Poker Anthology

I just realized the site that hosted Pr0crast’s 2+2 Anthology has been down since November 2008, so I put it up here on my blog. Make sure you check it out if you play poker and like money.

Poker Math: Extending the 2/4 Rule

Three more math books arrived today, now I have a stack of 9 to get through, maybe 1-2 years worth if I learn fast. That means even less hope for poker, so I might as well pass on another idea I’ve had that I probably won’t have time to work on. Continue reading

Breakeven Fold Equity

EDIT: It has come to my attention that I defined “break even” incorrectly. Instead of defining it to be 0 EV, it should actually be defined as our EV if we go to showdown. This is because we need to compare the two best lines (checking vs betting) and see which one is better (ignoring getting raised off hands and having to c/f to a bluff). I will correct the chart soon.

This summer I did a little analysis of required fold equity (FE). I had high hopes for the project, but nothing great came of it. What did come out of it, however, was a chart that might be of use to you guys. It’s not what I wanted to release, but I don’t really have the time to do more meaningful analysis atm.

Required Fold Percentage

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Hold’em Manager HUD

I spent some time looking over the HUD options in Hold’em Manager. I really didn’t like the default one and basically replaced every element with my own.

I made one for Full Tilt 6-max tables that closely resembles the PA HUD-type layout, but with the powerful new 3-bet stats of HM. If you want to use it for other sites, you’re going to have to tweak the stat positioning a bit to match it up to different seat layouts.

HM HUD in action

HM HUD in action

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Poker Math : Required Fold Equity

This is a pretty basic poker equition, but it will eventually become part of a larger project. I’m putting it here because I managed to mess it up twice and would really like to have the correct version in the future.

EV = our expected value
f = probability our opponent folds to our bet
p = current pot (before our bet)

Note: I’m completely ignoring any further play
EV = (fold equity) + (SD equity given call)
EV = f*p + (1-f)*(SD equity)
EV = f*(p – (SD equity)) + (SD equity)
We of course want EV > 0, so
f*(p – (SD equity)) + (SD equity) > 0
f > -(SD equity)/(p – (SD equity))

(SD equity)/(SD equity – p)” width=”147″ height=”41″ />

To make this equation complete, let
w = probability of winning at showdown when called
b = our bet

SD equity = w(p + 2b) - b

These equations make sense because:

  1. When we have 0% chance to win if called, our showdown equity is –b, so we have:
    f > b/(b+p)
  2. On the other hand, when we have a lock (100% chance to win), our equity is p+b (the pot plus opponent’s call), so we have:
    f > (p+b)/(p+b-p) = (p+b)/b, which means we never want the villain to fold
  3. This also tells us that the result “f > 1” lies somewhere between 0% and 100% to win. This is obviously because of pot odds, since we win (p+b), but lose only b, we don’t actually need a lock to want the villain to call every time (ex: when you have straight vs set, you never want opponent to fold, even though a set will suck out quite often)

Related Post: Chart of Required Fold Equity