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Portfolio Type II -- The Dice Game


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Is there an equation to figure out the probability that Ann wins for a given amount of rolls each player gets? for example if you want to know what is the probability that Ann wins if both Ann and Bob roll 4 times. there's got to be a simple equation to figure it out. Otherwise its going to take ALOT of calculating to do.

If Ann and bob roll once, the probability is 15/36

If Ann rolls twice and Bob rolls once, the probability is 125/216

If Ann and Bob each roll twice, the probability is 505/1296

So based on that I know that the denominator of the equation is 6^(A) times 6^(B)

(A = number of rolls Ann gets, B = number of rolls Bob gets)

But I have no Idea how to figure out what the numerator would be.

Any Help?

yes there is a formula, but it is very complicated. since i did this portfolio, i'm less willing to give out much guidance. my one and only hint: sigma notation.

In terms of what variables did you get your formula and a formula for what did you find ? Did you find a formula for the probability for a player to win with n players and n trials or two separate? or something else ?

Edited by ykobe23
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I'm about to start this IA, but the problem is that I don't see how I can account for things like errors or limitations because the problem is entirely probability. Also, when "applying the model to other situations," do the suggestions for accounting for extra players or multiple rolls count?

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Its fairly simple when both roll twice, you should get some pattern use a table for different numbers in each table vary what bob gets on his first roll so basically u shud get 6 tables and from that u can calculate ann's probability of winning in each and every case! then at the end ull get some pattern I'll offer you a hint it has something to do with cubics, I used matrices in my case and then used graphs! My teacher seems to reject the cost/probability hypothesis he says its something to do with expectation, anyone got ny ideas of how I would go about it with expectation?

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This is how I've done it, I dont know if its right

if cost > probability of player winning x payout then the game favours the bank

if cost < the game favours the player

if its equal its fair!

And also r we allowed to choose the probability, dont we have to use the probability that we get from the first bullet point coz theyre both rolling twice! Anyway the casino would never agree to have a game where theyre chances of having to pay the player r more its not profitable for them!

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My teacher recommended creating a simulation using Java (which I'm capable of) and running it multiple times, analyzing the results. I hope this is adequate usage of technology.

My teacher recommended creating a simulation using Java (which I'm capable of) and running it multiple times, analyzing the results. I hope this is adequate usage of technology.

wow, i dont even understand what that means at all!!

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My teacher recommended creating a simulation using Java (which I'm capable of) and running it multiple times, analyzing the results. I hope this is adequate usage of technology.

I Take CS .. we use Blue J .. how are you going to do this using Java ??

I use JCreator. I'm not familiar with Blue J, so I don't know why you would see that as unfeasable.

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if u look at criterion D it says interpret your model, in this case I'm not sure how you do it?? Because all you have calculated is for 3 cases, and when you do get the general formula for any case..you'll have a very limited amount of data to test the fit of the model??

Oh and does using tables obviously this task I used an innumerable amount of them, contribute to marks in technology criteria? Coz its obvious without tables it would be pretty difficult to do the first 3 bullets!

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I sat for a while and actually managed to get a general formula that I know is right for the first four values (11 21 12 22) because I had already calculated them but it's quite complicated and I'm not even sure it's correct beyond that. Teacher is rest but probability is not her thing so not particularly sure how to check it, I mean I know that my logic is right just the formula does nottt look too pretty.

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I figured out the formula for the general case where Ann rolls x times and Bob rolls y times. Here's some help:

First, let's consider Bob's score.

There are six possible cases for Ann's number, 1 to 6. Say her score is k. What is the probability that Ann's score is equal to k (let's just call it P(A=k) for now) AND that all of Bob's rolls are less than k? This tells us the probability that Ann will win given her score is k. Your final answer is the sum from k = 1 to 6.

To actually find P(A=k), consider the case when k=1. There's only one possibility that all of her rolls are equal to one.

Now find P(A=2). This means that we find that all of her rolls have the outcome P(1 or 2) (and we do this x times). However, we need to ensure that at least one of her rolls is equal to 2. So we need to subtract the case when all of her rolls are equal to 1.

And we repeat this process until P(A=6). You should probably see the telescoping series. The formula isn't that bad, but it takes a little bit of thinking.

Edited by Dinstruction
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