pontoon
Simulate the game of pontoon and look at the probabilities of the player competing with the dealer from various player positions.
These experiments were carried out with 8000 sampled games for each probability calculation. The dealer is holding on 17 or greater. I may have not implemented the simulation correctly as I have not yet played at the casino.
(dealer0,player)=<dealer win,player win> (1,12)=<0.59225,0.40775> (1,13)=<0.60575,0.39425> (1,14)=<0.60425,0.39575> (1,15)=<0.603625,0.396375> (1,16)=<0.60825,0.39175> (1,17)=<0.444875,0.40475> (1,18)=<0.293875,0.558125> (1,19)=<0.160625,0.7055> (1,20)=<0,0.846625> (dealer0,player)=<dealer win,player win> (2,12)=<0.634875,0.365125> (2,13)=<0.63475,0.36525> (2,14)=<0.630625,0.369375> (2,15)=<0.646625,0.353375> (2,16)=<0.635625,0.364375> (2,17)=<0.485,0.36925> (2,18)=<0.348,0.506375> (2,19)=<0.221375,0.64375> (2,20)=<0.095875,0.774375> (dealer0,player)=<dealer win,player win> (3,12)=<0.62075,0.37925> (3,13)=<0.6295,0.3705> (3,14)=<0.614,0.386> (3,15)=<0.6215,0.3785> (3,16)=<0.627875,0.372125> (3,17)=<0.4895,0.382125> (3,18)=<0.34175,0.519375> (3,19)=<0.2145,0.654625> (3,20)=<0.093625,0.78275> (dealer0,player)=<dealer win,player win> (4,12)=<0.612,0.388> (4,13)=<0.615375,0.384625> (4,14)=<0.611625,0.388375> (4,15)=<0.606625,0.393375> (4,16)=<0.6,0.4> (4,17)=<0.480375,0.386375> (4,18)=<0.341375,0.524> (4,19)=<0.203,0.6755> (4,20)=<0.088375,0.7935> (dealer0,player)=<dealer win,player win> (5,12)=<0.59675,0.40325> (5,13)=<0.593,0.407> (5,14)=<0.588625,0.411375> (5,15)=<0.58025,0.41975> (5,16)=<0.587,0.413> (5,17)=<0.454125,0.413875> (5,18)=<0.323375,0.55125> (5,19)=<0.2015,0.675125> (5,20)=<0.092,0.78975> (dealer0,player)=<dealer win,player win> (6,12)=<0.54775,0.45225> (6,13)=<0.556375,0.443625> (6,14)=<0.547875,0.452125> (6,15)=<0.546875,0.453125> (6,16)=<0.551375,0.448625> (6,17)=<0.459375,0.455> (6,18)=<0.336375,0.53725> (6,19)=<0.201,0.6745> (6,20)=<0.087375,0.795375> (dealer0,player)=<dealer win,player win> (7,12)=<0.68525,0.31475> (7,13)=<0.693375,0.306625> (7,14)=<0.687875,0.312125> (7,15)=<0.678625,0.321375> (7,16)=<0.684125,0.315875> (7,17)=<0.338375,0.318875> (7,18)=<0.257875,0.656875> (7,19)=<0.170375,0.732875> (7,20)=<0.07125,0.835875> (dealer0,player)=<dealer win,player win> (8,12)=<0.70275,0.29725> (8,13)=<0.719,0.281> (8,14)=<0.711875,0.288125> (8,15)=<0.717875,0.282125> (8,16)=<0.712875,0.287125> (8,17)=<0.5655,0.282125> (8,18)=<0.22,0.448125> (8,19)=<0.152875,0.775125> (8,20)=<0.067375,0.8405> (dealer0,player)=<dealer win,player win> (9,12)=<0.74,0.26> (9,13)=<0.73775,0.26225> (9,14)=<0.729125,0.270875> (9,15)=<0.736875,0.263125> (9,16)=<0.730625,0.269375> (9,17)=<0.605,0.2565> (9,18)=<0.445875,0.4105> (9,19)=<0.125,0.540875> (9,20)=<0.059375,0.885375> (dealer0,player)=<dealer win,player win> (10,12)=<0.768875,0.231125> (10,13)=<0.76225,0.23775> (10,14)=<0.749375,0.250625> (10,15)=<0.7575,0.2425> (10,16)=<0.76075,0.23925> (10,17)=<0.626375,0.25075> (10,18)=<0.488875,0.378375> (10,19)=<0.35325,0.50975> (10,20)=<0.037625,0.645875>
(dealer0,player)=<dealer win,player win> (1,7)=<0.51325,0.45075> (1,8)=<0.46425,0.48875> (1,9)=<0.387125,0.552375> (1,10)=<0.371375,0.5925> (1,11)=<0.57575,0.385625> (1,12)=<0.60975,0.35375> (1,13)=<0.640125,0.325> (1,14)=<0.681,0.2825> (1,15)=<0.710625,0.2555> (1,16)=<0.741125,0.225> (1,17)=<0.784,0.190375> (1,18)=<0.844625,0.14375> (dealer0,player)=<dealer win,player win> (2,7)=<0.549125,0.416375> (2,8)=<0.502375,0.452375> (2,9)=<0.449875,0.493625> (2,10)=<0.411375,0.550625> (2,11)=<0.599625,0.36725> (2,12)=<0.63825,0.32625> (2,13)=<0.655875,0.306375> (2,14)=<0.69175,0.267375> (2,15)=<0.719,0.245125> (2,16)=<0.75375,0.2085> (2,17)=<0.799125,0.1755> (2,18)=<0.851,0.13875> (dealer0,player)=<dealer win,player win> (3,7)=<0.54725,0.4175> (3,8)=<0.490625,0.46475> (3,9)=<0.43975,0.505625> (3,10)=<0.401875,0.561125> (3,11)=<0.592375,0.373875> (3,12)=<0.630875,0.3315> (3,13)=<0.652,0.312875> (3,14)=<0.693625,0.278> (3,15)=<0.720125,0.24425> (3,16)=<0.753125,0.21125> (3,17)=<0.794125,0.179625> (3,18)=<0.853125,0.137> (dealer0,player)=<dealer win,player win> (4,7)=<0.51925,0.446125> (4,8)=<0.48025,0.473625> (4,9)=<0.421125,0.524875> (4,10)=<0.378625,0.589375> (4,11)=<0.582125,0.386875> (4,12)=<0.620875,0.34675> (4,13)=<0.644625,0.32475> (4,14)=<0.690125,0.275375> (4,15)=<0.70975,0.25725> (4,16)=<0.752375,0.210875> (4,17)=<0.79575,0.18375> (4,18)=<0.845625,0.1425> (dealer0,player)=<dealer win,player win> (5,7)=<0.512125,0.4555> (5,8)=<0.459875,0.498875> (5,9)=<0.40475,0.541125> (5,10)=<0.3745,0.5955> (5,11)=<0.593,0.376375> (5,12)=<0.607625,0.359> (5,13)=<0.66,0.30825> (5,14)=<0.67875,0.2905> (5,15)=<0.721125,0.248> (5,16)=<0.748375,0.2195> (5,17)=<0.79325,0.185> (5,18)=<0.85075,0.138375> (dealer0,player)=<dealer win,player win> (6,7)=<0.48125,0.496875> (6,8)=<0.447375,0.5125> (6,9)=<0.380125,0.567625> (6,10)=<0.357625,0.614125> (6,11)=<0.562625,0.4085> (6,12)=<0.598,0.37275> (6,13)=<0.6205,0.34925> (6,14)=<0.675375,0.297375> (6,15)=<0.710375,0.26675> (6,16)=<0.7535,0.219> (6,17)=<0.793875,0.18575> (6,18)=<0.84825,0.142375> (dealer0,player)=<dealer win,player win> (7,7)=<0.5435,0.372875> (7,8)=<0.48975,0.456875> (7,9)=<0.43675,0.502375> (7,10)=<0.40725,0.552875> (7,11)=<0.597875,0.359375> (7,12)=<0.6125,0.338375> (7,13)=<0.65325,0.303125> (7,14)=<0.6785,0.277125> (7,15)=<0.7035,0.2545> (7,16)=<0.727625,0.22825> (7,17)=<0.78425,0.204125> (7,18)=<0.847625,0.144> (dealer0,player)=<dealer win,player win> (8,7)=<0.618375,0.344375> (8,8)=<0.511625,0.388125> (8,9)=<0.45675,0.483875> (8,10)=<0.4305,0.521375> (8,11)=<0.615,0.338625> (8,12)=<0.646875,0.30375> (8,13)=<0.68125,0.270875> (8,14)=<0.695,0.26025> (8,15)=<0.717375,0.239> (8,16)=<0.740625,0.207875> (8,17)=<0.783875,0.18275> (8,18)=<0.844875,0.149125> (dealer0,player)=<dealer win,player win> (9,7)=<0.63375,0.327375> (9,8)=<0.5985,0.353375> (9,9)=<0.485875,0.41125> (9,10)=<0.467625,0.4835> (9,11)=<0.656375,0.2905> (9,12)=<0.6705,0.2735> (9,13)=<0.700125,0.2475> (9,14)=<0.725125,0.222> (9,15)=<0.744875,0.201125> (9,16)=<0.760625,0.186875> (9,17)=<0.796625,0.164125> (9,18)=<0.838,0.1325> (dealer0,player)=<dealer win,player win> (10,7)=<0.66175,0.307625> (10,8)=<0.610625,0.344125> (10,9)=<0.5495,0.394375> (10,10)=<0.493375,0.47525> (10,11)=<0.684875,0.281875> (10,12)=<0.7085,0.257> (10,13)=<0.728375,0.2395> (10,14)=<0.742875,0.220875> (10,15)=<0.769,0.198625> (10,16)=<0.788875,0.179625> (10,17)=<0.816875,0.161125> (10,18)=<0.863,0.125>