Suppose a BS player is sitting at second base with a civilian at first base. It is a single deck game dealt to the very bottom (just for sake of simplicity).

The civilian is dealt a hard 20 and is contemplating splitting 10s. The BS player was dealt an 8,3 and decides to double down hoping to catch a 10. He pleads with the civilian not to split 10s for fear he might hurt his chances of drawing a 10 on his double.

At this very moment, the composition of the remaining deck is 10 cards (8 high, 2 low). Assuming the civilian stands on his 20, the BS player has an 80% chance of catching a 10 for a total of 21.

Now, what are the BS player's chances of drawing a 10 assuming the civilian splits his 10s and can only take one card on each 10 with no re-splitting allowed?

According to my calculations, the probability of the BS player drawing a 10 to go with his 8,3 is 74.4% assuming the civilian splits his 10s. So, the civilian has hurt the other player's chances of drawing a 10. Is this correct? I thought that the chances of catching high cards or low cards are not affected by how others play their hands.

Thanks for any responses.
MJ