Your chance is p - how much would you bet ?

[punter11235]

Hello,

I know its general question but there was a hand I played yesterday that made me think about it. I was playing NLHE max buying 100$ (blinds 0.5/1) and was doing pretty well having 220$ (at this table). There was a guy who raise preflop to 10$ having any decent ace (but no big pairs, with them he was raising less), and I was dealt KK. Now I knew that if I went all-in he would call, which happened at the table, he turned AK and I lost this 2-1 coin flip (he had me covered).
As I have bankroll enough to play NL100$ but still playing NL200$ with short stack (sth like buy in 90 and cash out around 160) this was painful loss. My decision was influenced (I know, irrationally) about net profit this day which was big enough to cover one 440$ coinflip.
I know about Kelly rule (telling you to bet 2p-1 of your bankroll in such cases) and about other variations of it...

But now... your chance is p, how much would you bet ?
How % of your bankroll would you bet for KK vs AK chance ?

Best wishes