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 Statistical analysis of the "Stones" game at Raven Inn
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Jones
 Monday, February 23 2009 @ 01:59 AM UTC (Read 1833 times)  
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Here's a little something I put together to decide whilst thinking about the best strategy for the Stones mini-game:
http://stelio.net/stiki/Games:Stones

Joe: If you'd rather not have such statistical analysis performed on Improbable Island, just delete this topic. Big Grin

The conclusion is rather fitting with Improbable Island as a whole though: although one choice is better than than the other, the variance is so low in comparison to the mean that the results are unpredictable unless you play the game *thousands* of times.


 
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Rosin
 Monday, February 23 2009 @ 04:38 AM UTC  
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An interesting analysis, however it doesn't make much difference. The probability (or rather, Improbability) of the results is close enough that unless one were to play with every second of their day, it wouldn't much matter. Example, the probability of having a single six sided die come up six is 1/6, but it is possible to roll a six 80/100 or more rolls.


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Jones
 Monday, February 23 2009 @ 09:29 AM UTC  
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Absolutely. Smile But unless I'd done the analysis, I wouldn't have known the true probabilities. It's not obvious that it's a balanced game since the premise isn't clearly symmetric (and indeed actually isn't symmetric; it's just close enough though that it makes no practical difference).

I would always have been wondering whether one of the options was clearly better than the other. Thankfully such issues don't bug me for long since I have the knowledge and tools at my disposal to answer them definitively.

So, yes: in practice the game is near enough to balanced that it doesn't make much difference. But if you are going to bet on it, bet on 'unlike pairs'.


 
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CavemanJoe
 Tuesday, February 24 2009 @ 12:28 AM UTC  
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Interesting. I'd like to see more of this sort of thing. I'll let you know if any analysis gives away too much. (or I'll change the formulae without telling anyone Wink )

It's worth noting that, as with all games of chance, the house will always win in the end. The hallmark of a good gambler is knowing when to walk away - and most people are not good gamblers.

If two people, both equipped with a million pounds, toss a coin with a bet of a pound a round, then after roughly nineteen squillion coin tosses one of them will have two million pounds and the other will have nothing. Let's say for the sake of example that Player A won and walks away with two million, while Player B lost and walks away with nothing.

But what happens when we feel sorry for Player B, hand him a Suitcase of Infinite Wealth, and drag Player A back to the table with the lure of potentially winning a large proportion of that Unlimited Wealth? Well, after umpty-bajillion coin tosses, Player A walks away empty-handed. Even if we then give Player A ten billion pounds, he'll still lose against Player B if he doesn't know when to walk away, even at 50/50 odds. Granted, it'll take him a long, long time to lose, but lose he shall.

Thus, the mathematics of gambling and the actualities of gambling do not necessarily match up, simply due to human nature - and that goes doubly true in games like this where the house has access to literally unlimited wealth.

I've said it before, and I'll say it again - imaginary gambling is fun. Real-world gambling is a mug's game. Wink


 
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