Is this a drawn position?
In the last round of the Women's World Team Championship, in the match between Vietnam (in last place) and China (who wound up winning the event, on tiebreaks, ahead of Russia), White (the Vietnamese player) went 37.Bc5 and offered a draw. The position is not only won, it's easily won and - even better - cannot be honestly lost by anyone not massively intoxicated. White could play on for hundreds of moves without the slightest risk, even though it shouldn't take very long to win the game outright.
But no, the game was drawn, the Chinese drew the match, and won the title. Nice. Perhaps White thought, or will claim to have thought, that the opposite colored bishops guaranteed a draw after something like 37...Bb7 38.Rxa8 Bxa8. In fact White should avoid the rook swap, but even with it, and even with the assumption that Black can draw, it's hard to see why White didn't even try.
To make sure I hadn't lost my mind, I decided to play the position after 38...Bxa8 against Rybka. No takebacks, no looking at its suggestions, just mano-a-computer. Here's the result:
39.Ke3 Kf5 40.Bd6 Bd5 41.a3 Bc6 42.Kd4 Bb5 43.Bb8 (This is a loss of time - I come up with a better plan next move. But the key point here is that it doesn't matter at all. Black can't do anything, White has no risk, and can switch from one plan to another until a successful one is found.)
43...Ke6 44.Be5 Kf5 45.Bc7 (This is the right square, at least for what I have in mind. I'm going to put the bishop on g5 and play h4 so I don't have to worry about the kingside pawns, then bring my king towards the a-pawn. He can take my d-pawn if he wants to, but my pending passed b-pawn will decide matters. Black will not be able to cope with the combined strength b- and f-pawns. Crucially, even if he* can get rid of both at the cost of his bishop, I still have the h-pawn
and the right colored bishop.)
45...Ke6 46.Bd8 Kf5 47.Bg5 Ke6 48.h4 Kf5 49.Kc5 Ba4
(This came as a surprise, but 49...Bxd3 50.a4 followed by 51.b5 is hopeless as well. For instance: 49...Bxd3 50.a4 Ke6 51.b5 axb5 52.axb5 Kd7 53.b6 Be4 and now we switch to the kingside: 54.Kd4 Bf3 55.Ke5 Be2 56.f5 Bc4 57.Be3 Ba6 58.Kf6 Bd3 59.Kg5 Be4 60.f6 Ke8 61.Kxh5 followed by pushing the h-pawn, with an inevitable overload of Black's bishop. Or, alternatively, bringing the king back to the queenside. Everything wins. Back now to the main line.)
50.d4 Ke6 51.d5+ Kd7 52.f5 Bb5 53.f6 Ke8 54.d6 Kf7 55.Kb6 Kf8 56.Kc7 Ke8 57.d7+ Bxd7 58.f7+ Kxf7 59.Kxd7 and now White's win is so easy, even a caveman could do it. So if I can beat Rybka, a player only about 150 points weaker than I am should have excellent chances against someone 500 points weaker than Rybka.**
More on this
here - and note that this was not the only controversial game in the match!
* The generic pronoun; I haven't changed my opinion about computers!
** I realize that such a scale doesn't always apply, for various reasons. But I think the general point does apply in this case.