The 2000 rated player would win without much difficulty. Even with a 2 pawn advantage he would win.
Hmm... with the piece I'd be very confident, as others have said, a piece is a piece, all you have to do it not make a stupid error.
Two pawns I'd be less confident though, not least because removal of pawns gives some compensation in the form of open lines. I'm not sure I'd back myself to beat Kasparov or Houdini with 2-pawn odds, and if I did it would be an achievement.
Ok, I got the engine Bison9.11 from their site and it has a rating of 2754 here. Houdini 1.5 has a rating of 3146 here.
Each use only 1 processor. Only two 15 minute games. Houdini won 1.5 - 0.5 lol. Engines are fairly terrible at odds games it seems. Humans fare much better (e.g. FM Meyer). Although I'll note Houdini's kN/s were quite a bit higher, and so it was going a few moves deeper each time. Still, I'm surprised how poorly Bison did.
A dozen years ago Kasparov played a two pawn odds match against a maybe 2200-ish Terence Chapman (British under 14 Champion in 1970 and FM in 2013), and won 2.5-1.5:
http://www.telegraph.co.uk/news/uknews/1317037/Kasparov-makes-it-a-knight-to-remember.html
Just goes to show, a 2700 only seems indestructible until something much stronger comes along and punishes it for everything it missed. (Just as to me for example, an IM only seems invincible because I am not strong enough to see a flaw in his play 
)
It's an interesting question that I won't claim to know the answer to, but my guess would be: probably not.
Keep in mind that an extra piece is only an advantage if the piece is in the game, exerting some influence. In the Houdini vs. Bison game above (the second one), the the black king's knight eventually gets pushed over to b6 where it remains until the end of the game, doing nothing, while the white bishops are both very active.
Plus, Kasparov is a beast tactically, and would probably try to steer the game in that direction.
Just goes to show, a 2700 only seems indestructible until something much stronger comes along and punishes it for everything it missed. (Just as to me for example, an IM only seems invincible because I am not strong enough to see a flaw in his play )
An oddly worded and very solid point. You sir, deserve the medal of common sense.
Wow I think you guys are far too confident in your abilities.. Kaspy is one of the all time greats, remember - I think a piece deficit against a far inferior and likely less experienced player is not a guaranteed loss, I think the 2000 would still have to play great chess to convert the win, and a draw would be a more likely result.
Just goes to show, a 2700 only seems indestructible until something much stronger comes along and punishes it for everything it missed. (Just as to me for example, an IM only seems invincible because I am not strong enough to see a flaw in his play )
And yet, FM Meyer won 4-0. And when I played Houdini it had all 4 processors and "permanent brain." (Although my game was stale. Any complications and I probably would have folded very quickly).
I think maybe the better lesson is, computers seem amazingly good until you realize they have no clue how to play chess 
Edit -- well maybe also that it's amazing how concrete calculation can trump everything else. Computers aren't terrible of course, they're just so impractical.
I think even kasparov would have a hard time against a 2000 player a whole piece down, if the player played correctly. Usually players 2000 rated know what their doing, and being a whole piece down is hard to come back from, even if your kasparov. I don't think that the analogy "comparing say a 1300 to a 2000" would be the same. I can play a 1300 player a piece down, and still probably win, simply because the 1300 doesn't have enough experience, or knowledge, to convert the advantage. But a 2000 player should hold the position. I will say that maybe kasparov can figure out the most precise way to draw, but realistically, a piece down, it would be hard, even for kasparov.
Yes, but neither the 3100 nor the 2700 know how to play chess; it's not like the 3100 can take advantage of this very thing that it falls victim to.
You would think the 2700 would simply be too good to be able to throw away such an advantage; that it simply wouldn't make mistakes large enough. Granted it may make positional errors, but it would have seemed almost impossible to believe that they would stack up to an entire piece when a human would have trouble exploiting such a thing even giving no odds at all.
"Computers aren't terrible of course, they're just so impractical."
Even so, it's an impractical 2700, not an impractical patzer.
Indeed it seems like whether the player has a human style matters; how it can matter to such an incredibly high degree, to the point where a 2700 computer can actually make enough blunders to lose even starting with an extra piece (in fact it's hard to even imagine how such a thing is possible regardless of its opponent), remains extremely baffling to me.
"But a 2000 player should hold the position."
Perhaps, but I don't think 2000 is as strong as people think it is :)
To me, a 2000 is like a wannabe titled player, who knows that certain advantages are enough to win a game. He's passionate about converting them, yet at the same time doesn't do it properly
Ok, that's probably an exaggeration, but my point is, though I think a 2000 is well aware of how an advantage can be exploited in theory, in practice they have a tougher time.
All of that applies to me as well, as I'm a bit under 2000. I've played many experts. They're good of course, but I think their play is loose enough that the above tends to apply.
Still, waffllemaster, your human examples are convincing . I'll have to try this experiment this week, even though I generally dislike odds games.
I've looked through this, and it surprises me that nobody asked if the 2700 has positional compensation for it.
Though the 2700 might not start with positional compensation, as the game goes on he may manage to create some compensation :)
True. I was thinking of including that but thought my post was already convoluted enough. Yes, FIDE 2000 is probably pretty decent 
If I'm correct that computers work by evaluation, then they do not understand either piece up or piece down positions nearly as well as an equally rated human.
For a computer a position a piece up is about +3, regardless of which move it makes, so it should fail to find the best moves or plans.
Similiarly, the piece down position is -3, and it will just play for the best evaluation rather than like a human player who tries to pose concrete problems for his opponent.
Kasparov prefers dominant positions, it's in his character, why would he be giving out piece odds and voluntarily play from a disadvantaged/inferior position?
shepi, if that were the case, I'd hardly have to worry against houdini even if I dropped a piece against it -- I would just count on houdini to hide, move back and forth, and just say "I have an extra piece!" The engine of course continues to look for the best move -- even if it is up a piece, it will be looking to add as many advantages as possible, for example space, or targets (these kinds of things are also factored into the evaluation).
I do get your point, but simply playing strong moves should naturally lead to a win. And that was something the 2700 engine couldn't always do. Not only that, it must have outright blundered (!) a few times.
The only thing is that, due to the horizon effect, it probably doesn't appreciate how it's often easiest to utilize an extra piece in a simplified endgame. Still, as I said, being such a beast at chess in general, I hardly expect that to matter; if it was really such a big deal, we'd have loopholes as in the first paragraph.
You can run engine matches on a personal computer easily. I don't have a 2700 rated engine though. It's hard to believe the weaker engine would lose. I'll try to find a download and try it out. I only have houdini 1.5 though.
Also, Houdini 3 is rated 3200 here. Not sure how you got 3300 for Houdini 2.