I guess this is an accurateish probability distribution of my credence in different estimates of King's Bounty.

< 1.0B: 1%

1.0B - 1.19B: 4%

1.2B - 1.39B: 15%

1.4B - 1.59B: 30%

1.59B - 1.79B: 25%

1.8B - 1.99B: 20%

> 2.0B: 5%

I basically arrived at my 75% confidence interval by extrapolating from the progression observed among the Sweet commanders.

- Cracker: 860M
- Smoothie: 932M (+72M)
- Katakuri: 1.057B (+125M) (125 = 72 * 1.736)

For the Beast Pirates we have:

- Jack: 1.000B
- Queen: 1.320B (+320M)
- King: 1.876B (+556M) (320 * 1.736 = 0.556)

I assigned 20% probability to that bracket and 5% to above that bracket.

For my lower bound, I assigned 20% probability to "same bracket as Queen or lower". 15% went to 1.2B - 1.39B, 5% to a lower bracket than Queen.

Deciding how to divide the remaining 50% probability mass between 1.4B - 1.59B and 1.59B - 1.79B was pretty difficult, and I'm not very confident in my numbers for there (and may change it later). Things I kept in mind:

- Relationships between Zoro and Sanji's bounties.
- Excluding the anomalous WCI arc(s) it has been:
- EL: 77M vs 120M.
- Dressrosa: 177M vs 320M.

- There's no consistent multiplier, and it's probably not a geometric progression. Besides WCI boosted Sanji above Zoro, so the argument isn't very credible.

- @TheAncientCenturion's arguments that King is the Marco equivalent.
- Queen appears to be closer to King than to Jack, with the latter showing deference to the former two.
- Arguments that King shouldn't have a bounty above the fifth Yonkou Luffy.
- I'm reasonably confident that Beckmann would have a higher bounty than Luffy, so I don't have much credence in this argument as it should also apply to Beckmann.

- Some conservatism factoring in my tendency to overestimate Zoro (and hence his opponents).

I pulled numbers right out of my ass, but those pulled numbers can serve as my priors, and I can try updating them as new information reveals itself.

My expected value for King's bounty would be:

(0.01*1.0)+(0.04*1.1)+(0.15*1.3)+(0.3*1.5)+(0.25*1.7)+(0.2*1.9)+(0.05*2) =

**1.604**.

So I guess I'm predicting 1.6B - 1.79B.