Problem 3

DARTBOARD PROBLEM

#Dart Board Monte Carlo Simulation


# n:number of darts thrown
dartsim = function(n){
  score = rep(0,n)
    for (i in 1:n){
        rad = runif(1,0,12) #two coordinates per throw, 0:12 for a radius of 12 dartboard
        if(rad<.5){
            score[i]=50
        }
        else if (rad>=.5 && rad<1){
            score[i]=25
        }
        else if (rad>=1 && rad<5){
            score[i]=sample(1:20,1)
        }
        else if (rad>=5 && rad<5.5){
            score[i]=3*sample(1:20,1)
        }
        else if (rad>=5.5 && rad<8.5){
            score[i]=sample(1:20,1)
        }
        else if (rad>=8.5 && rad<9){
            score[i]=2*sample(1:20,1)
        }
        else if (rad>=9 && rad<=12){
            score[i]=0
        }
    }
    #cant have if using other function
    #return(c("total score is:",sum(score)) ) 
    return(sum(score))
}
#Throwing 3 darts
dartsim(3)

## [1] 74

dartrep = function(n,repeats){
    totscore = rep(0,repeats)
    for (i in 1:repeats){
        totscore[i] = dartsim(n)
    }
    avgscore=mean(totscore)
    sdscore=sd(totscore)
    return( c("mean:",avgscore,"std dev:",sdscore) )
}

#1000 games 
dartrep(3,10000)

## [1] "mean:"            "34.4948"          "std dev:"        
## [4] "22.2007400832951"