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Subject: Testing the cube tower stats- help! rss

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Louise Holden
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Supposing that I was both sad enough and had enough time on my hands to want to run some stats tests on the cube tower...

The probability of cubes staying in the tower on going in seems easy enough to test; empty tower, add 10 cubes, count number emerging and repeat ad nauseam.

However if there is, say, a 30% chance of an individual cube coming out if 10 are put in at once, does this mean that there is still a 30% chance of an individual cube coming out if it is put into an empty tower singly? Or do the cubes interact significantly?

The probability of cubes coming out of the tower seems even more likely to be affected by the numbers involved. I feel intuitively that putting 10 cubes in at once is more likely to dislodge a cube already there than putting in 10 cubes singly. But I could be wrong.

Any thoughts before I just launch into lots of cube throwing? Particularly, any other significant variables? Or any suggestions of useful trial set-ups? Or *please* if anyone's done this already point me towards it!





 
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Maarten D. de Jong
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louiseh wrote:
The probability of cubes staying in the tower on going in seems easy enough to test; empty tower, add 10 cubes, count number emerging and repeat ad nauseam.

Of course, that is dependent on the number of cubes you put in. I suspect there will be a some sort of cut-off beyond which the ratio of cubes thrown in versus cubes coming out remains more or less a constant. But to test that you would need to run N tests with 1 cube, N with 2, N with 3,... You have my sympathy.

Quote:
However if there is, say, a 30% chance of an individual cube coming out if 10 are put in at once, does this mean that there is still a 30% chance of an individual cube coming out if it is put into an empty tower singly? Or do the cubes interact significantly? The probability of cubes coming out of the tower seems even more likely to be affected by the numbers involved. I feel intuitively that putting 10 cubes in at once is more likely to dislodge a cube already there than putting in 10 cubes singly. But I could be wrong.

See above.

Quote:
Any thoughts before I just launch into lots of cube throwing? Particularly, any other significant variables? Or any suggestions of useful trial set-ups? Or *please* if anyone's done this already point me towards it!

Yes: in practice doing proper stats would be even harder, as in the game the number of cubes thrown in varies all the time. So your single throw test results mean next to nothing. You'd have to be extremely bored to want to do this sort of sequential testing. Alternatively, you might want to develop some sort of physical model of wooden cubes bouncing off this particular make and shape of cardboard depending on their velocity just before impact, calculate how far it 'jumps' on average, and then combine that information with the cross-sectional area of the tower. That could actually be a worthwhile project on M.Sc.-level. And then you still leave out the interactions of the cubes themselves. It is not, by any standard, an easy problem to solve.

In other words: learn to live with the unpredictable nature of this bloody thing :-).
 
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Nick Case
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Even if you do establish a graph for a cube dislodging ratio does this really help? There will still be times when 6 attacking a 1 will fail and tiny armies demolish enormous legions.

I genuinely feel that the tower is more predictable than a dice based system but crunching stats must surely only heighten the frustration when 'statistically you can't lose'.....and you do.
 
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Louise Holden
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I'm mainly interested to know whether the SpielByWeb percentages are a reasonable simulation. I'm quite happy with the random nature of the dice tower (even though I just got run over by farmers again!); just curious as to whether its the same kind of random on the online version.
 
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Nick Case
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Indeed this was posted by milksheikh


What I do at the moment is use a 30% probability that a cube being dropped in the tower will stay in there, and a 30% probability that a cube in the tower will come out.

I imagine that the real probabilities are somehow dependent on the number of cubes in the tower, and the number of cubes being dropped in (the higher those two numbers are, the less likely a cube being dropped in will stay in the tower, and the more likely a cube in the tower will come out).

I welcome any empirical research, or suggestions of methods/functions, that may simulate the tower better...


As you can see the man himself appreciates the variety offered by cube numbers dropped and invites people with time to waste to throw cubes about for weeks on end to create a model.

I'd say fwiw that the 30% rule is more predictable than the tower. If you ever have a peep down the tower mid game (assuming that's not a house rule no no) you can often see cubes neatly tucked into a corner which continue to be still locked in at the end.

Ultimately, both sides have the same '30%' chance of coming out so its far more useful to keep track of respective numbers of each colour (especially farmers).
 
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Jim Cote
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It's more complicated than that. To better simulate the real cube tower, you need to assign each cube in the tower a "dislodge" value. Some cubes end up in the corners, and stay there almost the entire game, while other are perched perilously close to the edge of a narrow shelf. This doesn't affect overall probabilities perhaps, but it does cause some serious distribution issues. If one of your cubes gets stuck in a corner, you will be hurt the entire game.
 
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Nomadic Gamer
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This is why I use a shotglass and try to hurl the armies into different corners......cool
 
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