As you can see from the other
sections, PokerCruncher can compute odds and stats for a limitless variety of Hold'em scenarios, both simple and
complex scenarios. It would be very difficult and intractable to solve every
possible Hold'em scenario exactly using math and probability, or by
enumerating all of the possible cases (because most of the time there
are way too many possible cases).
This is especially true if we want to handle PokerCruncher's advanced features like hand ranges
and partial simulation. So PokerCruncher
takes a flexible approach called Monte Carlo simulation. The beauty and
simplicity of this method is that it automatically and implicitly takes
all math and probability considerations into account through its random
card and random hand generation process, and converges on an accurate
answer as you simulate more and more hands.
What is
Monte Carlo simulation? You can google it of course but here's our brief
explanation using an example. Say you want to compute the value of pi. A Monte Carlo approach is to draw a square
whose sides are 2 units long centered at the origin, and a circle
of radius 1 also centered at the origin. Then toss many random
points onto the square:
...
and see what fraction of the points land inside the circle, which is an easy
distance test to make: sqrt(x^2 + y^2) <= 1 (actually no need for the sqrt()
here since the right-hand-side is 1). The fraction gives you the area
of the circle, which gives you the value of pi. As you toss more and more
random points you get closer and closer to the value of pi. So the Monte
Carlo method has reduced a difficult computation to a simple distance
test using random numbers.
Similarly
given a Hold'em scenario, PokerCruncher tosses many random cards and
random hands at the unspecified (not nailed-down) parts of the scenario,
counts the win/loss/tie results and stats on each random simulation, and converges on accurate
odds and stats as it simulates more and more hands.
Complete
Enumeration
However
if the scenario is simple enough, PokerCruncher computes the exact odds
and stats by doing complete enumeration of the possible cases. It does this for postflop situations with specific players'
cards, which is a common situation. For such scenarios only the turn and river cards are unspecified,
a manageable number of combinations (on the order of 1000), so PokerCruncher simply enumerates all
possible cards for the turn and
river.
Some odds
calculators aren't able to compute exact odds and stats even for simple
scenarios.
