R expert Required -- 2

R expert required for solution of a question
Dice game - I have 2 dice, one of them is a cube (6 faces), the other is a regular dodecahedron (12 faces). Both dice are unweighted - the probability of landing on each face is equal - and the faces on each are numbered from 1-6 and 1-12 respectively. I roll both dice simultaneously, with the intention of offering a market for 'highest score - cube vs dodecahedron'. The fair price for each selection in this market changes depending on the payout in the event of a tie, with the 3 possible options being (a) dead heat rules (half payout for both sides), (b) void (all bets returned), and (c) 3 way market (offer the draw as a selection). What is the fair price to back the cube in all 3 scenarios? Extension 1 - same question, but with each dice weighted by the value of each face Extension 2 - back to unweighted, but include an (unweighted) regular tetrahedron numbered 1-4 and create a tetrahedron vs cube vs dodecahedron game, under dead heat rules - prices for each dice Extension 3 - as per Extension 2 but tetrahedron sides numbered 5-8, and cube sides numbered 4-9