Mathlete and arbiter supremo Jonathan Berry takes up the improbable method of the US winning a medal via tiebreaks. Apparently even the silver is still within reach, if you just have a bit of imagination. It will require a massive score against Ukraine tomorrow (at 10am local, 4am EST) and then considerable help from their enemies. The Poincaré Conjecture was child's play.
The reason you wrote that 'taint so was to sucker somebody into doing the arithmetic. US Championship needed that a couple of times, eh? It's a conceptual stretch, but "arithmetically" USA can pass Ukraine with a 3.5 or 4 victory. With a 3.5 victory, they can get a bronze behind Armenia (if it defeats China) and either Israel or Netherlands. With a 4 victory, USA wins a silver if NLD defeats Israel 2.5 to 1.5. Both scenarios also require Spain to tie or defeat Russia. Here are the ciphers for that last scenario:
ARM wins. RUS doesn't. USA 4-0 UKR NLD 2.5-1.5 ISR
USA tiebreak = 266 (after rd 10) + 4x17 = 334 UKR tiebreak = 309.5 + 0x17 = 309.5 NLD tiebreak = 292 + 2.5x16 = 332
ARM would win with 19 USA second on tiebreak with 17, ahead of NLD, UKR. ESP might be involved in the 17-tie, but tiebreaks too low to pass USA.
Note: there is some variance because the tiebreak due to teams played already in rounds 1-10 will change. The assumption is that that change will balance out. But if IND, HKG or RSA win in round 11, that improves USA's prospects. Game points do count (ducking).
Who knew? AP chess guy and bearded wonder Rob Huntington adds from Dresden:
One point about Jonathan Berry's improbable but mathematically possible scenario for the U.S. winning a medal. It depends on the teams that the U.S. played outperforming the teams that the Netherlands played in the last round. It is thus conceivable that the decisive games for determining a medal could be played between Bangladesh and Thailand (the Netherlands beat Bangladesh 3.5-0.5).
Of course that sort of thing has long been an absurd part of Olympiad tradition. It has gone as far as top teams like the USSR coaching a weak team they beat earlier in the event before their last-round adjournments in order to squeak out that last crucial tiebreak point. So game on! Everything to play for! Go USA! Go umm, Netherlands (but only 2.5!), go Spain! Go India! Go South Africa! Go Thailand! Go Hong Kong (just in case)! On Dasher, on Dancer!