What are the Odds? (Surprise)

Last Updated: 210804

When considering the relative power of thieves and assassins with Surprise, I realized I didn’t have a solid grasp of the probabilities surrounding  the number of segments of Surprise. It’s made more complicated because it’s also possible the PC is surprised, reducing the number of segments they can act. Or, worse yet, the thief|assassin could end up being on the wrong end of the Surprise stick!

Since I’m considering at the efficacy of the thief backstab (or assassin assassination), the below calculations assume the attacker has the standard chance of being surprised (2 in d6), and could increase the chance of Surprise by either being hidden (3 in d6), silent (3 in d6), or hidden and silent (4 in d6).

If the PC has 2 in d6 chance of Surprise

  • Odds of being Surprised 1 segment:  5 in 36 (13.8%)
  • Odds of being Surprised 2 segments: 4 in 36 (11.1%)
  • Odds of 1 segment of Surprise: 5 in 36 (13.8%)
  • Odds of 2 segments of Surprise (Complete Surprise): 4 in 36 (11.1%)

If the PC has 3 in d6 chance of Surprise (successfully hidden or silent)

  • Odds of being Surprised 1 segment: 4 in 36 (11.1%)
  • Odds of being Surprised 2 segments: 3 in 36 (8.3%)
  • Odds of 1 segment of Surprise: 6 in 36 (16.7%)
  • Odds of 2 segments of Surprise (Complete Surprise): 5 in 36 (13.8%)
  • Odds of 3 segments of Surprise (Complete Surprise): 4 in 36 (11.1%)

If the PC has 4 in d6 odds of Surprise (successfully hidden and silent)

  • Odds of being Surprised 1 segment: 3 in 36 (8.3%)
  • Odds of being Surprised 2 segments: 2 in 36 (5.6%)
  • Odds of 1 segment of Surprise: 6 in 36 (16.7%)
  • Odds of 2 segments of Surprise (Complete Surprise): 6 in 36 (16.7%)
  • Odds of 3 segments of Surprise (Complete Surprise): 5 in 36 (13.8%)
  • Odds of 4 segments of Surprise (Complete Surprise): 4 in 36 (11.1%)

Now, all of these odds for ≥ 2 segments of Surprise assume that the PC is magically silent and/or hidden. This is where the elven thief or elven assassin shines, with their built-in 4 in d6 Surprise. Of course, they have to be 90′ from the party and not in metal armor, which can be a problem when things go wrong.

If the PC is required to make Move Silently or Hide in Shadows rolls, their odds of surprising the opponent decrease significantly. Both Hide in Shadows and Move Silently have terrible odds, even for moderately high-level PCs. A 7th level thief (9th level assassin) has only a 55% chance of Move Silently, with a corresponding 43% chance of Hide in Shadows. Even for a 7th level thief (9th level assassin) the chance of rolling a successful Hide in Shadows AND Move Silently is only 24% (for the 3th level thief it’s 5%!). The odds therefore of a 7th level thief (9th level assassin) gaining 4 segments of Surprise under those conditions is only 2.7%!  *Yes, a thief of high Dex can increase those odds of being surprised under MS/HiS, but only slightly.

And now we get to encounter range. Encounter range for Surprise is 1″-3″ (33% chance for each OFC). So, back to our 9th level assassin, whose chance at 4 segments of Surprise just dropped to .9% with HiS and MS, and only 3.7% even if Ms/HiS aren’t required.

With ER calculated in for a 1″, 7th level thief 1 Surprise segment 2 Surprise segments 3 Surprise segments 4 Surprise Segments
2 segments possible 4.6% 3.7% x x
3 segments possible 5.5% 2.7% 3.7% x
4 segments possible 5.5% 5.5% 4.6% 3.7%
3 segments possible (MS) 3.0% 2.5% 2.0% x
3 segments possible (HiS) 2.4% 2.4% 1.6% x
4 segments possible (MS/HiS) 0.1% 0.1% 1.1% 0.9%

Then for each segment of action during Surprise, they still need to roll THAC0 or an assassination roll, cutting the chance of success even further, a good estimate is by another 50% if you don’t want the individual calculations.

But hey, worth a shot right? Not so fast. That same 7th level thief (9th level assassin) under the same situation has a 13.9% chance of being surprised for one or two segments by their opponent—four times more likely than the best case of gaining 4 segments of surprise.

The same high Dex can decrease their chance of being unable to act when Surprised all the way to 0%. Then they only have the same problem as when no one is Surprised when 90′ ahead of their companions, not in metal armor: 31% with a 4 in d6 chance of Surprise, 42% with a 3 in d6 chance, and 50% of the time with a 2 in d6 chance (plus whatever odds they avoiding with their Dex)— Rolling Initiative.

 

 

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