Less loss if BS&T defaults.
Please explain this. They believe in Pirate and want to maximize their profit, right? They are not risking the (1 + x) BTC / share, it's not their money. You are risking that money, they only risk the insurance.
In this round, for example, if they only invest 3000 BTC into Pirate and he defaults, they will only lose 960 - 113.95 =
846.05 BTC.
If they invest all 3113.95 BTC, and he defaults, they will lose the full
960 BTC.
Note that I'm
not saying that investing that additional BTC with Pirate is a bad idea, I'm just pointing out that it is a rational possibility. Holding that 113.95 BTC outside of Pirate decreases their profits if Pirate pays, but decreases their losses if he defaults:
Assuming the 113.95 BTC above the 3000 BTC is not invested with Pirate and not earning any interest (unlikely), if Pirate defaults, they will lose 960 - 113.95 BTC = 846.05 BTC - but only if he defaults before the first payment.
If he defaults after the first payment, they will lose 960 - 113.95 - (.07 * 3000) = 636.05 BTC.
After the second payment, 960 - 113.95 - (.14 * 3000) = 426.05 BTC.
After the third payment, 960 - 113.95 - (.21 * 3000) = 216.05 BTC.
If he does not default, they will make 3113.95 - 3000 = 113.95 BTC
An investment of 960 BTC into Pirate would lose 960 BTC if Pirate defaults before the first payment.
960 - (.07 * 960) = 892.8 BTC loss if Pirate defaults after the first payment.
960 - (.14 * 960) = 825.6 BTC loss if Pirate defaults after the second payment.
960 - (.21 * 960) = 758.4 BTC loss if Pirate defaults after the third payment.
And finally a .28 * 960 = 268.8 BTC profit if Pirate does not default.
This acts effectively as a partial hedge against their own investment, decreasing variance. Think of it as a similar effect to taking a slight fee at a PPS pool in return for more reliable payouts. (Not a literal analogy, but it might help clarify.)