Chances of getting a Legendary from Ancients
This question comes up a lot, so here’s the math on your chances to get a Legendary Champion from Ancient shards, during regular times as well as double summons. Spoiler alert – your chances of pulling a Lego with 100 Ancient shards during double summons is *not* 100%… The table below looks at the percentage chance of getting 0, 1, 2, 3, or 4+ legendary Champion pulls if you pulled 100 Ancient shards.
|0.5% (regular chance)||1% (Double summons)|
The math is pretty simple – p(x) = combin(y,x) * p(L)^x * p(!L)^(y-x), where:
- y is the number of pulls
- x is the number of Legos
- combin(x,y) is the number of combinations of x into y, where sequence doesn’t matter (showing it this way as it’s the Excel formula, so you can easily plug this into Excel yourself)
- p(L) is the probability of a Lego (i.e. 1% under double summons)
- p(!L) is the probability of something other than a Lego (i.e. 99% under double summons)
So the bad news is that, even with double summons, you have 36.6% chance (a little over 1 in 3) to get zero Legendary champs. On the bright side, it’s much better than the 60.6% chance of getting zero Legos during regular summons. Furthermore, in double summons you have about 26.4% (a little over 1 in 4) chances of getting 2 or more Legos.
If you want to “warm up” or get rid of some jitters, test things out using our Summoning Simulator. It uses the exact same probabilities as the game and allows you to toggle between regular and double summons.
Good luck and may the Legos be with you!