I guess I'm daft, but if they'd just flip a coin each time on who pays, in the long run they'd each pay the same, if each payment event were to be random (let's

I guess I'm daft, but if they'd just flip a coin each time on who pays, in the long run they'd each pay the same, if each payment event were to be random (let's even say within an upper limit, to keep the 'in the long run' within the lifespan of their relationship). Why wouldn't the dollar amounts of these events be essentially random?