The "magic" in Cover is the rebalancing effect across all of the multiplicities of all the possible portfolios. At least, assuming, or at least allowing for, infinite time.
In its presented form, take 2 securities and construct 101 portfolios, each containing 0-100% integer proportions of either. AND REBALANCE ALL OF THOSE MINUTELY / HOURLY / DAILY / MONTHLY /WEEKLY / MONTHLY etc. to always hold the same fixed proportion. That's really the "secret sauce". It really is.
To understand the intuition behind this, you need to revisit a couple of vanilla concepts in traditional portfolio maths, and combine them. Move it from the discrete case of an infinite number of infinitely-small portfolios to a continuous curve. That is no different to the Markowitz frontier between the two.
Cover simply proved that, with enough time, with a LOT of time, the rebalancing effect across the curve would end up generating an average return across the curve in excess of the return of the better single asset.
This is neither a simple "mean-reversion" nor a "momentum" effect. Aĺl of your portfolios are mean-reverting; but you're running with their momentum.
The intuition is the arithmetic vs geometric half-variance drag and rebalancing effect. Whatever the two assets's true return, vol, and correlation, the rebalancing portfolios will be biased to having a better risk-reward than their naked equivalent all across the curve. Cover' s insight was proving that letting the winning (rebalancing) portfolios run would, in the end, guarantee performance better than the winning asset. In the (VERY) long-run.
If you don't understand the central anomaly here, ask yourself what is the probability that any market will be X% up before being X% down? If you want to teĺl me it's a 50:50, then the theoretically optimal bet is to stake a quarter of my wealth it's down :-) Yes, that's crazy; but it's not wrong... market doubles or zeroes every day, buy or sell to hold? The same is true to diminished degrees with "fair bets" in general.
Any fair investment, ie zero long-term expected return, therefore has to have a (SMALL) positive expected return in the short-term.
Cover' s "Universal Portfolio" is simply an algorithm that exploits this effect it's "proof" is simply that , with infinite time, the rebalancing gains across the spectrum of weights will end up surpassing the performance differential between the sample assets.
That's the logic (and proven, assuming traditional assumptions with respect to normality hold true).