Simulating session results?

[joeg]

Hi everyone

I was thinking of writing a computer program to simulate different bankrolling plans, but my programing skill are far ahead of my maths skill (which isnt saying much), anyway, I need to know how to generate an accurate simulation for a session if I know my standard deviation, hourly rate, and time played for the sesison and was just wondering if anyone knows how to do this using numbers generated from a random number generator in visual basic. Also if anyone has any idea's for bankrolling plans that they would like me to test with this, or information that would be usefull in the results other than the obvious ROR and profit after X hours etc, let me know and when it is done I will run them off for you

Cheers

Joe.

[Lost Wages]

You might want to look at this post for some ideas.

Lost Wages

[jason1990]

The general theory of random walks tells us that a random walk, where each step has a positive EV, will eventually tend to infinity. Thus, there will a last time the walk is at zero, i.e. a time after which the random walk is always positive.

Translated into poker terms, if you have a positive winrate and a bankroll large enough to prevent you from going broke, then there will be some number of hands, N, such that after N hands, you will always be showing a profit. What is the expected value of N? What is the probability N<1000? 10000? 100000?

These are questions that are fairly straightforward to answer without simulation using probability theory. But simulation seems like it would be extremely difficult. How would you know, in a simulation, whether or not N had occurred? I think it would be quite a challenge to try to simulate this, and the results would be interesting.

[joeg]

Lostwages,

Thats great, I will be simulating in discreet hour blocks so that is exactly what I needed to know, just out of interest though, do you or anyone elsehere know how I would get a result for a different time period, say 2.5 hours for example?

jason1990,

I agree you can use probability to work out your risk of ruin with a given bankroll and your chances of being up after N hours, the purpose of the simulation is to experiment with different bankroll strategies such as moving up in stakes when you pass a given limit and dropping down in stakes when you drop below a given limit, and to see what effects different strategies have on your risk of ruin and long term E.V. and anything else interesting I can think of.

[jason1990]

Just in case you misunderstood me, I want to point out that I wasn't talking about the probability of being up after N hours. I was talking about the probability of being up after N hours and staying up from then on, forever (well, at least for the rest of your life).

I don't know if this N has a name. If I had to make one up, I'd call it the "profit point". It's the time when the negative oscillations end, and never come back. After the profit point, you will never again drop below your starting bankroll.

If you understood me in the first place, then I apologize for repeating myself.