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Storm over Arnhem» Forums » General

Subject: Dice vs Chit Draws rss

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David Orr
Canada
Kingston
Ontario
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I just wanted to point out the differences in the probabilities of outcomes when you need to roll or draw a chit. The optional rules state not to replace a chit when it is drawn. Here's an example of rolling or drawing an 11.

Rolling the dice: There are 36 outcomes possible when you roll 2 dice. There are 2 ways to get an 11 (1-2 or 2-1) so the probability of rolling an 11 is 2/36 or 5.6%. Now here's the important part. This probability does not change on the next roll or on any number of rolls. It is always 2/36.

Drawing Chits:The probability of getting an 11 changes as the chits are drawn and not replaced. At the start there are 36 chits with 2 of them with an 11 on them so the prob. of getting an 11 is 2/36. Let's say you draw a chit with 7 on it the first time you draw a chit (rules say not to return it to the cup for redraw). Now the next time you draw there are only 35 chits left and still 2 11's. Prob = 2/35 (5.7%) Suppose after 33 draws you still have not drawn an 11. The prob. of getting your 11 now is 2/3 (66.7%)...two 11's left out of 3 chits. On the dice the prob. is still only 5.6%
When you replace the the chit after each draw the number of chits returns to 36 so the prob. remains the same for an 11 each time you draw.
So if you want the probabilities for drawing and rolling dice to be the same then you must replace the drawn chip.

Note that at the end of each game turn all drawn chips are returned to the cup to start fresh for the next turn.
 
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Nick West
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"Only two things are infinite; the universe and human stupidity....
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They both have roles to play if you understand what you are trying to model.

If you are modelling something that should have a regression to the mean over time or where experience or repeated attempts should improve your chances then pick chits. Say the chances of catching a thrown ball, or the chances of being shot the longer you stand stationary in the open for a battlefield situation.

Where you have truly independent events - like the chances of being struck by lightning - use dice.
 
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David Orr
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Thank you for the quick reply. I was wondering why the designer would want the probabilities to change and your answer is a good one.
 
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Tom Drueding
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I believe chits were introduced to assuage those that fear a bad run of luck with dice. With chits your roll average will more consistently be close to "7". To avoid complaints about bad rolling you essentially lock the average.

Of course the end of turn can drive the luck.

And even when using the chits, you have the luck in the comparison to the opponents draw/roll.
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