who_wins_first

Two people try to toss the same coin. The first person, say F starts tossing first, followed by the second person S. Who ever gets N number of heads first, will win. P represents the probability of getting Heads. To call the function 10000 times, and find the probability that the first person wins, use the following function call. In the following example function call, the first parm 0.2 represents the probability of getting HEAD, and 5 represents the required number of getting Heads for the person to win.

mean(replicate(10000,who_wins_first(0.2,5)))

who_wins_first <- function(P,N)
{
  #Two people try to toss the same coin.
  #The first person, say F starts tossing first, followed by the second person S. Who ever gets N number of heads first, will win
  #P represents the probability of getting Heads

  #To call the function 10000 times, and find the probability that the first person wins, use the following function call
  #mean(replicate(10000,who_wins_first(0.2,5)))
  
  #HF represents the outcome when first person tosses the coin first
  HF <- 0
  HS <- 0
  repeat
    {
       #0 represents tails, 1 represents H, in the following sample function
       F <- sample(0:1,1)
       if (F == 1)
       {
         HF <- (HF + 1)
         if (HF == N) 
           {
           break
           }
       
       }

    S <- sample(0:1,1)
    if (S == 1)
    {
      HS <- (HS + 1)
      if (HS == N) 
      {
        break
      }
      
    }
}
if(HS == HF) return(-1)
if(HS > HF) return(0)
if(HS < HF) return(1)
}

mean(replicate(10000,who_wins_first(0.2,5)))

## [1] 0.5473

mean(replicate(10000,who_wins_first(0.6,10)))

## [1] 0.5359

mean(replicate(10000,who_wins_first(0.2,15)))

## [1] 0.5262

mean(replicate(10000,who_wins_first(0.5,5)))

## [1] 0.5509

mean(replicate(10000,who_wins_first(0.5,10)))

## [1] 0.5338

mean(replicate(10000,who_wins_first(0.5,15)))

## [1] 0.5223

mean(replicate(10000,who_wins_first(0.5,20)))

## [1] 0.5242

mean(replicate(10000,who_wins_first(0.5,30)))

## [1] 0.5156

mean(replicate(10000,who_wins_first(0.5,40)))

## [1] 0.5173

mean(replicate(10000,who_wins_first(0.5,50)))

## [1] 0.5177

mean(replicate(10000,who_wins_first(0.5,60)))

## [1] 0.5105

mean(replicate(10000,who_wins_first(0.2,20)))

## [1] 0.5235

mean(replicate(10000,who_wins_first(0.5,70)))

## [1] 0.5116

To find the variance or standard deviation of the probability, use the following function call:

mean(replicate(10000,who_wins_first(0.5,5)))

## [1] 0.5498

sd(replicate(10000,who_wins_first(0.5,5)))

## [1] 0.4982913

var(replicate(10000,who_wins_first(0.5,5)))

## [1] 0.2471945