[MarkGritter]

I tried a quick-and-dirty analysis here.

Suppose he has 3 cards less than 8 to start with. What does his hand range look like after drawing 1 and making a badugi? (Intermediate draws are harder because they might improve--- probably need to write some code to solve that. I also ignore the case where he broke a badugi.)

For example, an 876 can make K8, Q8, ..., 98 all 1 way each or 87 5 ways.

56 different starting hands, 45 distinct final hands (considering just top two cards).

If we allow any badugi, then there are 560 'result's, so the midpoint is about 280. That's a 93.

If we restrict the range to J or better, then there are 448 cases, and the midpoint is somewhere in the 87's.

My spreadsheet does not transfer well to bbcode, here's an attempt of just the distribution:

K8 K7 K6 K5 K4 K3 Q8 Q7 Q6 Q5 Q4 Q3 J8 J7 J6 J5 J4 J3 T8 T7 T6 T5 T4 T3 98 97 96 95 94 93 87 86 85 84 83 76 75 74 73 65 64 63 54 53 43

Subtotals 21 15 10 6 3 1 21 15 10 6 3 1 21 15 10 6 3 1 21 15 10 6 3 1 21 15 10 6 3 1 60 40 24 12 4 40 24 12 4 24 12 4 12 4 4
Running total 21 36 46 52 55 56 77 92 102 108 111 112 133 148 158 164 167 168 189 204 214 220 223 224 245 260 270 276 279 280 340 380 404 416 420 460 484 496 500 524 536 540 552 556 560

J or better 21 36 46 52 55 56 77 92 102 108 111 112 133 148 158 164 167 168 228 268 292 304 308 348 372 384 388 412 424 428 440 444 448

Maybe I should take a screenshot, the patterns are quite cool. (I decided not to use the code tag here as it was quite wide and not much more readable.)