Friday, March 5, 2010

p(busto)

I've spent some time today pondering the choice in front of me. I have decided I'm not quitting poker (so rest easy on that one) and the remaining fork in the road regards whether or not I'm going to continue propping. There are a lot of things going into the decision (life happiness, hours, professional courtesy, etc, etc), but the most important one to me is figuring out the probability that I go busto in either course of action. The long term goal is of course to be robusto, but for now I will settle for "non-busto". So I wrote some Java code (something I was once paid to do), estimated some variables and spit out some numbers. I used a $440 StDev (which I know to be quite accurate) and varying win rates from 30 to 50 dollars per hour. First I assumed a borderline unreasonable 150 hours of play per month:

150 hours/month p(busto)


30 0.08
35 0.045
40 0.025
45 0.015
50 0.006


If I play a reasonable 120 hours a month, the data looks like this. I have a (slightly) higher chance of going busto because my expenses catch up to me:

120 hours/month p(busto)


30 0.09
35 0.058
40 0.034
45 0.02
50 0.012

But all in all you have to admit that these numbers are extremely good. Historically my WR has been near the top of the range of values I used, and the Commerce games seem to be even better than the ones I'm used to in the Bay Area. So I'm willing to say that free-lancing presents a less than 5% risk of me going busto.

Now on to the prop job, which is much more difficult to compute since there are a lot more variables to consider. Again I start with $14K and have expenses of $2K per month. I assume 1000 hours worked in 6 months, and use my numbers from a pitiful 5.5 shifts of propping to access how often I'll be in which game (which so far are 8 hours of 20/40, 18 hours of 40/80 and 18 hours of sitting around). I also use my $440/hour StDev for 20/40, but drop my WR all the way down to $25/hour for that game. The games honestly haven't been that good, and most of the time I'm in them I sit with like 2-3 props. There are still fish and I think I'll still win, but nowhere near what I could free-lancing with table selection and away from my fellow 40/80 props. My 40/80 StDev is going to be much higher in terms of big bets per hour, because the game is going to be short handed and more aggressive. This is just true, trust me. So again I put in some numbers with two StDevs (12 and 14 big bets per hour) with varying win rates. The problem here is that I have no idea what my true win rate is in this game:

StDev 14 p(busto)


0 0.21
20 0.14
40 0.1
60 0.06


StDev 12 p(busto)


0 0.14
20 0.08
40 0.05
60 0.03

As you can see, if the StDev is as high as I think and my win rate as low as I fear, continuing to prop would incur a pretty substantial p(busto). Something like .1 seems reasonable, although it could be as high as .2 and realistically can't be below .05.

So what am I gonna do? I'm gonna think about it some more :)

As an add on here, I'd like to point out that the $14K is not "all the money I have in the world". It's not even really very close. It's just all the money I've decided I'm willing to lose on what was supposed to be just "a shot" in the first place. Second of all it is my hope to play 4 figures of hands online per week either way, shooting for more in the 2000 range if I go free lance. It is my hope that this experience will make me better and add a little to my bottom line. I left it out of the calculations here, though, just for simplicity.

7 comments:

jesse8888 said...

Here's the code if anybody is interested:

//propping case

double fortyStDev = (12.00*80.00);
double twentyStDev = (440.00);
int busto = 0;
for (int trial = 0; trial < 10000; trial++) {
double roll = 14000.00;
Random r = new Random();
for (int hour = 0; hour < 1000; hour++) {
int hourType = r.nextInt(44);
double result = r.nextGaussian();
if (hourType < 8) {
roll = roll + (result*twentyStDev + 25);
} else {
if (hourType < 27) {
roll = roll + (result*fortyStDev);
} else {
//do nothing I didn't play
}
}
if (roll < 0.0) {
busto++;
break;
}
if ((hour % 80) == 0){
roll = roll + 2800.00;
}
if ((hour % 175) == 0) {
roll = roll - 2000.00;
}
if (roll < 0.0) {
busto++;
break;
}

}

}
System.out.println("Propping Bustos: " + busto);

busto = 0;
for (int trial = 0; trial < 0; trial++) {
double roll = 14000.00;
Random r = new Random();
for (int hour = 0; hour < 900; hour++) {

double result = r.nextGaussian();
roll = roll + (result*twentyStDev) + 50;

if ((hour % 150) == 0) {
roll = roll - 2000.00;
}

if (roll < 0.0) {
busto++;
break;
}

}
}
System.out.println("Freelance Bustos: " + busto);

Going for it? said...

Jesse, thanks for all the words. Seems like it would be hard to share all this so open but it does help me to read and make decisions.

Wacky said...

You don't need to right a simulation to figure this out. This is the very common risk of ruin scenario that you are considering, and the following formula is what your program will converge too assuming you simulate enough hours and there is not a bug.

Risk of Ruin = e-2 x WR x BR ÷ (SD x SD)

WR = win rate
BR = bank roll
SD = standard deviation
e = well e, the exponential 2.7183 blah

Wacky said...

Rearranging the terms of the equation, you can also solve it for choosing an amount of risk you are acceptable taking, then what size bankroll would you need?

Here's my matlab routine to figure that out, but from that you get the general idea.

function y=risk_of_ruin(sd, hourly, risk)

y = round(-(sd^2)/(2*hourly) * log(risk));

jesse8888 said...

Yeah I know all that but having a little sub-routine where I can change all the parameters and see how it affects things is really helpful for me.

timilon said...

Alternative Jesse gameplan, fwiw:
Take a break (temporary or otherwise) from LHE. With small part of the roll, play some live 1-2/2-5 NL. Cultivate a style that suits you (which may be diff from old aggro LHE persona). You can coldcall in NL w/o feeling wimpish. See cheap flops. Use those MIT smarts to read/outplay villains in more ways possible than in LHE. Give it a mini-shot. Still enjoying the blog, and wishing you renewed success.

CT said...

you prolly don't need this, but maybe someone finds it useful...
http://www.evplusplus.com/poker_tools/variance_simulator/

Best of luck, whatever you decide, been following you for a while, would hate to see you go! And I don't even play limit!