the decision function

this might not end up being particularly useful, but i've noticed that i don't often take anything useful away from hand history discussions. in my experience, when faced with a question about a hand history, different people generally take a position and point out different aspects of the situation that provide support. if discussion continues at all it usually involves a lot of reiteration and little resolution...

so, i want to suggest a framework for considering poker decisions that would invite broad thinking, collaboration and finding a consensus. here it is:

D = C1X1 + X2X2 + .... + CnXn

where Xn represents the value of a condition (in +/-bb), and Cn the relative importance of that condition (for simplicity, let's say Cn is bound by 0 and 1). a bet is indicated when D is positive, and a check when D is negative.

as a simple example, consider the following hand:

SB ($312)

BB ($599)

CO ($40)

HERO ($207)

SB posts (SB) $1

BB posts (BB) $2

Dealt to HERO Kc  9d

fold,

HERO raises to $6

fold,

BB calls $4

FLOP ($13) 3s  4h  Ah

BB checks

HERO ...

in order to determine whether to bet or check, there are a number of conditions that hero could consider, some of which are represented in the following decision function:

D = C1*(stack size) + C2*(flop texture) + C3*(hole cards) + C4*(opponent tendencies) + C5*(perceived image) + ...

if i asked for opinions on whether or not hero should bet, some players would likely respond 'yes, that's a great flop to cbet', implicitly setting C2 = 1 and all other Cn ~=0. other players might consider the value of K9o, how frequently the opponent tends to call, whether we have an aggressive image, etc. to arrive at a decision. the following table illustrates these different approaches:

D (player type)	C1 (stack size)	C2	C3	C4	C5	...
texture expert	0	1	0	0	0	0
soul reader	0	0	0	1	0	0
deep thinking lag	0	0.5	0.1	0.7	0.2	0
fish	0	0	1	0	0	0

...you get the idea.

by identifying and considering the relevant conditions individually, we get in the habit of looking for additional bits of information and (trying) to objectively determine the relevance of those bits. as opposed to playing on auto pilot and focusing in on a single factor that is typically biased/tilted by recent hands or the weather or whatever we've been thinking about recently.

here's another example with more (and more complicated) conditions/factors:

SB ($289)

BB ($123)

UTG ($211)

MP ($203)

CO ($121)

HERO ($202)

SB posts (SB) $1

BB posts (BB) $2

Dealt to HERO 4s  2s

fold, fold,

CO calls $2

HERO raises to $7

fold,

BB calls $5

CO calls $5

FLOP ($22) As  8h  3s

BB checks

CO checks

HERO ...

both CO and BB appear fishy, but were essentially unknown at the time. hero had a clean standard tag image (if anyone was paying attention).

the decision function should look something like this:

D = C1*(stack size) + C2*(flop texture) + C3*(hole cards) + C4*(CO tendencies) + C5*(BB tendencies) + C6*(perceived image) + ...

my initial estimates are in the following table:

condition	Cn	Xn	Cn*Xn
stack size	0.5	-10	-5
flop texture	1	+2	2
hole cards	1	+2	2
CO tendencies	0.1	-2	-0.2
BB tendencies	0.1	-2	-0.2
percieved image	0.1	+2	0.2
total			-1.2

so, i checked back.

obviously, this isn't meant to be as formulaic as it might appear from that last example. but from there it would be easy for somebody to point out where their thinking differed and for both players to use that disparity to improve their thinking.