Bet into the shortstack?

[kroeliewoelie]

Usually I am trying to find tables without shortstacks, but this doesn't always work. I am quite new to this forum and to poker, so I tried to quantify a problem I struggle a bit with. I hope that some of you will check my reasoning and maybe someone else finds a use of these calculations.

The question I tried to answer is

"When should you bet into the shortstack given that he has a certain percentage of the pot left?"

The variables that go into this answer are:
1) x, the chance that the shortstack folds (0=<x=<1)
2) P, the potsize (which actually isn't important)
3) b, the remaining stack of the shortstack as a fraction of the pot
4) q, the chance that I hit good outs

First of all, the EV of betting is composed of 3 parts

1) inducing folds EV(f) = xP
2) betting and losing your bet EV(b,l) = (1-x)*(1-q)*b*P
3) betting and winning the pot + remaining stack EV(b,w) = (1-x)*q*(1+b)*P

EV = EV(f) + EV(b,l) + EV(b,w)
= P[x + (1-x)[-(1-q)b + q(1+b)]
= P[x + (1-x)(q-b+2bq)]

Now I want to know the break even point of betting. Solving that equation for q, gives

q = (b-x-xb)/(1+2b-x-xb)

On the flop q = 1-(47-#outs)(46-#outs)/47*46. This gives the following table. This can be read as:

given that b=0.5 and the shortstack folds 30% of the time, we need 0 outs to break even.

given that b=0.75 and the shortstack doesn't fold, we need 8 outs to break even.

b=----0.25-0.5-0.67-0.75-0.85-1
---------------------------------------------------------
x=0---4----6---7----8----8----9
x=0.1-2----4---6----6----7----7
x=0.2-0----3---4----5----5----6
x=0.3-0----0---2----4----3----4
x=0.4-0----0---0----0----1----2
x=0.5-0----0---0----0----0----0

Now the same exercise can be done for this happening on the turn. Your chance to suckout is now reduced:

q = 1-(46-outs)/46

So
b= ---0.25-0.5--0.67-0.75-0.85-1
------------------------------------------------------
x=0---7----11---13---14---14---15
x=0.1-4----8----11---12---12---13
x=0.2-0----5----5----10---10---11
x=0.3-0----0----4----6----6----8
x=0.4-0----0----0----1----1----3
x=0.5-0----0----0----0----0----0

Conclusion:

Given that
1) we have overcards on the flop with 6 clean outs
2) our shortstack won't fold
3) the shortstack has only 25% of the pot left in his stack.

We need to bet.

Comments are welcome. And does anybody know how to make decent tables? This looks rather bad.