/* truel.tc - tct - 8/18/9 - linux version only

/* a "truel" is a 3-way duel - please see http://www.yofx.org/?p=194 for
/* background on this interesting problem - in this case, Red=Zee,
/* Yellow=Toby (can't see a Black cat) and Blue=Luna

/* z vs t duel hit probabilities z(0)/z(1) and t(0)/t(1)
/* returns 1 if z wins else returns 0

duel int z(1),t(1) [
 if (random(1,z(1))<=z(0)) return 1
 if !(random(1,t(1))<=t(0)) return duel(z,t)
 return 0
 ]

dpf int n,d,p [
 /* display proper fraction n/d as decimal number
 /* with p digit precision 
 int w
 w=10*n/d
 if (p) [
  MC w,14
  dpf 10*n%d,d,p-1 /* recursive call
  ]
 ]

/* hit probabilities: zee z(0)/z(1) toby t(0)/t(1) luna l(0)/l(1)

int z(1),t(1),l(1) /* pointers to global numerators and denominators

contest [
 l(0)=l(1)=1 /* luna is a purrfek markscat
 int zr(1) /* pointer to work numerator and denominator
 zr(1)=1000 /* rounds
 int zwins1,zwins2
 int i
 for (i=1;i<=zr(1);++i) [
  zwins1=zwins1+duel(z,t)
  zwins2=zwins2+duel(z,l)
  ]
 /* pointers to work numerators and denominators
 int f(1),n(1),m(1)
 int o(1);o(0)=o(1)=1
 zr(0)=zwins1
 fracmult(t,zr,n)
 fracsub(o,t,f) /* probability t misses=1-t(0)/t(1)
 zr(0)=zwins2
 fracmult(f,zr,m)
 fracadd(n,m,l)
 ps "0.";dpf(l(0),l(1),5)
 ]

fracadd int nd1(1),nd2(1),nd(1) [ /* add fractions
 nd(0)=nd2(1)*nd1(0)+nd1(1)*nd2(0)
 nd(1)=nd1(1)*nd2(1)
 ]

fracsub int nd1(1),nd2(1),nd(1) [ /* subtract fractions
 nd(0)=nd2(1)*nd1(0)-nd1(1)*nd2(0)
 nd(1)=nd1(1)*nd2(1)
 ]

fracmult int nd1(1),nd2(1),nd(1) [ /* multiply fractions
 nd(0)=nd1(0)*nd2(0)
 nd(1)=nd1(1)*nd2(1)
 ]

main [
 char black,red,green,yellow,blue,magenta,cyan,white
 char lo,hi
 black='0';red='1';green='2';yellow='3'
 blue='4';magenta='5';cyan='6';white='7'
 lo='0';hi='1'
 hilo hi
 color red;pl"  ."
 color white;pl" / \"
 color yellow;pl".";color white;ps" _ ";color blue;ps"."
 pl"";pl""
 color blue;ps "truel.tc - 8/18/9 - tct";color white;pl""
 pl"Please enter hit probabilities for the first two shooters.";pl"";pl""
 ps"Player 1 numerator (e.g. 1): ";z(0)=gn
 ps"Player 1 denominator (e.g. 3): ";z(1)=gn
 ps"Player 2 numerator (e.g. 2): ";t(0)=gn
 ps"Player 2 denominator (e.g. 3): ";t(1)=gn
 int howmany;howmany=11
 while (--howmany) [pl"simulation";pn 10-howmany;ps ": ";contest]
 pl"";pl"The expected value for example probabilities is 25/63=0.3968"
 pl""
 color blue
 pl"Please visit http://preview.tinyurl.com/mpolsb"
 pl""
 hilo lo
 ]