Gain insights into tackling uncertainty in C# programming. Delve into improving System.Random class with powerful techniques for efficient problem-solving and fewer bugs. Discover new language uses.

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There are a lot of problems we face in programming that deal with uncertainty, statistics, and probabilities. Unfortunately, the majority of the general-purpose languages that we use on a daily basis don’t provide a great approach to solving them.

This is particularly the case in C# with the System.Random class. The implementations of this class have been pretty poor for some time. System.Random in C# regularly leads to unexpected, buggy outcomes.

If you’re a C# fan who’s looking for new ways to use the language, then this course is for you. It proposes different approaches to improving the System.Random class, providing a number of powerful techniques that solve problems more efficiently and with fewer lines of code.

Fixing Random: Techniques in C#

# Application of the Stochastic Workflow Technology
You are probably familiar with the famous "*Monty Hall*" problem, but if not, here it is:



## Problem
You’re on a game show hosted by Monty Hall, the handsome Canadian fellow pictured above.
Before you, there are three closed doors. Behind a uniformly randomly selected door, there is a new car; behind the other two, there is nothing.
You get to choose a door, and you get what is behind it as a prize: either a car or nothing.
You randomly choose a door, again by some uniform process.

Monty — who knows where the car is — now always opens a door that meets two criteria: it does not have the car behind it, and it is not the door you chose.

To clarify: if you chose the door with the car, Monty chooses one of the remaining two doors by a uniform random choice. If you chose a door without the car, Monty only has one door he can open, and he opens that one.
Monty gives you the opportunity to switch your choice to the other still-closed door.
Assuming you wish to maximize your probability of winning the car, should you switch doors or stay with your original choice?


> We’ve tried to be very precise in our description of the game for the purposes of our analysis. In the real game as played on television, there were irrelevant details such as the "prizes" behind the other two doors were goats or other bizarre, undesirable items, and so on. But there were also germane differences between the real game and our model above; for example, in the real game Monty would sometimes offer choices like "do you want to switch your door, or forget about the doors entirely and take the prize that is in this box?" and it is not clear by what process Monty decided to offer those choices. In this simplified version of the game, we’ve removed all human agency from Monty; for our purposes, Monty is just a machine that is following an algorithm that involves generating random outcomes.

If you don’t already know the solution, work it out. The answer is below.

## Solution 
You are two-to-one more likely to win the car if you switch than if you stay. But don’t take our word for it. Let’s solve the problem with computers, not by thinking!

Plainly the key to the problem is what is the distribution of Monty’s choice? Monty chooses a random door but is observed to not pick a door with a car or the door which you picked. We can represent that as a two-parameter likelihood function:

```C#
IDiscreteDistribution<int> doors = SDU.Distribution(1, 3);

IDiscreteDistribution<int> Monty(int car, int you) =>
    from m in doors 
    where m != car 
    where m != you 
    select m;
```

There’s no logical difficulty in adding more parameters to a likelihood function; think of the parameters as a tuple if that makes you feel better.

Now we can answer the question. Here’s the probability distribution of winning if you do not switch:

```C#
var noSwitch1 = 
  from car in doors
  from you in doors
  from monty in Monty(car, you)
  select car == you ? “Win” : “Lose”;
Console.WriteLine(noSwitch1.ShowWeights());
```

And the output is:
```C#
Win:1
Lose:2
```

As predicted by thinking, you are twice as likely to lose if you do not switch. Computers for the win!

> **Exercise:** Wait a minute, we never even used the value of range variable monty in the query. How is it possible that adding a `from` clause to the query changes its outcome when the sampled value is not even used?






In this lesson, we will be discussing an interesting problem called the Monty Hall Problem. It can be solved using the stochastic workflow technology.

Monty Hall Problem

Introduction to System.Random in C#

Introduction to Fixing Random

Fixing Random - Discrete Distribution

Fixing Random - Continuous Distribution

Conclusion

Appendix

Monty Hall Problem

Application of the Stochastic Workflow Technology

Problem