How to refer to how long ago an event was

Ok here's my scenario. My buddy and I were about to play a game. We've been playing the game one time each day. My last win was on Tuesday. We tied on Wednesday and he won on Thursday. So today, Friday, as we were about to start, I said "I haven't won in 3 games." I meant that as in, "3 games ago was my last win."

Anyway, he said I was phrasing it wrong and that if I say "I haven't won in 3 games," that means I've lost three in a row. I disagreed, saying that it was basically the same as saying "I haven't won since 3 games ago."

So literally every person I've asked so far has disagreed with me, but I still think I'm right. Here's why. Saying "I haven't won in 3 games" is identical to saying "I haven't eaten in 3 days." And if you were to say that, would you not be saying that Tuesday, 3 days ago was the last time you ate? In the same way, when I say I haven't won in 3 games, I'm saying that the third game ago (just like Tuesday is the third day ago) was the last time I won.

Just like an NFL team that won their first game then lost their second game, as they warmed up for their third game they would say "we haven't won in 2 weeks." Totally true statement. Is it not interchangeable with "we haven't won in 2 games"?

I think there's a case to be made for my way, though I wonder if there are actual grammatical rules that dictate how we talk about the past in such cases. Is it different if you refer to the unit of time (3 days) as opposed to referring to the event (3 games)? I could see that. But I want to know if there is an actual standard for this.

I also think that people almost universally refer to it the way I did in the example but just don't realize it at the time.