Let’s say for the sake of hypothesis that the current Federal Budgetary process is so badly broken and divorced from any legitimate concern for the American commonweal that we could describe it as five pirates deciding how to divide up the spoils from looting America. Mathematician Ian Stewart proposed a mathematical game that could describe how this situation could work itself out.

There are 5 rational pirates, A, B, C, D and E. They find 100 gold coins. They must decide how to distribute them. The pirates have a strict order of seniority: A is superior to B, who is superior to C, who is superior to D, who is superior to E. The pirate world’s rules of distribution are thus: that the most senior pirate should propose a distribution of coins. The pirates, including the proposer, then vote on whether to accept this distribution. If the proposed allocation is approved by a majority or a tie vote, it happens. If not, the proposer is thrown overboard from the pirate ship and dies, and the next most senior pirate makes a new proposal to begin the system again. Pirates base their decisions on three factors. First of all, each pirate wants to survive. Second, given survival, each pirate wants to maximize the number of gold coins he receives. Third, each pirate would prefer to throw another overboard, if all other results would otherwise be equal. The pirates do not trust each other, and will neither make nor honor any promises between pirates apart from the main proposal.

The five pirates in question would be President Obama as Pirate A. Pirate B would be House Speaker John Boehner. Pirate C would be First Mate Harry “Scurvy-Bones” Reid. With Mitch “Polly Wants an Earmark” McConnell as Pirate D and, Nancy “Cap’n Afterthought” Pelosi would be Pirate E. This set up would favor President Obama and he will probably emerge from this whole sordid affair in better condition than he deserves. What still remains up for grabs will be how the loot taken off the hard-working American population gets distributed amongst the DC Rapscallions.

A so-called fair distribution could work something like this. For N as the size of the pot, we could distribute every value of n(Mod 15)= 0 until no further value >= 15 remained as follows: A gets 5n, B gets 4n, C gets 3n D gets 2n and E gets n. If DC’s brigands were ever that co-operative, they would divide a pool of 100 Golden Quatloos in an orderly fashion six times until we got to 90. President Obama would have 30, John Boehner, shiver me timbers, would walk out with a sum of 24, “Scurvy Bones” would get 18 and “Polly Wants an Earmark” would get 12. “Cap’n Afterthought” could squawk all she wanted, but would still get a measly sum of 6. The problem would remain what to do with the other 10 Quatloos.

This is in essence what House Speaker Boehner was attempting to do by piecemeal funding every part of government other than ObamaCare; which in the minds of Conservative Republicans represented the problematic last 10 Quatloos. That would accomplish what Senator Cruz and Senator Lee essentially angled for when they kicked off the fracas that initiated this game. ObamaCare would dominate the partisan back-and-forth in DC at precisely the time its websites were going down like the Ottoman Fleet at Lepanto.

This was not what President Obama wanted done. He considers ObamaCare finished business. He is further enabled because he could count on getting affirmative support on any offer he made from Pirate C and Pirate E. There was a fair to middling chance that he could even flip Pirate D. At this point Pirate B would be overwhelmingly forced to glumly walk the plank.

The recent Senate Compromise offer that may or may not reach the House by tomorrow could be the flipping of Pirate D. The House GOP, unlike the pirates in Stewart’s game, could realize that letting Pirate B go swinging from the yardarm was not in their interest and block the deal unilaterally.

Rejection would be an optimal strategy because otherwise, they would get nothing. Under this framework, Pirate C (Harry Reid) would move up to Pirate B. Pirate D (Mitch McConnell) would stay Pirate D and Pirate E (Pelosi) would be promoted to pirate C. The 10 Quatloos represented by ObamaCare would be off the table and all 100 Golden Quatloos could (as a best case for the GOP) be divided as follows. nMod(10) = 4n President Obama, 3n Senator Reid, 2n Congresswoman Pelosi, and n Senator McConnell. So for 100 Quatloos, you get 40 Obama, 30 Reid, 20 Pelosi and 10 McConnell.

Thus, the House GOP is very well served rejecting the current offer in detail and letting this go past the Oct 17th witching-hour proclaimed by Sec Treasury Jack Lew. The 17th is not an ironclad default date. Bills come due thereafter and incur more and more credit risk as time passes. If John Boehner wants to start a game of Russian Roulette instead of voluntarily taking a plank-walk, it will work as follows.

“It’s not that you know there’s one date where the whole thing is going to go kaboom,” said Shai Akabas, a senior analyst at the Bipartisan Policy Center. “It’s that you have increasing risks, because we’ve never encountered this series of events in our modern history so we really don’t know what’s going to happen. But it’s fairly safe to say that the further we go without a resolution, the more the risks increase.” The Bipartisan Policy Center, a Washington-based nonprofit research group, estimates that the Treasury will actually be unable to pay all the government’s bills on time at some point between Oct. 22 and Nov. 1. While the Treasury will probably be able to delay the true drop-dead date for a few days, it is unlikely to be able to do so beyond Nov. 1 because several large payments are due before then, the center says.

It’s at some point between Oct 17 and Nov 1 that the five pirates will realize that they need a workable Nash Equilibrium. Or maybe they won’t. I can’t help but remembering from The Guns of August how nobody really believed a war would erupt in Europe over the shooting of some noble until The Von Schlieffen Plan was actually attempted in 1914.