What probability distribution applies?

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SUMMARY

The discussion centers on determining the appropriate probability distribution for a betting scenario involving Peter and Paul, where each bets one dollar per game with varying probabilities of Peter winning (p values). The key focus is on calculating the probabilities that Peter is ahead by $10, $100, and $1000 for specific p values: 1/10, 1/3, 0.49, 0.499, 0.501, 0.51, 2/3, and 9/10. The participants suggest using a calculator to create a table of these probabilities, emphasizing the need to consider winning streaks versus halting wins in the analysis.

PREREQUISITES
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  • Familiarity with binomial distributions
  • Basic knowledge of stochastic processes
  • Proficiency in using statistical calculators or software
NEXT STEPS
  • Research binomial distribution and its applications in betting scenarios
  • Learn about Markov chains and their relevance to winning streaks
  • Explore the concept of gambler's ruin and its mathematical implications
  • Utilize statistical software to simulate betting outcomes based on varying p values
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Homework Statement



Peter and Paul bet one dollar each on each game. Each is willing
to allow the other unlimited credit. Use a calculator to make a
table showing, to four decimal places, for each of p = 1/10, 1/3,
.49, .499, .501, .51, 2/3, 9/10 the probabilities that Peter is ever
ahead by $10, by $100, and by $1000. (p is the probability of Peter winning the game)



Homework Equations



I don't know.

The Attempt at a Solution



I don't know what distribution applies, or how to choose the variables.

Thank you very much for any help.
 
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If winning is in streaks of 10, 100, 1000 then each p is raised to those powers.
But if it is done haltingly (e.g., to win 10 games ahead of Paul, Peter wins 7 in a row, then loses 2, then wins again 5 in a row) how could this be represented?

Thank you, if anyone still looks here.
 

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