Monte Carlo probability calculation in Python

[Paul Moore]

On Thursday, 5 February 2015 16:57:07 UTC, Rob Gaddi  wrote:
> You don't need the whole scipy stack, numpy will let you do everything 
> you want.  The trick to working in numpy is to parallelize your problem; 
> you don't do a thing a thousand times; you do it on a thousand-length 
> array.  For example:
> 
> def dice(throws, per, sides=6):
>     """Return an array throws long of rolls of (per)d(sides)."""
>     all_dice = np.random.randint(1, sides+1, size=(throws, per))
>     return all_dice.sum(axis=1)

Thanks, that's a help. I see the principle, but a couple of questions. With bigger problems (deal 52 cards into bridge hands a million times, for example) would memory become an issue? Also, how do you handle things that don't fit into the built-in numpy operations? (For example, Monopoly - roll 2 dice and take the sum, unless you roll a double, in which case reroll, but if you roll 3 doubles you fail - return NaN in that case).

As examples of a few more problems I'd use this for:

1. Roll 4 dice, and sum the largest 3.
2. Roll 9 dice, count how many different numbers you get.
3. Deal 4 hands of 13 cards from a full deck, determine the length of the longest suit anyone has.
4. Monopoly rolls (see above, 2 dice but reroll doubles up to 3 times)

All of these are reasonably easy to write as Python functions, but it becomes progressively harder (for a non-numpy expert) to know how to convert them into parallelizable numpy primitives.

I'll have a play with the approach you suggest though, and see how it handles some of the more complex problems my friend was showing off with :-) (his worst example was a horrendous expression to score Cribbage hands, that if I read his note correctly took about a minute to simulate 10,000,000 deals)

Paul