The chance of winning (without dealer busting) if you double down P11 vs D10 is ~ 50% (7/13 for you and 7/13 for the dealer). Basic strategy says to double down the P11 vs D10 every time (depending on the rules, I'm talking about S17, NDAS). Does the idea behind this strategy comes because of the dealer busting? Counting the biggest chance to win if the dealer busts getting a 6, hitting 16 (1/2 + 1/13 * 8/13) is ~ 55%. It might be more than 55% including all the possible outcomes but you get the point.

Not sure if that's correct, and if it's, why given P10 vs D10, doubling down isn't a correct basic strategy move? Winning the double down bet on P10 vs D10 without dealer busting is also ~ 50% and including the highest chance of bust (1/13 * 8/13), also ~ 55%. I'd guess there are few more combinations where the chance is only 50% or even lower but with the bust, the edge goes over to the player. Something has to be wrong with my calculations cause I don't think the basic strategy creators didn't think about it. Maybe adding those outcomes of dealer winning with 3+ cards makes a huge difference.

I'd guess the end chance if we calculated all the possible outcomes (there are a LOT of them), would be ~ 50% for both. The dealer could win with 3+ cards but I'm not sure if that's enough to take over the edge from the player (he could also hit something below 17 and get a good score as well).

*P - player
-D - dealer