Firstly the name of the battle would be different, likely the battle of Mont saint Jean or the Belle Alliance.
A Napoleon's victory means less tactical errors and also one more tactical masterpiece comparable to Austerlitz.
Napoleon is in good form, he slept very well and his hemmoroids ans stomach don't make him suffer today, he will not take Laudanum too
His flair is still intact, he guessed the plan of Bluecher and Wellesley, he decided the day before not to remind Grouchy despite reviews of his generals.He knows that time is against him and decided to finish quickly despite the rain and the mud.
Doesn't he have the best Army of the world?
He knows that his strong defensive position constrains Wellesley to stagnation and he decides to take advantage of it.
-1/ The attack of diversion to Hougomont of the brigade Bauduin (3,030 men) begins at 10 instead to 11.30 and with less reinforcements.
After they have repulsed the Nassauvian soldiers from the wood in the south of Hougomont, French don't insist against the strong fortified farm, Napoleon finding that Wellesley doesn't send any reinforcements.
Therefore most part of the Reille's corps is available for another actions.
2/ The grande batterie (80 guns) begins its bearing at 11.30 instead of 13.00 in real history.
As in real history the Anglo Dutch brigade Bylandt suffers heavy casualties because it's very exposed, the other allied troops suffer much less because they are protected behind the crest.
At 12.00 the big and decisive attack in the centre begins.
As in real history the 1st Corp of D'Erlon attacks La Haye Sainte and Picton's positon, supported on its left flank by cavalry (1 or 2 brigades).
Division Quiot in charge of the attack of the Haye Sainte is reinforced by artillery of the reserve, this allow it to use a combined attack against the 2d battalion of the King's German Legion (Major Baring).
The attack in the centre ,also, involves the 4th Army Corps of Lobau against the position of Alton on the left wing of the Haye Sainte, reinforces by one division of the Reille Army Corps and preceded by the same powerful charge of cavalry than in real history (Ney, Kellerman) reinforces by lancers.
-3/ Despite intervention of the cavalry of Uxbridge and a fierce resistance of Picton who dies as in real history, the situation quickly becomes desperate.
The allies are forced to face the thread of cavalry which made their defensive edge terribly vulnerable to the artillery and infantry fire that follow and support the cavalry.
At 13.00 La Haye Sainte Submitts to the combined attack of the infantry and the artillery of Quiot and the Picton's Division is in big difficulty faced to the attack of the divisions Donzelot and Marcognet, Papelotte submits too to Durutte .
A 13.30 Wellesley launch his famous quote "give the night or Prussians",😨 but unfortunately for him, it's too soon, the night fall only around 20.30
and Blucher is still far away from the battlefield.
The situation is without issue, the allies are forced to immobilism and can't escape from this trap.
14.00 Cooke attempts to help Alton but his cavalry is repulsed and his infantery is immobilised, Clinton doesn't move and Dutch begin to retreat.
Prussians scouts report the situation to Bluecher who decide giving up to their plan "immerhin war es kein Ligny"
(after all he hasn't been here at Ligny).
15.00 the allies centre collapse, rout begins, Wellesley decides to remain on the battlefield with his last devoted.
Clinton and Cooke retreat with heavy casualties.😧
Napoleon claims the evening of the battle " say that he wanted to stop me with mud".