.

The problem with this is that it's counter-intuitive, because the call only has to be right about a quarter of the time, so you might feel the call is a losing play when, in fact, it isn't.

That's part of my general feel that opponents are getting out very early if they can't beat TPTK, and are flat-calling the flop and raising the turn if they can.

I can think of various possible counter-plays to this, but I can't really think which one is best.

I can also think of several metagame solutions (play something else, play lower levels, spend more time finding good games, good seats, don't play at all, just play at weekends, focus on NL, focus on MTTs, etc).

I'll really have to do a diligent trawl of a whole host of hands/scenarios. I'm fairly sure I'm doing something seriously wrong on either the flop or the turn (the numbers for the river and pre-flop don't look so bad) which is turning a winning scenario into a losing one. All I have to do is find out what the flaws are, and that is a long slow job.


+++++++


Mr Bowles responded in a PM about my previous piece, stating that it reminded him of two articles by Thomas and Chris Ferguson. The algebra was a little bit beyond me, but I understood the conclusion. In fact the article is covered in very similar ground by Chen & Ankemann in The Mathematics of Poker

Where I depart from this line of thought is that Ferguson and Ferguson "solve" the problem with optimal play on both sides. As was observed in another poker book, if you are playing against a player who is playing optimally, you should find another opponent.

Andy Ward has adapted his own style in tournaments on just these empirical grounds. Opponents do not tend to play optimally, so your all-in pushes have to be adapted in strength to adjust for an increased likelihood of folding. Note that for Andy's numbers, he doesn't need to adjust his hands for an increased likelihood of calling, but he could adjust the M factor upwards. Hmm, I hadn't thought of that before. That's a point worth following up.

So, I am not attempting to solve heads-up poker betting games, but to look for a system that provides the best play, no matter how sub-optimal your opponents' play is

As the Fergusons observed, in their game the "range" of bets goes; bet your worst hands, then check-fold, then check-call, then bet your best hands.

However, if you are up against an opponent who folds very rarely, the range of "bet your worst hands" shrinks. Against an opponent who folds often, this range increases.

Chen & Ankemann don't like this fuzzy line of thought. They say that opponents are dynamic. That they learn.

Indeed they do, and part of the skill in poker is staying one step ahead of them. If the opponent learns enough to play optimally, then you go somewhere else (a 'metagame' concept not touched upon by Chen or the Fergusons, because it is outside their remit).

What I would like to get is some system that distills a player's PT stats into an empirical likelihood. That gives a decision on whether to bet or not.

I know that this is straying somewhat into bot territory, which isn't what I'm aiming for. I want to create a system that can be applied aby a player, in real time, with some accuracy, that doesn't descend into the vagaries of "usually", "mainly", "nearly always" or, worst, inaccurate uses of the terms "never" and "invariably".

PJ

Duvet Stuffing Part One

Just to show how frustrating this R&D stuff can be, here's an hour's work (without looking at a single specific hand, just looking at the stats).

I analyzed 27,000 hands from Jan 06 to Nov 30, and 16,000 hands from Dec 01 06 to the present, all on Ultimate Bet, at all levels, where I raised first in, regardless of position, and there had been no previous callers.

I analyzed it for all hands, and specifically for AKo.

For these two periods I was up $540 (in open play) for the first period, and down $301 for the second period. The net result after bonuses and rakeback was plus approx $1800 for the first period and plus $$500 for the second period.

One would, therefore, expect a deterioration between period one and period two.

Not so.

1: OVERALL FIGURES

Jan-Nov 2006: All hands, +0.38BB per hand (+$2,495).
Jan-Nov 2006: AKo, 0.35 BB per hand (+$187.50)

Since Dec 2006: All hands, + 0.51BB per hand (+$2082.75)
Since Dec 2006: AKo, +0.66BB per hand (+$149.25)

Jan-Nov 2006: Won when saw flop: 47.72%
Jan-Nov 2006: AKo won when saw flop: 51.28%

Since Dec 2006: Won when saw flop: 52.29%
Since Dec 2006: AKo won when saw flop: 57.14%

Jan-Nov 2006: Went to showdown: 33.36%
Jan-Nov 2006: Won $ at showdown: 61.52%
Jan-Nov 2006: AKo went to showdown: 36.36%
Jan-Nov 2006: AKo won$ at showdown: 62.5%

Since Dec 2006: Went to showdown 36.39%
Since Dec 2006: Won $ at showdown 62.99%
Since Dec 2006: AKo went to showdown 43.24%
Since Dec 2006: AKo won $ at showdown 62.5%


In other words, there's a consistent improvement of my performance across the board when I have raised first in.

I broke this down into hands that went to showdown, hands I won without showdown, and hands where I folded pre-showdown.

SHOWDOWN HANDS

Jan-Nov 2006: Went to showdown: won 1.23BB per hand ($1,901)
Jan-Nov 2006: Went to showdown: AKo won 0.93BB per hand ($120)

Since Dec 2006: Went to showdown won 1.38BB per hand ($1,454)
Since Dec 2006: Went to showdown AKo won 1.27 BB per hand ($80)

Interesting to note that AKo actually does worse than average at showdown than the "average" raising hand. However, figures are once again better for the past five months than the previous eleven months.



I FOLD PRE-SHOWDOWN

Jan-Nov 2006: Folded for -1.81BB per hand (minus $3116)
Jan-Nov 2006 AKo folded for -2.02BB per hand (minus $193)

Since Dec 2006: Folded for -1.76BB per hand (minus $1,706)
Since Dec 2006: AKo folded for -1.91BB per hand (minus $90)

Although the figures are an improvement, and although the net figures for AKo are positive, it's interesting that AKo wins less than average when you go to showdown, but loses more than average when you fold. Is this inevitable? Or am I continuation-betting too often? Note that AKo wins pots more often than the average hand when you see a flop, so the only conclusion you can reach is that it wins small pots and loses bigger ones, because (presumably) of the continuation bets when you miss.

A possible conclusion from this is that I shoulc continuation bet less. I've already abandoned a CB if I have three or more opponents and I miss. I'm wondering about abandoning it if I have two or more opponents and I miss, particularly if the texture of the board is distinctly horrible (say, J98 two of a suit or three of a suit).

The final numbers just complete the picture, hands where I won without showdown:

Jan-Nov 2006: Won without showdown for 1.16BB per hand ($3,720)
Jan-Nov 2006: AKo won without showdown for 1.16BB per hand ($246)
Since Dec 2006: Won without showdown for 1.17 BB per hand ($2354)
Since Dec 2006: AKo Won without showdown for 1.16BB per hand ($126)

Is this a statistical anomaly that all the numbers are so similar? Probably not.

For all my frequent raising hands, the range was from 0.96 to 1.5 BB per hand (we can perhaps look at the performance of various hands when we do go to showdown at another time). For my "rarer" raises (poorer hands that I would only raise with as a steal, and then not 100% of the time), the average win per hand looks slightly higher, but that might be counterbalanced by a greater number of preflop folds and a poorer performance at showdown. That might be worth looking at.

So, conclusions.

My raising first in has improved, so this is not the reason for the deterioration in my results.

However, some general points are of interest. 1) AKo does worse than average when you raise with it first in. (Interestingly, it does better than average if you raise first in with it from the CO or the button). I suspect this might be because a number of opponents "put" you on AKo as the default if you raise from a non-steal position.

Possible conclusion. Limp first-in with AKo from non-steal positions?

Or, possibly, limp first in with AKo half the time? Then you can either call or reraise a raiser behind (depending on that raiser's aggression factor and the number of other players in). If there is no raiser behind, you just get away from the hand if you miss. If you hit, play it aggressively to the end, going into call-down mode if there is a lot of action against you.

And I must remember that this is just for Ultimate Bet. It will be interesting to see how the numbers for Party (where I have a far larger hand database) and Full Tilt (smaller database) compare.