# 
# Written by:
# -- 
# John L. Weatherwax                2006-12-31
# 
# email: wax@alum.mit.edu
# 
# Please send comments and especially bug reports to the
# above email address.
# 
#-----

u = 0.5
d = 0.5 
p = 0.6 
L = 260 

n_star = ceiling( - L * log( 1 - d ) / log( (1+u)/(1-d) ) ) 
p_win  = 1 - pbinom( n_star-1, L, p ) # pbinom is the binomial cummulative distribution 
print( sprintf( "p_win= %10.6f", p_win ) )

pWinL = c()
for( ll in 1:500 ){
  n_star = ceiling( - ll * log( 1 - d ) / log( (1+u)/(1-d) ) )
  p_win  = 1 - pbinom( n_star-1, ll, p )
  pWinL = c(pWinL,p_win)
}

#postscript("../../WriteUp/Graphics/ChapterXXX/", onefile=FALSE, horizontal=FALSE)
matplot( 1:500, pWinL )
#dev.off()

spot = match( max(pWinL), pWinL ) # what index gives the largest P_win
print( sprintf( "p_win is largest for L= %d with p_win= %10.6f", spot, pWinL[spot] ) )