Probability of a Type 4 Ride Chain

Grade 1:(41*41*43*43)/(2*3*23*23*47*47)=0.443304343262069 is the probability of not drawing it normally

Therefore, 1-(41*41*43*43)/(2*3*23*23*47*47)=0.556695656737931 is the probability of getting the Grade 1

Grade 2:(41*41*43*43*39)/(2*3*23*23*47*47*43)=0.4020667299353649 not drawing it normally

[((41*41*43*43)/(2*3*23*23*47*47))*((41*41*43*43*39)/(2*3*23*23*47*47*43))*[1-(42*41*40*39*38*40*39*38*37*36)/(49*48*47*46*45*47*46*45*44*43)]*[1-(38/42)*(37/41)*(36/40)*(35/39)*(34/38)*(33/37)*(32/36)]]=0.0767069311739243 Using the G1 skill to correct a misride

[1-(41*41*43*43)/(2*3*23*23*47*47)]*[1-(39*38*37*36*35*34*33)/(43*42*41*40*39*38*37)]=0.2909784728780507 Using G0 skill to search it.

[1-[((41*41*43*43)/(2*3*23*23*47*47))*((41*41*43*43*39)/(2*3*23*23*47*47*43))*[1-(42*41*40*39*38*40*39*38*37*36)/(49*48*47*46*45*47*46*45*44*43)]*[1-(38/42)*(37/41)*(36/40)*(35/39)*(34/38)*(33/37)*(32/36)]]]*[1-[1-(41*41*43*43)/(2*3*23*23*47*47)]*[1-(39*38*37*36*35*34*33)/(43*42*41*40*39*38*37)]]=0.6546346616401753 Failing to search it

(41*41*43*43*39)/(2*3*23*23*47*47*43)*[1-[((41*41*43*43)/(2*3*23*23*47*47))*((41*41*43*43*39)/(2*3*23*23*47*47*43))*[1-(42*41*40*39*38*40*39*38*37*36)/(49*48*47*46*45*47*46*45*44*43)]*[1-(38/42)*(37/41)*(36/40)*(35/39)*(34/38)*(33/37)*(32/36)]]]*[1-[1-(41*41*43*43)/(2*3*23*23*47*47)]*[1-(39*38*37*36*35*34*33)/(43*42*41*40*39*38*37)]]=0.2632068177080094 Failing to search or draw it normally

Therefore, 1-(41*41*43*43*39)/(2*3*23*23*47*47*43)*[1-[((41*41*43*43)/(2*3*23*23*47*47))*((41*41*43*43*39)/(2*3*23*23*47*47*43))*[1-(42*41*40*39*38*40*39*38*37*36)/(49*48*47*46*45*47*46*45*44*43)]*[1-(38/42)*(37/41)*(36/40)*(35/39)*(34/38)*(33/37)*(32/36)]]]*[1-[1-(41*41*43*43)/(2*3*23*23*47*47)]*[1-(39*38*37*36*35*34*33)/(43*42*41*40*39*38*37)]]=0.7367931822919906 is the probability of getting the Grade 2

Grade 3: (41*41*43*43*39*38*37)/(2*3*23*23*47*47*43*42*41)=0.3282844496452515 Not drawing it normally

(1-(41*41*43*43)/(2*3*23*23*47*47))*((1-(41*41*43*43)/(2*3*23*23*47*47))*(1-(39*38*37*36*35*34*33)/(43*42*41*40*39*38*37))+((41*41*43*43)/(2*3*23*23*47*47))*((39*38*37*36*35*34*33)/(43*42*41*40*39*38*37))*(1-(39*38*37*36*35*34*33)/(43*42*41*40*39*38*37))=0.2235558142348121 G0 check, both for if you don't have the G2 in hand and the top 7 doesn't have a G2, and if you do have a G2 in hand, and check straight for the G3.

(1-(1-(41*41*43*43)/(2*3*23*23*47*47))*((1-(41*41*43*43)/(2*3*23*23*47*47))*(1-(39*38*37*36*35*34*33)/(43*42*41*40*39*38*37))+((41*41*43*43)/(2*3*23*23*47*47))*((39*38*37*36*35*34*33)/(43*42*41*40*39*38*37))*(1-(39*38*37*36*35*34*33)/(43*42*41*40*39*38*37)))=0.7764441857651879 Failing to search Grade 3

(41*41*43*43*39*38*37)/(2*3*23*23*47*47*43*42*41)*(1-(1-(41*41*43*43)/(2*3*23*23*47*47))*((1-(41*41*43*43)/(2*3*23*23*47*47))*(1-(39*38*37*36*35*34*33)/(43*42*41*40*39*38*37))+((41*41*43*43)/(2*3*23*23*47*47))*((39*38*37*36*35*34*33)/(43*42*41*40*39*38*37))*(1-(39*38*37*36*35*34*33)/(43*42*41*40*39*38*37)))=0.2548945522041801 Failing to draw or search out the Grade 3

Therefore, 1-(41*41*43*43*39*38*37)/(2*3*23*23*47*47*43*42*41)*(1-(1-(41*41*43*43)/(2*3*23*23*47*47))*((1-(41*41*43*43)/(2*3*23*23*47*47))*(1-(39*38*37*36*35*34*33)/(43*42*41*40*39*38*37))+((41*41*43*43)/(2*3*23*23*47*47))*((39*38*37*36*35*34*33)/(43*42*41*40*39*38*37))*(1-(39*38*37*36*35*34*33)/(43*42*41*40*39*38*37)))=0.7451054477958199 Probability of getting grade 3

Probability of Grade 1*Probability of Grade 2*Probability of Grade 3=(1-(41*41*43*43)/(2*3*23*23*47*47))*(1-(41*41*43*43*39)/(2*3*23*23*47*47*43)*[1-[((41*41*43*43)/(2*3*23*23*47*47))*((41*41*43*43*39)/(2*3*23*23*47*47*43))*[1-(42*41*40*39*38*40*39*38*37*36)/(49*48*47*46*45*47*46*45*44*43)]*[1-(38/42)*(37/41)*(36/40)*(35/39)*(34/38)*(33/37)*(32/36)]]]*[1-[1-(41*41*43*43)/(2*3*23*23*47*47)]*[1-(39*38*37*36*35*34*33)/(43*42*41*40*39*38*37)]])*(1-(41*41*43*43*39*38*37)/(2*3*23*23*47*47*43*42*41)*(1-(1-(41*41*43*43)/(2*3*23*23*47*47))*((1-(41*41*43*43)/(2*3*23*23*47*47))*(1-(39*38*37*36*35*34*33)/(43*42*41*40*39*38*37))+((41*41*43*43)/(2*3*23*23*47*47))*((39*38*37*36*35*34*33)/(43*42*41*40*39*38*37))*(1-(39*38*37*36*35*34*33)/(43*42*41*40*39*38*37)))))=0.3056195770260605

Probability of Grade 1*Probability of Grade 2=(1-(41*41*43*43)/(2*3*23*23*47*47))*(1-(41*41*43*43*39)/(2*3*23*23*47*47*43)*[1-[((41*41*43*43)/(2*3*23*23*47*47))*((41*41*43*43*39)/(2*3*23*23*47*47*43))*[1-(42*41*40*39*38*40*39*38*37*36)/(49*48*47*46*45*47*46*45*44*43)]*[1-(38/42)*(37/41)*(36/40)*(35/39)*(34/38)*(33/37)*(32/36)]]]*[1-[1-(41*41*43*43)/(2*3*23*23*47*47)]*[1-(39*38*37*36*35*34*33)/(43*42*41*40*39*38*37)]])=0.4101695644960698

Probability of the entire chain=30.6%

Probability of riding Grade 1 *and* Grade 2=41%