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Olympiad Rithmatik: Hope for USA

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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!


thats why board points are the way to go

Why not have both?
1st match and then board , and in case of need a gun with one bullet only.

It's basically up to Ukraine to decide how badly they want to beat USA. And that in turn depends probably on what is going on in Armenia vs China.

Just did some tiebreak calculations (too complicated to explain in detail and not 100% sure I got things right): If Armenia beats China 2.5-1.5, Ukraine has to win 4-0 against the USA to keep some theoretical chances on closing the TB2 gap and getting gold (all matches from earlier opponents of UKR and ARM have to get the right result in Ukraine's favour - whatever happens, 3.5-0.5 against USA is not enough).

So UKR-USA is an interesting match: both teams have to go for 4-0 to maximize their chances with respect to a medal and/or its colour .... . Yet, I wonder if the teams and their captains are in any way affected by these mathematical games.

Replace Armenia with Russia and chances for Ukraine to win 4:0 against the USA increase dramatically ... ;-)

I hope Armenia wins. After the tragic death of last time gold medal winner Karen Asrian if would be a very very nice thing if they could win again.

Raffael, you are obviously referring to 'tricky' (political) relationships between Ukraine and Russia providing extra motivation ... . I don't know if the Ukrainian players are anti- or pro-Russian [the country as a whole is pretty divided] or not caring about politics at all. In any case, I guess they are highly motivated anyway - but so are the Americans, so I predict a rather tight match.

Just realized that the women's competition has an even stranger and more unpredictable final. China looked like the dominant winner for many rounds ... before losing track completely and now they seem to have no chance whatsoever even for a medal. Poland suddenly came out on top - however, they have an extremely bad tiebreak (they had lost 0.5-3.5 against China ....), so if they lose against Ukraine tomorrow they will be out of the medals again!

Concerning the man's winner, I also keep my fingers crossed for Armenia - for the reason you gave and also because they started as clear underdog if one believes in ratings ... .

The US women's team looks to be in good shape if they win. Because of their good TB points, a win gets them a medal unless:

1. Poland v. Ukraine ends in a draw, AND
2. Serbia does not defeat Georgia

Both 1 & 2 is by no means an impossible scenario, but it's probably a good bit less than 50%. Go USA!


That would be a good idea (minus the Russian Roulette). My preference would actually be match points, then head to head (if applicable) then board points. It seems strange to rank a team ahead of another team that beat them if they both finish the event with the same score.


Kamsky-Ivanchuk 1-0
Onischuk-Eljanov 1-0

Shulman up a pawn and looking good.
Nakamura has winning chances but a win will not be easy.

Ukraine, Smukraine.

Maybe Ukraine decided they did not want to beat USA at all ... and that they don't care about the gold medals ?

No seriously, there are always two teams (eight players) involved, all doing their very best. Maybe it was a question of nerves, maybe Ukraine was unlucky to face USA in the final round [because the USA gained momentum throughout the tounament]. In any case, this Olympiad has shown that it is tricky to predict results before the match has even started.

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    This page contains a single entry by Mig published on November 24, 2008 10:49 AM.

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