Interesting, those seem almost impossible odds. The game is helpmateish if such a word exists.
Pion Coiffé

The "pion coiffé" is certainly greater than queen odds. As the notes explain, the pawn must deliver mate without being queened, and if Black captures the pawn, White loses immediately.
It's hard to imagine winning without active assistance from Black. How hard could it be to sac his queen for the pawn?

I guess looking at it black tried to make moves to capture the g pawn instead of playing normally. b6 for Bb7, h5 for Rh6-g6 and ended up in a mess. I can't imagine a way for black not to win under these conditions. Can you not just play something like 1.d5 2.Nc6 3.Bg4 4.Qd7 0-0-0 regardless of whites moves? Then it's impossible to mate with the g pawn.

If black castles queen side you would have to somehow force it back over to the king side, probably would be easiest in an endgame being up multiple pieces (although good luck protecting your mating pawn until then).


Famous game:

Here is Staunton's game, above, as given in Napoleon Marache's "he Chess Palladium and Mathematical Sphinx"

Simon Williams a few weeks ago made and succeeded in fulfilling a similar contract on chess.com in a game played for live viewers.
The applause was tumultuous, or would have been had we viewers all been in the same room, although Simon's innocent glee would have probably drowned it out!

Howard Staunton also referred to pion coiffe four times in his chess columns in The Illustrated London News.
May 24, 1845 (he refers to the "marked pawn" in his response to correspondent Pedona:
http://www.chessreference.com/StauntonColumns/1845/05-24.JPG
June 18, 1859 (response to first correspondent, CREOLE)
http://www.chessreference.com/StauntonColumns/1859/06-18.JPG
June 1, 1872 (response to J. J. W, Edinburgh)
http://www.chessreference.com/StauntonColumns/1872/06-01.JPG
June 8, 1872 (another response to J. J. W, Edinburgh)
http://www.chessreference.com/StauntonColumns/1872/06-08.JPG
Note also that in this response, Staunton says that one of his pion coiffe games is published in the Chessplayers Companion, page 384.

Howard Staunton also referred to pion coiffe four times in his chess columns in The Illustrated London News.
You're the guy with all the antique chess sets!
Thanks for the references. I would have found those quite difficult to find.
I took the liberty of transposing Staunton's game from the "Chess Player's Companion" into a pgn.

Thanks for posting the Pion Coiffé game from Chess Players Companion. Funny-looking game! IMHO I think Pion Coiffé odds aren't quite as big as queen odds, because the stronger player should be able to cover up the marked pawn then wipe out the opponent's forces, then checkmate with the pawn.
As a digression -- if it's at all helpful for your chess research, here's a spreadsheet I put together with all of Staunton's ILN columns "keyworded" with different topics, with URLs to JPGs of the columns themselves. (It took a while but I perhaps 10 years ago I managed to acquire all 1440+ issues of ILN from 1842 through 1875, containing all of Staunton's chess columns 1844-1874.) BTW note that I put 1844 here rather than the official date of 1845; here's an article I wrote about Staunton's ILN chess columns, that explains why I believe his column commenced in 1844
https://worldchess.com/2016/11/27/the-mighty-pen-of-howard-staunton/
Anyway, here's a link to the Staunton ILN Excel spreadsheet.
http://chessreference.com/Projects/StauntonColumnSpreadsheet.xls
It'll download and then you can just use the Excel "filter" command on any keywords in column B to bring up that exact topic, then click on the hyperlinks in column C to bring up the columns associated with that keyword. For instance, try filtering on the keyword Morphy to bring up all Staunton columns referencing Morphy. (The first one is quite interesting because it doesn't reference him by name, but rather Staunton is responding to Charles Maurian about the "young Philidor in New Orleans.")
Sorry for the digression but I thought this might be helpful at some point!
Here is a Cappped Pawn game from "Le Sphinx" 1866.
The idea is that a pawn is marked (sometimes with a ring or a thimble) and the player is required to give mate with that pawn, in this case the King's Knight's Pawn . Capped Pawn or Pion Coiffé odds is considered to be the equivalent of Queen odds, but I think it may be even greater odds. The player receiving such great odds must, by virtue of the difference, be a very weak player, as is the case here. In this game White is Sam Loyd the Puzzle King and Black a NN. I left the notes in the original French.
Les Blancs s'obligent à donner le mat avec le pion du Cavalier