Please see revised OP, it matches what you wrote.
My understanding is Nellie only draws from 9 pirates? Someone above wrote this, but I haven’t seen a source on this? So the actual probability is ~75%.
Where did you read this from? The above posts referring to 9 pirates was hypothetical to show how stats worked and was no where rooted in truth.
The 9 out of 19 is something different.
There are 19 pirates it draws from, but 9 of those are chosen by Nellie in the battlecry
Hmm… yes I see that up there. I think that poster meant that there are 19 pirates in the pool and Nellie will show you a total of 9 to choose from. Now, it’s not exactly 9 to choose from, but I don’t think that poster meant there are only 9 Pirates in the Nellie pool.
The only other oddity that might be at play here is if the unselected Pirates from the first and second discover panel do not get recycled back into the pool. Obviously the selected Pirate does not go back into the pool, but if the unselected Pirates also get discarded from the pool, the chance to pull Smite will be significantly higher. But someone else is gonna have to write out that math. I’m tired.
Okay in this case the probability is 409/969 ~ 42%, which does make me think what I am seeing is an anomaly. Would be curious what other players are seeing, is the actual rate at which Mr. Smite picked available from HSReplay?
Personal experience and bias can lead to unlikely generation. I don’t know the figures, but 95% off of Nellie seems exaggerated. This is not to call you a liar or anything of the such. I think you might have the match wrong in an overall sense. Perhaps in this finite experience of yours the probability of discovering Mr. Smite was high. However, we need to look at the more general experience of the playerbase collectively to discern the actual and overall likelihood of situations like this happening. Instead of jumping to conclusions based on personal experience and potentially unlucky occurrences, it is best to instead look at the true statistical likelihood of these things happening, using large sample sizes as opposed to your singular experience where this might have been the case.
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They do not, which is why the calculations is MUCH easier than you guys realize
EDIT:Or at least I have yet to see it… Which is very possible
Yes, I agree, I’d like to verify this empirically at a larger scale but I don’t have access to this data; is this something HSReplay can give access to?
I applaud you for being so reasonable, @yellovvsnovv for realizing that your experience isn’t necessarily (and probably isn’t) representative of the overall probability of generating Mr. Smite,
I, too, would love to get to the bottom of this. Can you think of any ways we can devise an experiment to proof or disprove the hypothesis that there is as high an occurence of Mr. Smite being generated as you experienced. I think you may have been exceptionally unlucky in this particular case.
How many miles per hour is Smite charging at if he leaves the station at 1pm and will arrive 30 miles away at 5pm?
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Is this match class? 
Edit: My experiece is no more valid than others. However, in my experience I believe I’ve only had Mr. Smite generate from Nellie and from the Juggernaut about 5 tmes in the course of playing versus Pirate Warrior (if that’s the class we’re referring to). My suspicion here is that our friend @yellovvsnovv was unlucky.
I know that HSReplay stores entire game replays, but I don’t think access to those is given to anyone. The obvious thing to do would be to parse either logs of those games or whatever format they come in, and determine the number of times Nellie generates Mr. Smite.
Otherwise, the only way to reasonably test this that I can think of without access to such data would be to run repeated trials in games vs AI, but this would take days to acquire enough data samples.
And also, you’re considering Nellie’s generation. But, we should also take into account the numerous ways to discover additional Mr. Smites as well as the one already in the deck, as well as from Juggernaut. I’d wager you’re more likely to see Mr. Smite now more than ever before. It actually seems to be a high probability that this happens, considering all of the ways to find him.
It isn’t inaccurate to say that you will almost certainly run into at least one Mr. Smite during the course of these matches.
This is actually all I care about, because it is the only thing I’ve observed anecdotally. Also, pirate warrior is irrelevant at the rank I play at.
My impetus for bringing this up is that given there is already an established bug with Nellie (not a minor one, but a severe one that was recently fixed,) it’s entirely possible (and more likely than with other cards) there are much harder bugs to track down with this problematic card.
I haven’t played yet since the latest patch. Is Nellie still bugged? I know they claimed to have been working on a fix for today. Forgive me if this is partially off-topic, but I’d really like to know.
42% feels about right from my experience with Nellie.
Definitely remember the times you see smite more than the times you don’t though.
And the Smite that gets hard run / discovered via amalgams can give the 3 pirates charge anyway, so it’s not even particularly necessary that they get it on Nellie itself.
7.5 miles per hour
Dude is slow as hell. Smite gotta be at least double that speed mate.
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But there isn’t 9.
I did a bunch of testing and none of the tests refuted this. (No one can prove a negative, so I couldn’t prove this.)
The Pirate pool for Standard Warrior is indeed 19.
So the chances of no Smite off of Ship directly are
18!/9!/(19!/10!) = 18!*10!/(19!*9!) = 52.6%
The chances of no Smite and no Amalgam are
17!*10!/(19!*8!) = 26.3%
So there’s a 47.4% chance they’ll get Smite, plus a 26.3% chance they won’t get Smite but will get an Amalgam.
If they get Amalgam, the chance they won’t get Smite off the last Discover is
17!*15!/(18!*14!) = 83.3%
meaning there’s a 16.7% (1 in 6) chance they will.
47.4% + 26.3% / 6 = 51.78%
So slightly more than half the time Nellie will either serve up Smite herself, or an Amalgam that does.
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I was hoping you’d show up and clear up the math lol. I wish there was a way to tag posters in Threads. Or maybe there is and I don’t know about it
And you have this data recorded somewhere, yes?