Bitcoin mining pools attacking each other for profit?

So after posting our new Bitcoin book, my buddy Tim Swanson alerted me to the problem of Bitcoin mining pools attacking each other.

Reminds me of the recent Tax Interaction Effect post, where I had to unearth the core of a counterintuitive result: in this case, the claim that not redeeming some of your solutions can increase your return.

I don't think I'm entirely there, but I at least have an analogy to understand the mechanics of the attack.

Bitcoin mining model:As you might know, mining is like buying a bunch of (positive sum) lottery tickets. A fixed reward is given out every hour, then divided equally among the winning tickets. Some people join into pools, where they buy tickets with the proviso that *if* it's a winning ticket, they share the winnings equally among all the tickets in their pool.

The attack: You use some of your money to buy tickets for someone else's pool (call it the "attacked pool", but hide and destroy the winning tickets for that pool.

The effect: There are fewer total wins per period. Each (non-destroyed) ticket gets a larger fraction of the hourly reward. The attacked pool gets a smaller fraction the reward.

My response/confusion: This increases the return to all winning tickets, not just those of the attacking pool, so the attacking pool effectively subsidizes all the others, and dilutes the value of its own tickets across the set of all players.

But maybe I'm missing something here.