A hustler wants to play the Gambler’s Ruin game with you, in which you pay him...
A hustler wants to play the Gambler’s Ruin game with you, in which you pay him $1 if his coin comes up heads and he pays you $1 if it comes up tails. But you object when you discover that he will use a biased coin that has probability 2/3 of coming up heads. “I’ll be a sport and give you a big advantage,” he replies. “I will start with only $1 and you can start with $2. Whoever gets all $3 first can keep it.” Do you now have an advantage, even though you use his biased coin?
Find out by computing p1, where pi is the probability that the hustler wins the game starting with $i, for 0 ≤ i ≤ 3.
You are required to solve this using the following method: from a given position, condition on the outcome of the next coin flip.
Give an exact value for p1 as a simplified fraction. Do you indeed have an advantage in this game? Give a 1-2 sentence to explain your reasoning.
Homework Answers
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A hustler wants to play the Gambler’s Ruin game with you, in
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This is discrete mathematics If you do it right, I must give praise. You must use probability spa...
This is discrete mathematics
If you do it right, I must give praise.
You must
use probability space is a triple relative
acknowledge.
S: is a
sample sapce
E=p(s) is
the set of all events
P:
E-->R is a function.
The important thing that I need to say three times:
If you don't know how to do it, please don't do
it.
don't copy others,
especially for question (a), give sample space, probability
measure
The important thing that I need...
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35. You and I play the following game: I toss a coin repeatedly. The coin is unfair and P(H) = p. The game ends the first time that two consecutive heads (HH) or two consec- utive tails (TT) are observed. I win if (HH) is observed and you win if (TT) is observed. Given that I won the game, find the probability that the first coin toss resulted in heads?
This is discrete mathematics
If you do it right, I must give praise.
You must
use probability space is a triple relative
acknowledge.
S: is a
sample sapce
E=p(s) is
the set of all events
P:
E-->R is a function.
The important thing that I need to say three times:
If you don't know how to do it, please don't do
it.
don't copy others,
especially for question (a), give sample space, probability
measure
The important thing that I need...
3) James made a game that costs $5 to play and stafames noticed the letter die. If HEADS you try to get a 1,3, or common. If tails you try to get a 2 ora because they start with the letter T. His logic is ads and 1,3, or 5 you win $10; heads and the others outcomes is tals with 2 or 3 wins $20 and tails with the other outcomes e dollar amount because he doesn't know money...
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