I can't seem to access the server with the article right now, but generally the easiest way to get there is as the limit of the discrete case as the timestep δ

I can't seem to access the server with the article right now, but generally the easiest way to get there is as the limit of the discrete case as the timestep δ -> 0 and the payoff scaled down so they still add up to the same macro conditions. I suspect it would be the same but less interesting, though. The smaller you make the increments, the closer the optimal stopping point is to 21. At the limit, the stopping point would be 21, and -- I think -- all N players plus dealer would have an 1/(N+1) chance of reaching it. Basically, without jumps, it just becomes a situation with all players waiting for a continuous counter to reach 21, and then stopping precisely as it does. The one who was lucky to have the fastest counter (on average) wins. (With jumps as in discrete Blackjack, the fastest counter not necessarily the best!) What might make it more interesting is if you did introduce discontinuities in the otherwise continuous process. So basically each player is fed with what looks like the absolute values of stock price movements, and has to stand somewhere. That should be easy to simulate and maybe even fun to play!