When you put it like that it makes me think that Baku's number is 10 after all. There's still one thing that bothers me and still hasn't been directly addressed (AFAIK), and that is whether or not the Dotty considers numbers chosen with one of the two numbers being an excluded number due to a previous input as valid. In other words, is Baku's 13 input a valid input (with Baku's bead number being 10) considering that Suteguma chose 14 previously, thus eliminating 3 as one of his possible bead numbers (Eliminating 10+3 as a possible combination)? Or does the Dotty automatically take the eliminated possible numbers into account and expect the enemy to keep that in mind when entering their choice, making it an invalid input? I'd say that most likely the Dotty doesn't go that far, and only considers whether your input is valid in consideration of YOUR number only, which would make Baku's input of 13 valid even with 10 beads. This plays into what
@Veshv mentioned about Suteguma's 14 input also "locking away" 13 as a possible choice for Usogui if he has 10 beads. Since although it was not explicitly stated that this sort of "impossible" input is valid in the Dotty, the price you pay for being wrong and gambling on it would be too great to attempt. Which would make perfect sense for Baku to gamble on just that! So yeah, if Baku's number is 10 then his 13 pick was an insane double layered gamble. If it turns out to be 8 or 9 then I don't really see why it would be a risky move, except for the part where he's trying to let Suteguma believe his number is 6 or 7, which would happen anyway.