Help building a simulation based on probability

**one11** · 11-12-2010, 05:31 PM

Hi

My final objective is to create a graph that will show the rate at which a player accumulates coins in a game. (I need to know how much coins the player has at any day#)

Here are the conditions: (numbers represents coins gained)

Winning a game 100
Fast win 16
First win (bonus valid once every 24hours) 150
Loosing a game 70

and this is a sample player profile:

Avg #games played per day 3
Win probability 60%
Fast win probability 35%

Any suggesstion as of how to tackle this issue wihtout coding in VBA ?

Cheers!
N

**6StringJazzer** · 11-12-2010, 06:30 PM

Originally Posted by one11

Here are the conditions: (numbers represents coins gained)

Winning a game 100
Fast win 16
First win (bonus valid once every 24hours) 150
Loosing a game 70

Just to be clear, I gain 70 coins if I lose a game?

**one11** · 11-12-2010, 06:42 PM

That's correct. (you gain coins even if you loose) The reward system is based on playtime more than performance.

**6StringJazzer** · 11-13-2010, 12:24 AM

Press F9 to rerun the simulation.

This is not a highly generalized solution. The number of columns depends on how many games you think someone might play in one day. Given the average of 3, I assumed that the number of games played will range from 0-6, so I have six sets of results which are accumulated through the day.

I show 29 days of games but it's easy to add rows; just copy the formulas down.

The Parameters sheet has all the probabilities and other values. It is fairly easy to change to a different set of probabilities for different outcomes, add more outcomes, and change coin gains.

This sort of simulation is called a Monte Carlo simulation, where you set parameters and probabilities for possible outcomes, and run random scenarios to get a forecast for likely outcomes. We do this for project scheduling, for example.

I plotted your outcomes with day on the x axis, but also look at the Histogram sheet to see the daily winnings distribution for each run. The more days you simulate, the more consistent the histogram will be. There is a clump of 0 winnings because there are some days that the game is not played.

**one11** · 11-14-2010, 11:14 AM

Thanks! very impressive

All this time I thought that the "Monte Carlo simulation" was something exclusive to gambling (yknow what they say about assume :P)

On top of that, this is a lot neater than coding VBA

Thanks a lot for your time on this, i'll spend some time reading up on the Monte Carlo method

Cheers,
N