A probability problem!

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hdadashi

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Hello fellows,
I have a question about probability.
Assume I have a chance of 0.5 to lose and 0.5 to win a gamble. I have zero scores in the beginning and I want to reach 5500, for instance. If I win a match I win 200 scores and if I lose I lose 20 scores. The question is, How many matches should I participate to reach my goal (5500)?
Also, it's impossible to have negative scores.
I exactly want the formula as well.
So many thanks,
 
hdadashi said:
Hello fellows,
I have a question about probability.
Assume I have a chance of 0.5 to lose and 0.5 to win a gamble. I have zero scores in the beginning and I want to reach 5500, for instance. If I win a match I win 200 scores and if I lose I lose 20 scores. The question is, How many matches should I participate to reach my goal (5500)?
Also, it's impossible to have negative scores.
I exactly want the formula as well.
So many thanks,
Click to expand...
Please follow the rules of posting in this forum, as enunciated at:

READ BEFORE POSTING

Please share your work/thoughts about this assignment

What is your "expected" score for each match?
 
hdadashi said:
Hello fellows,
I have a question about probability.
Assume I have a chance of 0.5 to lose and 0.5 to win a gamble. I have zero scores in the beginning and I want to reach 5500, for instance. If I win a match I win 200 scores and if I lose I lose 20 scores. The question is, How many matches should I participate to reach my goal (5500)?
Also, it's impossible to have negative scores.
I exactly want the formula as well.
So many thanks,
Click to expand...
So for example if you lose the 1st game match you score is still 0?? Can we see your attempt at working this problem?
 
What is the expected value of the points earned for a single match?

Divide 5500 by this to obtain the expected value of the number of matches you should participate in to reach 5500.

The expected value is the best you can do. Random games do not admit exact answers.
 
Romsek said:
What is the expected value of the points earned for a single match?

Divide 5500 by this to obtain the expected value of the number of matches you should participate in to reach 5500.

The expected value is the best you can do. Random games do not admit exact answers.
Click to expand...
I think it should be (0.5*220)+(0.5*20) due to p*Win + (1-p)*Lose. However, Im not sure if its true.
it should have an exact answer, if not it should have a range of answers like 10 to 12 matches he should participate in which, with 95% confidential level we can say he can attain his goal.
 
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hdadashi said:
I think it should be (0.5*220)+(0.5*20) due to p*Win + (1-p)*Lose. However, Im not sure if its true.
Click to expand...
So how much is that?

That would be "expected" value after one game.

How many games you would be expected to play to collect 5500 points?
 
I
Subhotosh Khan said:
So how much is that?

That would be "expected" value after one game.

How many games you would be expected to play to collect 5500 points?
Click to expand...
I mean I think the answer is 5500/((0.5*200)+(0.5*20))=5500/110 which is 50 matches. Is it correct? Because the matches are independent of each other and each one has Bernoulli's probability function and EV of Bernoulli is p*Win + (1-p)*Lose, so I think the answer of 50 might be correct.
 
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hdadashi said:
I think it should be (0.5*220)+(0.5*20) due to p*Win + (1-p)*Lose. However, Im not sure if its true.
it should have an exact answer, if not it should have a range of answers like 10 to 12 matches he should participate in which, with 95% confidential level we can say he can attain his goal.
Click to expand...
This raises some issues I don't think you mentioned previously.

First, if this problem was given to you, please state it completely as given. If it requires a confidence interval, that is an important part of the problem, which is now very different from the expected value that has been discussed. If you made it up, then we need to know what the real goal is, as well as what you know about this sort of problem (which is clearly not "nothing").

Second, why do you indicate the values of winning and losing as 220 and 20, respectively? In the problem as stated, wouldn't they be 200 and -20 (unless the result would be negative)? Or have you done some thinking you haven't shown, that transforms the problem into a new one?
 
Dr.Peterson said:
This raises some issues I don't think you mentioned previously.

First, if this problem was given to you, please state it completely as given. If it requires a confidence interval, that is an important part of the problem, which is now very different from the expected value that has been discussed. If you made it up, then we need to know what the real goal is, as well as what you know about this sort of problem (which is clearly not "nothing").

Second, why do you indicate the values of winning and losing as 220 and 20, respectively? In the problem as stated, wouldn't they be 200 and -20 (unless the result would be negative)? Or have you done some thinking you haven't shown, that transforms the problem into a new one?
Click to expand...
Thanks for your response, but I made the problem up by myself and it originates from an experience in my personal life. However, I think I made a mistake and you are completely right. its +200 and -20 which changes the result. I think the answer should be [5500/((0.5*200)+(0.5*-20))]+1=[61.11]+1 which is 62 matches now. Am I right?
 
hdadashi said:
I think it should be (0.5*220)+(0.5*20)
Click to expand...
No! Since you lose 20 points the expected value should be (0.5*220)-(0.5*20). I even have some trouble with that as this is NOT correct on your first try as it would be (0.5*220)-(0.5*0) as you do not lose anything IF it would make you negative. This really complicates things and to be honest I do not want to think about how to overcome this. I am sure that someone else will help you.
 
The fact that "it's impossible to have negative scores" definitely complicates things, and we'd have to try some relatively complicated techniques (that I don't have in my back pocket) if this were for a class.

But if it's just for something personal, presumably it doesn't need to be provably exact in any sense. Unfortunately, we don't know what you actually need this for, so it's hard to decide how rough an answer is acceptable.

Why do you want to know "How many matches should I participate to reach my goal (5500)?" -- given that, as you've been told, there is no exact answer, and in fact it might take forever! There are no guarantees in gambling.
 
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