Calculations that prove the solution you gave is wrong? To quote a YouTuber I watch, this will be super easy. Barely an inconvenience.
Let the
semi-useless semi-pointless math begin. (Edit - how can I forget my own catchphrase?)
Versus from
@Jackluyt 's shared document.
Best Chest is at the top of list, using the least Sky Essence; worst at the bottom.
The goal is to maximize Artifacts, which is Grand Prizes, which is feathers.
Your assertion is that the your list, weighted by Average Bonus SE regardless of Chest Cost or Feathers per Chest, is the order that will give the "highest odds of the highest payout", better than that of the typical computation that includes Chest Cost and Feathers per Chest.
I started to compare your proposed top performer, the 129 Chest, again that of the typical computation's best, the 77 Chest. According to your list, I think you would expect a drastic difference, given the averages of 25 vs. 15 for 129 vs. 77 (129 supposedly about 66% better than 77). However, the typical computations rankings put them at very close values, with SE to Feather ratios of 20.7 vs 20.8 for 77 vs. 129 (77 about 0.5% better than 129). When I did the math the difference between the two chests fell in the rounding error, which while I recognized as demonstrating the 0.5% superiority of 77 over 129, it's not a very satisfactory demonstration.
Instead, let's look at your #2 and 3, the 112 and the 77 chest, which still have a wide difference with the averages of 22 vs 15 (112 supposedly about 46% better than 77), while by the typical computation they would be ranked #3 and 1, with SE to Feather ratios of 22.5 vs. 20.7 (77 about 8.6% better than 112). Having now done the math I will present below, I'll say that the results very clearly show which of the two approaches is correct.
For the 112 chest, starting with 5,000 SE, you could open 5,000/112 = 44 chests with 72 ES left over. At 4 Feathers per chest, that's 44*4 = 176 feathers directly. With an average 22 bonus SE per chest, that would be about 44*22 = 968 bonus SE, realistically between 9 or 10 successes, so 900 or 1,000 bonus SE.
For the 77 chest, starting with the same 5,000 SE, you could open 5,000/77 = 64 chests, again with 72 ES left over. At 3 Feathers per chest, that's 64*3 = 192 feathers directly.
192 is better than 176 (about 9% better). With an average 15 bonus SE per chest, that would be about 64*15 = 960 bonus SE, realistically between 6 or 7 successes, so 900 or 1,050 bonus SE.
900 or 1,050 is equal to or better than 900 or 1,000.
Repeat through use of the bonus SE, and the numbers will continue in like fashion.
Done.
But wait... What if I'm luckier and get more bonus chests with the 112? Well, you need to get lucky enough in the first round to get 4 additional chests (16 additional feathers) in the second round
just to equal what the 77 chest made in the
first round, while the 77 chest player without additional luck again makes more in his second round than you, and so is still ahead. Give the 77 chest player equivalent luck, and he's again beating you, round after round.
Done-er.
So no. Your chart does not list the "chests that have the highest odds of the highest payout." Maximizing Bonus SE rates, ignoring the costs of the chests and the Feathers the chests give out does not maximize your total feathers received. Your chests are in the wrong order, and a player who plays prioritizing chest selection based on that list does not "have the highest odds of the highest payout."