Hmmm, Excel doesn't like 317! Had to brute-force 317!/(317-n)!...
Okay, got the numbers, got the presentation, but as setup, let me first try and describe what I think the scenario at hand is...
So, yeah, sure, the 27 chest gives the best
average payback, but look at that bonus payoff in those large chests. 200, 300 SK! If I'm lucky and get above average results, that'll be way better, right?
Well first of all, look at the above average numbers. The 89 and 80 chests scored 560 SK and 1060 SK fewer bonus than did the 27 chest. It's going to take 3-5 additional bonuses to almost match the performance of the average 27 chest.
Then, consider how lucky you have to be to get 3-5 additional on those chests, and ponder what the payout for the 27 chest would be for a similarly lucky player... or even a half lucky player...
Lets just look at first order effects from our previously established baselines of opening 317, 93 or 89 of each of the 27, 80 and 89 chests.
27 vs 80 vs 89 Chest
Bonus Count | Odds | Cumulative Odds | Total SK | Flags | | Bonus Count | Odds | Cumulative Odds | Total SK | Flags | | Bonus Count | Odds | Cumulative Odds | Total SK | Flags |
---|
| | | | | | 2 | 10.05% | 14.20% | 6600 | 246 | | | | | | |
| | | | | | | | | | | | 7 | 6.92% | 14.84% | 7400 | 249 |
26 | 4.45% | 16.53% | 8080 | 299 | | | | | | | | | | | | |
27 | 5.33% | 21.86% | 8160 | 302 | | | | | | | | | | | | |
| | | | | | | | | | | | 8 | 9.67% | 24.51% | 7600 | 255 |
28 | 6.14% | 28.00% | 8240 | 305 | | | | | | | | | | | | |
| | | | | | 3 | 16.04% | 30.24% | 6900 | 258 | | | | | | |
29 | 6.80% | 34.80% | 8320 | 308 | | | | | | | | | | | | |
| | | | | | | | | | | | 9 | 11.87% | 36.38% | 7800 | 261 |
30 | 7.25% | 42.05% | 8400 | 311 | | | | | | | | | | | | |
31 | 7.46% | 49.51% | 8480 | 314 | | 4 | 18.99% | 49.23% | 7200 | 270 | | 10 | 12.95% | 49.33% | 8000 | 267 |
32 | 7.41% | 56.91% | 8560 | 317 | | | | | | | | | | | | |
| | | | | | | | | | | | 11 | 12.68% | 62.01% | 8200 | 276 |
33 | 7.11% | 64.02% | 8640 | 320 | | | | | | | | | | | | |
| | | | | | 5 | 17.79% | 67.03% | 7500 | 279 | | | | | | |
34 | 6.60% | 70.62% | 8720 | 322 | | | | | | | | | | | | |
| | | | | | | | | | | | 12 | 11.24% | 73.25% | 8400 | 282 |
35 | 5.93% | 76.54% | 8800 | 325 | | | | | | | | | | | | |
| | | | | | 6 | 13.74% | 80.76% | 7800 | 291 | | | | | | |
36 | 5.16% | 81.70% | 8880 | 328 | | | | | | | | | | | | |
| | | | | | | | | | | | 13 | 9.08% | 82.33% | 8600 | 288 |
37 | 4.35% | 86.05% | 8960 | 331 | | | | | | | | | | | | |
| | | | | | | | | | | | 14 | 6.72% | 89.05% | 8800 | 294 |
38 | 3.56% | 89.62% | 9040 | 334 | | 7 | 8.99% | 89.75% | 8100 | 303 | | | | | | |
39 | 2.83% | 92.45% | 9120 | 337 | | | | | | | | | | | | |
| | | | | | | | | | | | 15 | 4.58% | 93.63% | 9000 | 303 |
40 | 2.19% | 94.64% | 9200 | 340 | | 8 | 5.08% | 94.83% | 8400 | 315 | | | | | | |
Getting an extra 33rd bonus 27 chest gives only 80 SK.
Getting an extra 11th bonus 89 chest gives an extra 200 SK.
Getting an extra 6th bonus 80 chest gives an extra 300 SK.
But
Getting an extra 33rd bonus 27 chest is only a 7.11% increase in luck.
Getting an extra 11th bonus 89 chest is a 12.68% increase in luck.
Getting an extra 6th bonus 80 chest is a 13.74% increase in luck.
32 Bonus 27 chests produced a total of 8560 SK.
Getting 3 bonus 89 chests for 8600 SK is a 33.00% increase in luck.
Getting 4 bonus 80 chests for 8700 SK is a 31.46% increase in luck.
That same increase in luck would produce 6-7 additional bonus 27 chests.
Bottom line, semi-pointless math shows that better math is still better.
27 chest is still the superior chest. You have to be more than one-off luckier with 80 or 89 chests to match the average outcome with 27 chests, and if you're going to be that lucky that you surpass average 27 chest, you would have been better served being that lucky with 27 chests.