This work would not be possible without @_Ninji's reverse engineering efforts. This page is based entirely off of their reverse engineering. Thank you, Ninji!
I’ve personally heard of reports of bell prices which don’t follow any of the below patterns. Take this page - and any work based on Ninji’s reverse engineering - with a grain of salt. I personally trust Ninji’s reverse engineering, but it’s possible that the patterns may have changed after an update, or some other code overrides the patterns, or people misremembered their bell prices, etc.
The maximum sell price for turnips is 660 bells, which is extremely rare. If you see reports of prices above that amount, those people are probably editing their save files.
Daisy Mae will offer a sell price of 90-110 bells for each turnip. Then, from Monday morning to Saturday night, Nook’s Cranny (and its upgrades) will buy turnips with prices that changes every half-day - when Nook’s Cranny opens in the morning, and at noon. In total, there are 12 half-days in the week, and 12 possible prices you can sell turnips for.
All turnip prices are based on a percentage of Daisy Mae’s sale price on your island rounded up, except on the first week you buy turnips on your own island. As a result, all prices in this page will be a percentage relative to Daisy Mae’s sale price on your island. This means that buying turnips at 110 bells isn’t a bad thing - but if you have a friend’s island selling them for cheaper, you should buy theirs instead!
There are 4 turnip price patterns in AC:NH:
Two decreasing dips. All prices are 90-140%, except for two decreasing dips of 2 and 3 half-days each where the price starts at 60-80% at the start of the dip and decreases by 4-10% every half-day during the dip.
The dips are randomly spread throughout the week and have at least one half-day in-between them. The dips could be at the very start or end of the week!
Decreasing, high spike, low. Starts off at 85-90% and goes down by 3-5% every half-day. Some time between Monday afternoon and Thursday afternoon a 5 half-day spike will start, topping out on the 3rd half-day. The prices during the spike will be 90-140%, 140-200%, 200-600%, 140-200%, 90-140%. Afterwards, prices will be 40-90%.
Constantly decreasing. Starts off at 85-90% and goes down by 3-5% every half-day.
Decreasing, spike, decreasing. Starts off at 40-90% and goes down by 3-5%
every half-day. Some time between Monday morning and Thursday afternoon a 5 half-day spike will start,
topping out at 140-200% on the 4th half-day (which will be referred to as peak%). The
prices during the spike will be 90-140%, 90-140%, 140-peak% (minus 1
bell), peak%, then 140-peak% (minus 1 bell). Afterwards, prices
will start off at 40-90% and drop by 3-5% every half-day.
Note that the spike could start on Monday morning with no initial “decreasing” period!
The chance that you’ll get a pattern is determined based on the last pattern you got:
| Last pattern | Pattern 0 chance | Pattern 1 chance | Pattern 2 chance | Pattern 3 chance |
|---|---|---|---|---|
| 0 | 20% | 30% | 15% | 35% |
| 1 | 50% | 5% | 20% | 25% |
| 2 | 25% | 45% | 5% | 25% |
| 3 | 45% | 25% | 15% | 15% |
Using this, we can calculate the overall chance that you'll get a certain pattern (the stationary distribution of the above stochastic matrix). Overall, pattern 0 appears ~40% more often than other patterns, and pattern 2 appears ~40% less often than other patterns:
| Pattern 0 | Pattern 1 | Pattern 2 | Pattern 3 |
|---|---|---|---|
| ~34.63% (4530/13082) | ~24.74% (3236/13082) | ~14.76% (1931/13082) | ~25.88% (3385/13082) |
The first time you buy turnips on your own island, you are forced into Pattern 3 and the bell price used for calculating sell prices will be randomised.