It is commonly known that in non-key-shuffle modes there are biases toward progression in dungeons -- in other words, progression items are placed into dungeon locations more than you would naively assume based on raw counts of non-dungeon items in those checks compared to similar overworld checks. This could also be referred to as "The Skull Woods Effect" since Skull Woods is infamous for being the most biased dungeon in this way. This is a demonstrable and provable artifact of how the fill algorithm is implemented (currently, as of v31 of the randomizer). This page attempts to both explain and measure (via empirical simulation data) the effect of this bias.

Consider a contrived example where the game consists of 1 overworld location, and 99 locations inside a single dungeon. The items placed in the game are 1 "progression" item, 1 "trash" item, and 98 small keys inside the dungeon.

Because there is 1 non-dungeon item placed in the overworld and 1 placed inside the dungeon, you would naively expect the progression item to be placed into the overworld location 50% of the time and to be placed in the dungeon 50% of the time. However, this is not the case:

1. The first relevant step in the fill algorithm is to shuffle all possible locations in the game. Note that after this shuffle, the overworld location only has a 1% chance of being at the very end of the list.
2. Next, small keys are placed one by one in the first location possible according to key logic restrictions.
3. Assume that in this example there are no key placement restrictions. This means that the first 98 locations in the dungeon will be filled by small keys, with the final (99th) dungeon location being left unfilled.
4. The list is now reversed. After this, the overworld location only has a 1% chance of being at the very front of the list.
5. Progression items (in this case, just one) are now each placed into the first location they can validly be placed into, obeying logic rules.
6. Thus, the progression item only has a 1% chance of being in the overworld location, and a 99% chance of being in the remaining unfilled dungeon location.

The key detail is in step 4 above, where the list is reversed as opposed to being completely reshuffled. In an alternate implementation where the list is re-shuffled in step 4, the progression item would instead have a 50% chance of being in either the overworld location or a dungeon location.

The example above is intentionally contrived, but can illustrate some key points about the nature of dungeon progression biases:

• Dungeons with only a few non-dungeon items but many locations to put them in (e.g. many small keys relative to the number of non-dungeon items) are affected the most.
• Dungeons that have strict logical restrictions on where small keys can be placed are less affected. This is because instead of all of the "frontmost" shuffled dungeon locations being filled by small keys, some of those locations will be left unfilled due to key logic.

Data was collected by running a simulation as follows:

• 95 overworld locations were simulated (Ganon's Tower and Castle Tower were ignored).
• The key logic for each dungeon was modeled according to the ALTTPR source code.
• As in the actual seed generation process, all locations are shuffled randomly, then dungeon items are placed in each dungeon (big keys and small keys in first available placements, then maps/compasses in random empty locations).
• The locations are then reversed, as described above.
• Afterwards, the placement of 25 "progression items" was simulated (various other numbers were also used, with no significant impact in the results)
• Importantly, no item logic was simulated (only key logic). This allows us to find baseline results for dungeon progression bias without conflating against factors related to conditional item logic.
• The above process is repeated across 1,000,000 seeds, and statistics are tracked on how often a progression item is placed into each dungeon.
• The above process is repeated across another 1,000,000 seeds, but this time with the list being reshuffled instead of reversed after dungeon item placements.
• The two datasets are compared with each other to find how biased the first set of seeds is compared to the second one.

As shown in the table above, progression items were placed into Turtle Rock 5.48% of the time when the list was reversed, compared to 3.70% when the list was reshuffled. This means that progression was placed into Turtle Rock locations almost 1.5 times (148.12%) as much as you would expect given that it contains only 5 non-dungeon items. Similarly, progression was placed into overworld locations only 89.15% as much as you would naively expect.

The rightmost column shows the normalized progression bias of each dungeon, compared to equivalent overworld checks (which are assigned a baseline of 100%). In other words, a given item in Turtle Rock is 1.66 times (166.14%) as likely to contain progression compared to an overworld check. This is illustrated visually in the chart below.

The above chart shows the relative progression bias for each dungeon location, normalized against overworld checks, sorted from lowest to highest bias.

This second chart shows the number of non-dungeon items in each dungeon (or partial set of dungeon checks), combined with the actual "equivalent progression weight" of those items when compared to overworld checks.

Note: Mimic Cave (as an overworld check with no dungeon bias) was incorporated into the numbers for Turtle Rock as it is generally treated as a part of that dungeon despite being filled as an overworld check.

Conclusions from the above data are open to interpretation and should be evaluated against other factors on a seed-by-seed basis, but a few suggested takeaways are as follows:

• As is well known, Skull Woods is notorious for being biased towards progression -- the two items in Skull Woods essentially carry the weight of 4 equivalent overworld checks.
• Misery Mire carries nearly the same bias as Skull Woods, but is often unavailable due to the strict entry requirements, or undesirable due to being a relatively slow dungeon to clear.
• Turtle Rock is the most progression-dense dungeon in the game (though it often carries the steepest set of entry requirements), offsetting the lengthy time it takes to travel to and complete.
• Palace of Darkness benefits significantly from its bias -- even excluding the boss, it carries more progression weight than all 6 items in Swamp Palace.
• On the flipside, Swamp Palace benefits very little from bias, but is still relatively dense as a whole thanks to containing 6 checks to begin with.
• The biases for Misery Mire (191.45%) and Tower of Hera (146.52%) may dissuade runners from leaving behind items in the commonly-skipped vanilla big key chests of those dungeons, potentially more so than the case of the vanilla big key chest in Eastern Palace (120.04%).

An attempt to combine the progression weighting data of various dungeons with the approximate time it takes to clear those dungeons is presented in Dungeon Efficiency Analysis.

Accounting for full item logic placement restrictions is currently beyond the scope of this analysis (some empirical datasets for full seed generation can be found here).

A possible variant of the above analysis is to disallow items to be placed into locations where they can never logically be found (e.g. the moon pearl can never be placed in most Dark World locations). Although this does not account for the full complexities of item logic (e.g. validating logic sequencing and beatable seeds), it may provide numbers closer to the actual likelihood of progression items being in various locations -- for example, none of the checks in Turtle Rock can ever hold a glove, somaria, moon pearl, or hammer, so the overall chances of progression being in those locations is inherently reduced compared to an overworld check with no requirements.

This was intentionally omitted from the simulation and analysis above, for the following reasons:

• When playing a seed, dungeon locations typically only become relevant after their item requirements have already been satisfied (with the exception of sequence breaks). (In other words, the fact that Turtle Rock cannot contain either glove is largely irrelevant because accessing Turtle Rock means by definition that both gloves are already in your inventory, so none of the other unchecked locations can contain them either)
• In general, item logic considerations also bring conditional logic weights into play, which differ highly from seed to seed.