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I had never seen such a side bet before, and I was a bit baffled by it. It didn't seem like the side bet was hit that often, but when it was, at 10-1, the payoff was a nice one for the player.
The most confounding part was the way player's played. Obviously, they would rather tie the dealer than beat the dealer. For the most part, I felt like the players played the same way the dealer would with that hand, but with an eye on the dealer's up card, hoping for that tie.
I never played the side bet, not understanding the odds on it, and at one point, tied the dealer 4 times in a row. I got blasted by the other players for not playing the side bet. I still refused to play the side-bet, knowing that side bets are usually not in the player's favor.
However, according to the Wizard, the overall house edge with the side bet is 0.24% (from the above linked page). Using the Wizard's house edge calculator, I come up with the game (without a side bet) as having a house edge of 0.64%.
The numbers indicate to me that one SHOULD play this particular side bet, using the modified strategy as presented on the Wizard's page, as the house edge is 37.5% better when you play the side-bet. Is this right?
I actually feel bad now that I was annoyed by the players trying to get ties. I don't know that they were using your modified strategy, or any strategy for that matter, but now having seen the numbers, I know I shouldn't have silently ridiculed them for making the bet and then playing to win it.
Considering how side bets are generally considered Sucker Bets, it's amazing to see one as good as this.
It makes me wonder: Are there any other side bets that lower the overall house edge?
The wizzard modified strategy shows almost all stiff hands to be hit v 2-6. Very few people would know and play such correct modified strategy.
Black Tie Dress
Blackjack Tie With Dealer
Since the side bet reduces the house edge you can bet the side bet when the count is 0 negative and you play minimum. When the count increases to the point where is positive Ev you play only the main bet according to the bet schedule. This would probably work.
Have in mind that the Ev per Wizzard is 0,24% but based on the 1.5 units.
So the choice is say between $10 @ -0.64% = -$0.064 or $15 @ -0.24% = -$0.036. ie the 0,24% is actually 0,36% based on the initial bet only.
I am pretty sure that counting would also work with the side bet and Hi-Low would probably be a decent count to use because of the 20-20 tie. You will need simulations to confirm this and see how the Ev changes with the count. A better count system could probably be devised. It is a lot of work to do all this and also find indices for such a game.
But the bigger problem even if you get decent Ev, is the increase in variance to the game. The 10:1 payout on the side bet (1/3 of total bet) means the variance increases a lot and you need a big bankroll to play it.
Show How To Tie A Tie
Or I might just go to the casino and play and have fun. We'll see which one of those ideas ends up winning.