It was a good idea to allow Charlie to go first. This allows Alison to make a choice for her die that increases her changes of winning as follows:
1. Charlie will probably rush to pick the green die to have a chance at rolling 9. He only has an 1:3 of rolling 9. Alison should pick the blue die as in the case Charlie does not roll a 9, Alison has at least a 2:3 change of rolling a higher number.
2. If Charlie picks the red die, Alison should pick the green die. Alison has a 1:3 chance of winning the game if she rolls a 9. If Charlie rolls a 1, Alison has 3:3 chance of winning.
3. Lastly, if Charlie picks the blue die, Alison should pick the red die. If Charlie rolls a 7, Alison has a 1:3 chance of winning. If Charlie rolls any other number, Alison has at least a 2:3 chance of winning.