// max probability third coin protocol is initiated
multi ( Pmax=? [ F (s1=3 & r1=3) | (s2=3 & r2=3) ] , P>=1-0.10833260973166493*0.10833260973166493 [ G (c1=0 | c2=0) ] ) // k=2
multi ( Pmax=? [ F (s1=3 & r1=3) | (s2=3 & r2=3) ] , P>=1-0.061518025457429924*0.061518025457429924 [ G (c1=0 | c2=0) ] ) // k=4
multi ( Pmax=? [ F (s1=3 & r1=3) | (s2=3 & r2=3) ] , P>=1-0.031242851478116937*0.031242851478116937 [ G (c1=0 | c2=0) ] ) // k=8
multi ( Pmax=? [ F (s1=3 & r1=3) | (s2=3 & r2=3) ] , P>=1-0.020828194647463896*0.020828194647463896 [ G (c1=0 | c2=0) ] ) // k=12
multi ( Pmax=? [ F (s1=3 & r1=3) | (s2=3 & r2=3) ] , P>=1-0.015618082185381363*0.015618082185381363 [ G (c1=0 | c2=0) ] ) // k=16
multi ( Pmax=? [ F (s1=3 & r1=3) | (s2=3 & r2=3) ] , P>=1-0.012491262448108213*0.012491262448108213 [ G (c1=0 | c2=0) ] ) // k=20