When I was mucking around with Fudge, I wrote a program that simulated two guys whacking the other with swords. I did this to see how the number worked out over thousands of fight. I coded up GURPS Basic Combat and classic DnD Combat to use as comparison.
One of the things I did was randomized starting initiative at the beginning of combat. Then alternated sides from that point on. So I was playing around with it today and I noticed something interesting. When two combatant have equal stats with random starting imitative the odds look like this for 10,000 fights.
Alex Wins 5060
Brian Wins 4940
Average Rds 4.1268
So when I gave Alex starting Initiative all the time. The result was this
Alex Wins 5575
Brian Wins 4425
Average Rds 4.08065
Then switched to Brian
Alex Wins 4512
Brian Wins 5488
Average Rds 4.0986
The implication is that having initiative all the time increases your odds of winning combat by 4.5%. This is especially relevant to DnD 5th edition where the default is to roll initiative once.
Note: Both Alex and Brian had AC 12, +1 to Hit, 1d8 damage, and had 10 hit points.