Random determining of who goes first - increase likelihood?

I’m developing a mobile game where two players play against each other. The game determines who goes first with simple random number generation.

The 50/50 chance 100% of the time may not be a good idea. Some context:

1) The advantage the player going first has is significant. “Quick Play” matches are finished rather quickly. This advantage is/can be increased further due to having items the other player doesn’t (a huge focus on solid, fair matchmaking will help solve this).

2) The game includes a “Competitive Mode” which includes a skill ranking system, although much simpler compared to highly complex, popular AAA titles. Although this has a different GameMode (therefore slightly different rules) and longer match times, coin toss winners still have a slight advantage (matchmaking will be geared towards rank and less on items players have, so item collection will have significant impact on the player who wins the coin toss).

With that being said, to my question: if a player is unlucky and getting 3+ games in a row losing the coin toss, I’d like to very slightly increase their odds, nothing dramatic, with these odds increasing even more if they get a 4th and 5th loss in the coin-toss, until they finally get to go first.

What would be best solution this?