workings of a calc

[mongoose]

sorry for not contributing before asking a question. this is my first post on the boards.

i'm interested in how holdem calcs, specifically the one at cardplayer.com work. am i right in thinking the prog runs a set of simulations given the user-provided starting info and just reports the results. i just ran a series of calculations using the same starting sets of cards, and each result the calculator gave was slightly different that the one before it.

which would make sense if it's just reporting on a set of simulations it ran.

also, how many simulations do you think you would need to run to get some accurate results? 10,000 hands, 100,000 hands, 1,000,000 hands?

anyone with any thoughts on it?
- mongoose

[Adamm]

With simulations, you'll never be totally accurate to the exact figure. The more hands you run though, the closer to the exact figure you'd get.
You asked: "also, how many simulations do you think you would need to run to get some accurate results? 10,000 hands, 100,000 hands, 1,000,000 hands?"
That depends on what your definition of accurate is naturally. With 1 million hands, you'll get a pretty close number (probably) but you have to consider that the there is a small chance that it'll be off. That chance goes down depending on the number of hands you run.
With the calculator we're working on right here, I just used plain algebra. I'll plug it again actually (it's all over this odds forum, even though it's not done). It's at http://www.texasholdem-poker/calculator.php
Using just plain math rather than simulations provides an exact result. It just gets really difficult when you want to compare multiple hands over multiple turns though, which is why it doesn't compare hands. It would take too much to do. Also, I'm still saving those hellish equations for a future day.
But if you just apply the equations we have there (extend them to the river instead of just the flop), and add some more to compare hands against each other, you could have a perfectly sound hand comparison calculator.
I guess the point is that simulations are quicker to assemble and faster but have variance. Using the math of it gives a correct answer, but is tough to assemble and is probably a lot slower.
I don't think anyone has created a "no simulation" holdem calculator to compare hands that fits onto the internet without a download. Better would be a database of figures rather than something that calculates on the go. Anyway, I've blabbed long enough.

[Sente]

I don't know why the numbers keep changing. If you input 2 starting hands. There are exactly 1,712,304 unique boards. There are 200 million combinations total. Consider that As-Ks-Qs-Js-Ts is the same as As-Qs-Js-Ts-Ks same as Qs-Ts-As-Ks-Js etc. Each 5 card group can come down 120 different ways. That's how it goes from 200m down to 1.7 million. I think a computer can calculate the relatively quickly and calcuate the exact odds.

[UnluckyKyle]

the key thing to remember with simulations is that they only reflect statistical probabilities, not the true prob. of say, making that 7-2o actually take down AA.

Also, accuracy with these programs relies much more on volume. Is a million hands enough? No. You need a significantly large data set to get anywhere near the true values. Lets say you flop that straight flush, and want to know how many times it'll get cracked (and by what hand). Well, you've got to have that happen enough in your test run. how many times will it happen in a million hands? Once or twice, maybe.

Without getting too technical, in most proability courses they tell you that you'd need at least 30 discrete examples in order to use the Central Limit Theorem and have an approximately normal distrobution (normal is the standard dist'n for probability). So, to have 100% accuracty you'd have to run a rediculous ammount of hands.

[martini]

Use the calculator at pokertips.org. It gies you an exact rundown.