Let's say you're in a 6-player cash game, and 3-players swap action such that they share their net-profits and losses equally. How much is each player's variance reduced?

Likewise, how would the math change if 2 players, or 5 players, swapped action at a 6-player table?

(At the most extreme example, it would be 5 pros swapping action against 1 whale. How much bigger stakes could they afford to play?)

Five players "swapping action" at a table against one whale is called collusion.

When one of the pros stacks another they actually both lose $0, which is a terrible incentive.

You're basically splitting the fish's variance among 5 pros.

Even just two players at the same table doing it is cheating.

In a tournament, the colluders would obviously have a major +EV advantage by softplaying. But assuming they don't share hole cards, would the colluders have an edge in a cash game, and if so, how?

True, in a raked game, the pros should always fold to each other.

What they're doing is splitting the Whale's expected losses among each other equally. But the advantage is it allows them to play higher stakes.

The essence of my question is: If you have a bankroll to play X stakes, how much higher stakes could you afford to play by engaging in this type of staking?

In a cash game, how would the colluders have an edge?

FWIW, I've heard of this type of situation before. For example, Andrew Robl staking JRB. I don't believe it's cheating if it's fully disclosed to the table.

This type of stuff does happen (more commonly with people just having a small percentage of others). If players go out of their way to disclose the arrangement and play each other honestly it's not necessarily anything nefarious.

It's just the incentives will naturally lead to situations that will encourage the players sharing action to soft play or collude. This is even more true if they're sharing 100% like you suggested.

Example: Three way pot where whale is shorter stack. Player A bets, whale goes all in for a small amount more, and player B yet to act has a strong but vulnerable hand.

With no profit sharing player B would be incentivised to raise to isolate whale.

However if they're sharing 100% Player B would be incentivised to just call and allow player A to also call. This lowers the whales EV and benefits the players sharing action.