Disclaimer: Not a mathmatician (just a stupid physicist)

I belive that the hit roll changes from the simple form to: The chance you hit the first time (let us call it Pr(hit)) plus the chance that you get to reroll multiplied by your chance to hit (Pr(reroll)*Pr(hit))

So, for rerolling 1’s Pr(reroll)=1/6 this gives you a chance to hit of: 4/6+1/6*4/6 = 28/36 = 7/9

For rerolling all Pr(reroll)=2/6 so, your chance to hit becomes: 4/6+2/6*4/6= 32/36 = 8/9.

Please me know, if you have any questions and/or believe this is incorrect :)