Robert tells Ned that Drogo has one hundred thousand men in his horde. Meaning, if he were preparing for a Dothraki invasion, he'd be expecting that many men. However, we learn that Drogo really had "only" forty thousand men in his horde and had promised Viserys only ten thousand. So off the bat, Viserys is showing up with a tenth of the Dothraki that Robert thinks he has. And that's assuming that all of the ones who set sail from Essos even make it to the Westerosi mainland; they could be stopped either through generic storms or piracy in the Narrow Sea or through Westeros' naval defense.
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So Robert is thinking in terms of one hundred thousand men but, at the most, would have to face only ten thousand. So he'd probably be wildly overcompensating.
It is true that Viserys was banking on other Westerosi houses joining him when he landed. But if Dothraki are pillaging the countryside and are vastly outnumbered, how many houses are going to put their necks on the line here? Probably very few.
That doesn't even take into account the Dothraki's inability to carry out long-term sieges and the demonstrated superiority of Westerosi knights and their armor over the Dothraki and their arakhs. Look at how Jorah, a very good but not "outstanding" knight, does against them in the first book.
So what was the rationale for the invasion? Robert probably got the ten thousand number from Varys, because who else would be informing him? Why would Varys tell Robert a vastly higher number than would actually be the case? Probably because Varys planned for the invasion to fail. On the one hand it gets rid of Dany and Viserys, or at least makes them absolutely loathed. On the other, even if Robert wins, he's weakened and it looks like he's incapable of preventing an invasion. And in swoops Aegon, who as a result looks a lot better than either Daany or Viserys or Robert.
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