Presented before you are 4 unusual 6-sided dice:

has the numbers 5, 5, 5, 5, 1 and 1 on its sides

has the numbers 6, 6, 2, 2, 2 and 2 on its sides

has the numbers 6, 4, 4, 2, 2 and 1 on its sides

has the numbers 3, 3, 3, 3, 3 and 1 on its sides

I inform those that are unaware that the average value they would roll with each of the 4 dice are (roughly) 3.66, 3.33, 3.17 and 2.67 respectively. All dice are fair and players find it impossible to cheat when rolling them.

I request a $1 payment from you to play. You may choose any one die. Then I may choose any of the remaining dice. We then roll. If you roll more than or the same as me, I return your original $1 stake and a bonus $1 prize. If I score more than you, I keep your stake and you win nothing.

What would be your strategy if you wanted to walk away from my stall with the most amount of money possible?

(Thanks go to an old university professor would showed us something similar, which instantly intrigued me, in a Probability lecture)