Some Math
Fri, 16 Oct 2009

The Back Story

So in IRC today there was some discussion on whether you could shove with less than 50% equity and it could be a +EV play, even if you had no fold equity. This sounded rather wrong, but there was talk of a calculated over at Deuces Cracked called "The Dude" that did these sorts of calculations so I thought I'd check it out.

Lo and behold, when I plugged the numbers in, I found that if:

There is $5 dead money in the pot. (blinds are always going to fold, or something?)

Hero and Villain have $100 effective stacks

Villain bets $16

Hero shoves, and has only 49% equity against villain's calling range.

...then the calculator informs me I need no fold equity at all to make this a +EV play.



The Problem

Now, this seems to make sense as with the dead money in the pot we stand to gain more than we stand to lose. However it also seems very counter-intuitive to be putting more money into a pot with less than 50% equity.



The Math

So I changed the situation somewhat to assume that there was no more betting to come after this (if this assumption changes something and makes the below math invalid, somebody please let me know!) and came up with the following math:

0.51 * -100 = -51 (we're risking 100, and lose 51% of the time)

0.49 * (5+16+84) = 51.45 (we win the villain's stack and the dead money 49% of the time)

EV = 51.45-51 = $0.45

It is indeed +EV. However, let's look at if we had just called the villain's $16 bet instead of shoving over it. (Note: Since villain has a FE of 0 to a shove, our equity against his betting range here is the same as against his shove-calling range, so 49%)

0.51 * -16 = -8 (we lose our call 51% of the time)

0.49 * (5+16) = 10.29 (we win the villain's bet and the dead money 49% of the time)

EV = 10.29 - 8 = $2.13



So we can see that while both plays are technically +EV, calling here is vastly superior to raising.



The Bonus math: Where does that EV go when we shove?

$0.45 - $2.13 = $-1.68 (the EV we lose when we shove)

$84 = the amount we're shoving, not including the calling of villain's bet.

(0.51 * -84) + (0.49 * 84) = $-1.68

So we can see that in fact shoving over isn't a plus EV play, it's just that when we shove we make enough back in EV on the call of the villain's $16 that the whole play becomes +EV, although not optimal.



A step back and a step forward
Wed, 21 Oct 2009

I'm moving out of home next year, which means I'm going to have to pay rent and for food on top of my current expenses (read: beer and coffee). I'm a student, so the government will loan me money each week, which covers rent and food but not much else. Life in New Zealand is fairly cheap, so I decided a couple of weeks ago that if I can make and withdraw one buy-in at 25NL per week, then that should be enough to cover the rest of my costs. This also has the advantage that I'm not really putting much pressure on myself or on poker as my essentials are already covered by student loan- if I have a bad week of poker then it just means no going out that Saturday night.

University, and therefore student loan, doesn't start here until March, so from November till March I'll be covering all of my beer/coffee expenses without student loan, and from January onwards I'll also have to cover rent/food. I've enough money saved that divided over those nine weeks it basically amounts to the same as student loan, so no worries there, that just means that from November I have to be making and withdrawing one 25NL buy-in per week and I'm set.

However I had a period of run-good and got greedy, and decided about a week or two ago that I could live off of this saved money from now until January, not withdrawing anything from my bankroll and thus grind my way to 50NL by Jan 1st, and live off of that. That would mean that unlike in the first scenario I would need to be making some money from poker each week, rather than money from poker just going towards beer and coffee. Cue pressure, cue downswing.



Anyway, the stupidity of this choice only really hit me today, which is why I'm blogging about it now. I posted a hand in IRC and asked a fairly arbitrary question. Spoon's response, something along the lines of "the root of the problem here is you haven't put villain on a range yet" really hit home how far back into bad habits I've slipped, with my goal of hitting the bankroll for 50NL by the end of the year.

I play 500 hands of 25NL every day (750 on weekends) on two tables, which takes me about 2.5 hours. I review the big wins and losses of my days, and maybe analyse a hand I'm not sure about if I can be bothered. I don't do any other poker-related learning. Suddenly I realise I've been telling myself that playing and getting the hands in has to come before study and learning, and there'll be plenty of time for study once I've reached 50NL, I just need to get there.



So anyway, the point if this long post, as much as for posterity (can you say that when I mean I'm writing it for me in the future, rather than others? I'm not quite so arrogant as to suggest the latter), is that now that I've stepped back and identified some of my bad habits and thought processes, it's time to take a step forward and fix them.
Two and a half hours of play-time is absolutely fine, given that I have no other commitments in my life aside from a bit of study for my exams coming up (and after November 7th, none whatsoever), so I don't think I need to cut that down for the sake of study time, I think I can just add study time. From experience, to follow through on this ambition I'm actually going to need a schedule of sorts. My current plan:

8am: Wake up hereabouts. Shower, and have eaten breakfast by 9am.

9am: Start first session with my morning coffee, which will be 1.5 hours (300 hands)

1030am: Have a half hour break, do whatever.

11am: Poker study for 45 minutes. This can be watching poker videos (actively watching, and taking notes, not just watching it like TV) or reading poker books. This should not be hand history analysis, as that comes later.

1145am: Fifteen minute break.

12pm: Play my hour-long session for the day, knocking out my last 200 hands.

1pm: Review the days hands, analyse any interesting hands but even if I don't find an interesting hand pick one hand - however mundane - and analyse it fully in my blog. I've been using the excuse "oh no tricky spots" too often lately, when really practising putting opponents on accurate ranges and thinking about how they play them is useful, tricky spot or not. This plus the 45 minute study session at 11 should bring my daily poker study from five minutes up to at least an hour, every day. An acceptable start.



That gives me the rest of the day free to do as I please, which is of course nice. The hardest adjustment will probably be getting myself in bed by 11 to be asleep by 12 (I don't fall asleep very well), but hopefully I'll manage to maintain that.



On a more general note, I will be reverting to the plan of using poker to pay for my shit as of November, and if that means I don't hit 50NL by the end of the year then that's absolutely fine, a month or so's extra wait is worth never putting myself in a position where I'm relying on earnings from poker to survive from week to week.



I have four exams coming up over the next two and a half weeks, so there may be four days that I miss the above schedule, but other than that I have no excuses. And once my last exam (Nov 7th) is over, I shall review how things are going, and change anything as necessary. I will probably also bump up the number of hours per day I devote to poker, and possibly try playing three tables instead of two, since I will really have nothing else that needs to be occupying my time or mind over the summer break.



Wish me luck!