Dealer Busts SB when known holecard

Hey, could you help me verify some quick math I did? So basically the casino with the Dealer Busts side bet put in a promo where they introduced a Joker(JK) into the shoe, what this does is that I’m able to see when the dealer has a T under another T thanks to the way they need to check the JK as it counts as an Ace. I thought I have an edge over the sidebet and this is the following calculations I did:
4/13 times the dealer will have a T so no sidebet worth playing and 1/13 an A so the hand is over (there’s only 2 JK in the deck so I think the effects on this are redundant)
So 8/13 times the dealer will have an unknown card that can possibly busts, more specifically 5/8 as the 7,8 or 9 will just be a stand. I looked online and took the product of the bust rates of hard 12 to 16 (I don’t think the game being H17 or S17 affects this as a soft hand will never take place) and it gave me 46.16. So when I play the sidebet on a dealer’s exposed Ten 8 out 13 times, of that 8 times the dealer will bust 28.85%. As the sidebet pays 3:1 this gives me around 1.154 or 15.4% advantage over this sidebet in this specific situation. (If I’m not mistaken until this point, I will try to calculate the EV) This means that of 4/13 times the dealer has a T exposed, 1 in 5.55 hands will present the situation where the sidebet is playable, assuming a House Edge of 0.5% over the main bet I’ll lose around 2.5 units until this situation presents where I’ll win 15.4 units, at around 100 rounds per hour on a $100 bet I’m making $1290/hr? I just want to make sure all of this is correct before proceeding any further, thank you.

If I understood correctly the casino adds 2 jokers to each deck and thus needs to check the dealers downcard every hand.
However I did not get your further analysis. If you place your bet before the game starts then the jokers will just be bad for you. If you place the bet after the initial cards were dealt then the payout shouldn't be fixed but rather based on the upcard. Could you give more information about the game/sidebet. Also you assume 52 cards but with 2 jokers you're at 54 cards and this can affect the calculations.

This is the first calculation I did but checking back I made some errors, using bust rates as: Hard 16= 0.615385
Hard 15= 0.576923
Hard 14= 0.538462
Hard 13 = 0.5
Hard 12 = 0.461538

I incorrectly divided them by 5, just taking into account the hands that can bust and this will incorrectly interpret as I’m only placing the bet when I know the dealer has a stiff hand, but this is incorrect as I will unknowingly also place the bet when the dealer has a hole card of 7,8 and 9 and the bust rate is 0, so I updated the calc and divided it by 8, giving me 0.336539. Given the fact that when I win this bet I get paid 3 times my bet and keep my original bet, this means I yield a 34.61 edge over the house with this sidebet.

Yes, your análisis on how I get the downward information with the jokers is correct, this is in a 6 deck game so the jokers being 2/314 cards I think they are irrelevant. The sidebet is placed after I’ve seen the dealer upcard, and after they have checked for BJ, so that’s why I also removed the A from the equation. The payout is in fact just based on the upcard as that’s how the game is intended as the player is only able to see the up card when he has to place the sidebet

This still hasnt fully answered all my questions but if you are confident in your calculations then go for it. However I don't understand how they checking the card could tell you wheter it is a ten or not. If the dealer has a T as a upcard do they check to see if the hidden card is a ace? If so thats a pretty good table tbh. But still this wouldnt tell you wheter the hidden card is a ten or not, only if it's an ace or not?

The game is a standard H17 6D Blackjack, the casino I play in has a promotion where they introduced 2 jokers into the shoe, they count as an Ace and can be used by the player in other advantageous ways (instantly winning your hand, or waiting for the dealer to play theirs for potentially paying double your bet, you can also double with a joker in your hand for 4x your bet) since the jokers count as an Ace for the dealer, when he has to check for an A under, he also has to check for a potential Joker, but the way they are printed makes the dealer check them in a different way, this allows me to get a view in their mirror and I can see when they have a T under because they check for a Joker the same way they check for BJ with an Ace upcard, this allows me to have just the information of when a dealer has a T under, but not further information on any other card. They also have a sidebet called “Dealer busts” that just checks if the dealer busted regardless of the total cards it took to bust, it pays taking into account what was the initial upcard for the dealer. The pay tables are 2,7= 2:1; 3,4,5,6= 1:1 and 8+ 3:1. So if the dealer had a 7 exposed, flip a 5, and then drew a T it will pay you 2:1, as the initial upcard was a 7.