Operating model design benefits from an initial workshop to understand the context of the operating model. These things will come up naturally in any discussion with the executive team. However, if you want to use a canvas style approach to ensure all areas are covered the below canvas is a good staring point:
Update: I get it now! See comment here: https://statisticsbyjim.com/fun/monty-hall-problem/#comment-9601
Like everybody else, my head spins thinking about the Monty Hall Problem. And like everybody else my intuition gives me the “wrong” answer.
For those not familiar with the problem, the unintuitive solution, and the logic behind the solution, this is a great overview: https://statisticsbyjim.com/fun/monty-hall-problem/
Although that explanation is excellent, I think it’s wrong. I know that means I’ll get lumped into all of the other people who don’t get it – so I’m going to briefly explain why I think it’s wrong.
Everybody who explains the solution goes to great lengths to explain the probabilities at the beginning of the game, the number of possible games, and how it changes because you know the host is going to reveal an empty door at some point in the game.
This is all true and I agree with it all – but I am drawing different conclusions from it. So I think the other explanations are wrong in two ways:
1. It is proposed that at the beginning of the game there is a one in three chance of choosing the correct door. This is true, but also at the beginning of the game you already know you will reach a point where a door is open, it’s not the door you have chosen, it doesn’t contain the prize, and there is only one other door. This means at the beginning of the game you already know you have a one in two chance of having already choose the correct door. This is the staring probability of choosing the correct door.
2. The explanation at the link above also says there are only nine possible games. This isn’t true. There are 12 possible games. If you say there are only nine possible games you are missing three scenarios where and you have already picked the right door, so each scenario has two possible games as the host could open either of the other two doors. So, while you know the host will always open a door you can’t ignore the addition three games. This is because all of the games you are ignoring are the games where changing doors will cause you to loose.
The total 12 possible games are shown below:
As shown above – there are 6 games where staying with the same door wins, and 6 games where staying with the same door looses.
If you start ignoring games “because they don’t matter” then they don’t matter at the beginning of the game and your starting probabilities change.