The chances to roll a specific hero in Dota Underlords depend on their gold cost, the number of the same units in play, and your level.
Dota Underlords has RNG elements, so your success in the game is also influenced by your luck. There is no way to know in advance which unit you will find the most during a match, neither their alliance.
Generally, you can build a strategy based on the following factors.
If there are already several two or three-star units of a particular hero, your chances to find additional units of the same kind are drastically reduced.
Your level is also crucial because according to it you will find a distinct amount of units with a certain gold cost. For example, if you have tier 1-2 heroes that are close to reaching three stars, you should avoid levelling past 4 or 5 as the chance to find them will decrease.
Unit odds by level
The developers finally shared the odds of rolling each tier of hero in the shop with the patch released on June 27, 2019. I have gathered them in the table below; it will be updated over time as changes are made.
The table indicates the odds for each slot. For example, at level 9 each slot has a 3% chance to draw a tier 5 unit, so for each re-roll (5 slots) the chance to get at least one is 14.1%.
The table is responsive. If you are using a phone, you may have to turn it sideways for a full view. Otherwise, zoom in or click the grey area to swipe it.
|Tier 1||Tier 2||Tier 3||Tier 4||Tier 5|
The level 11 in the table is attainable only with the tier 3 item A Higher Class of Criminal, which gives the following effect: "units in shop offered as if you were 1 level higher”.
This item can be of great help during the transition from mid to late game (for example, if you are using the Scrappy alliance and need to get Techies as soon as possible), but it can literally screw your plans if you needed to upgrade a lower tier unit to three stars.
Hero pool size
Valve has not shared exact info on the hero pool size, but the unit odds by level are exactly the same used in Dota Auto Chess, so we can suppose that also the unit pools is still the same.
Update: Valve developer Bruno "Bruno" Carlucci confirmed that this is the current hero distribution.
There is a fixed hero pool size for each tier which is shared among all players:
Tier 1: 45
Tier 2: 30
Tier 3: 25
Tier 4: 15
Tier 5: 10
These numbers represent the total copies of tier X hero that exist in the shop, not the unique heroes. For example, there are 45 copies of each tier 1 hero, etc.
If a player is defeated or if some units are sold, the heroes go back into the common pool.
You must reach at least level 5 to find tier 4 heroes and level 8 for tier 5 ones. Considering the data above, upgrading a tier 5 unit to three stars is quite difficult, as you need nine out of the ten copies available for each hero.
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Header image (Blade and Bow loading screen): Valve