I am creating a program for an online, fake-currency, betting website where people bet on AI 2D fighters, Saltybet. This program just monitors the IRC chat and records win/loses as well as other important statistics. One important statistic I record is the betting ratio. Say fighter A had a total bet of $100,000 and fighter B had $1,000,000. The ratio for this match would of course be 1:10. Next let's say they fight again and the ratios are switched. I would want a way to average the ratios such that the average is 1:1 for both.

Treating the ratios as fractions and doing the traditional averaging results in a ratio of approximately 5:1 for each, which doesn't make sense. I've tried making ratios less than 1 negative and doing a traditional average, but that centers the mean around 0 when I want it to at least be displayed as 1. Behind the scenes what the number looks like doesn't matter, but when it is displayed I want the number 1 to appear for a case like the above. I've also tried a geometric mean, but that converges to fast. Even drastically large ratios after 4 or so recorded fights have very little effect. Does anyone have a good idea how to average the ratios in a way that makes sense?