### Re: Dial up some obscure stats for the Chutes and Ladders game

by Limbic~Region (Chancellor)
 on Jun 29, 2009 at 20:21 UTC ( #775798=note: print w/replies, xml ) Need Help??

toolic,
You are not nearly geeky enough. This all assumes that you have a "fair" dial, that age and strength don't have a bearing on the outcome and that the behavior is uniform over time (wear and tear don't affect the results).

Now if you were to do this MythBuster's style:

1. Calculate the average force by applied by yourself and then your child
2. Set up a robot that could apply that force in alternating spins
3. Set up a web cam to snap pictures at regular intervals
4. Write software to intepret the picture to both determine which number is landed on and when to trigger the robot (dial is not spinning)
5. Let it run over a prolonged period of time
6. Provide us all with the results and tell us if we can expect the same with our games at home

This is way cool by the way!

Cheers - L~R

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Re^2: Dial up some obscure stats for the Chutes and Ladders game
by toolic (Bishop) on Jun 29, 2009 at 20:43 UTC
You are not nearly geeky enough.
My wife would disagree. But, my son is young enough that he doesn't realize his father is one yet. I wonder how many years I have left before it dawns on him.
This all assumes that you have a "fair" dial
Don't get me started on the dial! The width of the line separating the numbers is comparable to the width of the arrow-head. This ambiguity forces far too many re-spins (that's harder to simulate with Perl :). Additionally, this ambiguity is a function of the person spinning the dial. My son claims he must re-spin when it is close and the number does not suit his needs!
My son claims he must re-spin when it is close and the number does not suit his needs!

Which you clearly agree with... meaning you are first Dad and only second geek. You may be in luck: your son may never discover you are a geek. You'll merely be his hero (at least until some long off Saturday night when you absolutely positively refuse to hand over the car keys - but that will be only temporary).

Pretty cool to have a Dad serve up an entire post of obscure stats in honor of his son - I imagine in the next installment, you'll start hand-crafting computer games for him :-) There are many ways to love a child - all of them count.

Best, beth

The width of the line separating the numbers is comparable to the width of the arrow-head. This ambiguity forces far too many re-spins (that's harder to simulate with Perl :).

Oh come on! (Width of line * number of lines) / ( 2 * pi * radius of arrow ) gives you a probability that a spin will land on a line. What's so hard about that? (I believe the width of the arrow point is irrelevant, or at least ignorable.)

Additionally, this ambiguity is a function of the person spinning the dial. My son claims he must re-spin when it is close and the number does not suit his needs!

So a per-player weighting factor needs to be applied to the above-mentioned probability. I will grant that assigning a "direction" to the weighting factor, based on the relative merits of two adjacent values on the dial, makes for a more challenging decision process.

I know... there's a certain degree of general fatigue induced by parenting young children, and this tends to limit the amount of time and effort that can be expended on purely geek pursuits. Been there, done that.

Of course, the engineering solution is to replace the poorly-designed spinner with a device with far fewer faults: a single die. I've yet to see a die land on its edge or corner. How's that for Laziness.
Maybe that's why we use a die. The chances of not hitting one of the 6 faces is too remote to worry about. You would have to account for die being thrown across room and under the sofa.
Re^2: Dial up some obscure stats for the Chutes and Ladders game
by duff (Parson) on Jun 29, 2009 at 20:34 UTC

you forgot the part where they rig the game with explosives just to blow something up :-)

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