## Wednesday, 17. August 2011

Aug 17

In the last part of this blog series I showed how we can utilize the DistributionMonad in order to solve the famous Monty Hall problem. This time I want to show you how we can use it to solve some basic Texas holdâ€™em poker questions.

We start by defining a model for poker in F#:

As you can see we model cards as tuples of a rank and a suit. The complete deck is just a combination of all ranks with all suits.

Now we need some additional helpers for the DistributionMonad, which will allow us to draw cards from the deck. You can find further explanations about these helpers in the excellent paper by Martin Erwig and Steve Kollmansberger called "Functional Pearls: Probabilistic functional programming in Haskell". Like the DistributionMonad itself, these helpers are already in the FSharp.Monad project and you get the bits from nuget.org.

Now we are ready to perform our first query. Let’s see how we can compute the probability of drawing the Ace of Clubs and the Ace of Spades:

But we can easily go a step further:

If you keep this model in mind you might come up with a poker odds calculator on a smart phone. This might be your chance to get rich. 😉

Tags:

F#,

monad
## Tuesday, 16. August 2011

Aug 16

In the last part of this blog series I showed a DistributionMonad, which allows to perform queries to probability scenarios. Today we will use this monad in order to solve the famous Monty Hall problem. This article is based on the excellent paper by Martin Erwig and Steve Kollmansberger called "Functional Pearls: Probabilistic functional programming in Haskell".

â€œSuppose you’re on a game show, and you’re given the choice of three doors: Behind one door is a car; behind the others, goats. You pick a door, say No. 1, and the host, who knows what’s behind the doors, opens another door, say No. 3, which has a goat. He then says to you, "Do you want to pick door No. 2?" Is it to your advantage to switch your choice?â€

[problem definition from Wikipedia]

Letâ€™s start by modeling the first choice using the DistributionMonad:

As we can see the solution is 1/3 as we expected and if we donâ€™t switch, we stay with these odds. But if we switch we might improve the probability for a car. Remember the host will always remove a Goat after your first pick. Letâ€™s analyze the second pick if we switch:

Car behind |
First choice |
Temp. Outcome |
Host removes |
Switching to |
Outcome |

Door 1 |
Door 1 |
Car |
Door 2 |
Door 3 |
Goat |

Door 1 |
Door 1 |
Car |
Door 3 |
Door 2 |
Goat |

Door 1 |
Door 2 |
Goat |
Door 3 |
Door 1 |
Car |

Door 1 |
Door 3 |
Goat |
Door 2 |
Door 1 |
Car |

If the Car is behind door 2 or door 3 the situation is symmetrical and therefor we can conclude, the following:

And if we run this, we get this nice solution:

Next time I will show how we can use the DistributionMonad to solve some basic poker scenarios.

Tags:

F#,

monad
## Monday, 15. August 2011

Aug 15

In part I of this blog series I showed a simple InfinityMonad, which allows to treat special calculations as infinity and in the second part I showed the UndoMonad, which defines an environment which allows to undo and redo state changes.

This and the following posts are based on a famous paper by Martin Erwig and Steve Kollmansberger called "Functional Pearls: Probabilistic functional programming in Haskell".

Letâ€™s start by looking at a small scenario:

This simple query calculates the probability of the event, that an dice roll gives a value greater than 3 and an independent coin flip gives â€œHeadsâ€. In order to do this the DistributionMonad enumerates all possibilities and calculates the joint probability using the following formula:

If we want the nice syntactic sugar we can easily define a computation expression builder:

In order to allow easier access to our monad, we define some helper functions and basic distributions for fair coins and dices:

In the next part of this blog series I will show how we can utilize the DistributionMonad in order to solve the famous Monty Hall problem.

Tags:

F#,

monad
Aug 15

In part I of this blog series I showed a simple InfinityMonad, which allows to treat special calculations as infinity. This time I want to demonstrate a ported version of the UndoMonad (see the Haskell version). This monad defines an environment which allows you to undo and redo state changes. You probably know this behavior from your favorite text editor.

Letâ€™s start by using this monad in a small sample:

The definition of this monad is easy if we use the StateMonad, which is already implemented in the FSharp.Monad project (you get the bits from nuget.org). We only need to define the kind of state which should be passed through the monad.

Now we need some helpers, which allow to access and manipulate our history.

In the next part Iâ€™ll show a DistributionMonad, which allows to perform queries to probability scenarios.

Tags:

F#,

monad
Aug 15

At the moment I am collecting some samples for the FSharp.Monad project (you get the bits from nuget.org) and I think I should describe some of these monads here, since they are not that common.

Today I will start with a very small monad which encapsulates infinity as a special value. I found the the idea to this specific monad at http://visualizationtools.net. Letâ€™s start with the basic definition. Like every monad we need a container type and the two functions *return* and *bind*. *Return* will be used to get values into the monad and *bind* allows us to chain functions inside the monad.

The next thing is to create a computation expression builder which allows us to use the nice syntactic sugar in F#.

Now we can start using the monad. As a small sample we define a safe division function which treats all â€œdivision by zeroâ€ cases as infinity.

And we can use this division inside computation expressions.

Remark: You can easily define this InfinityMonad in terms of the common MaybeMonad. You can see this in the UnitTests of the FSharp.Monad project.

Next time I will show an UndoMonad which defines an environment which allows to undo and redo state changes.

Tags:

F#,

monad