# Holy Avenger (+8) not Vorpaling at 20%

I still love that weapon btw.

Dagger of the Void is another weapon with neat tricks, for 9 Blue manas you get damage to last enemy + darkstorm + summon that doesnāt blocks your heroās mana at all. Pair with some class that favors daggers and other troops that favors blue and you get some fun teams.

What did you input as parameters? I can do a straightforward binomial calculation, but I donāt understand what the population variance should be in the link you gave.

There is an RNG that output ā1ā for ādecapitationā and ā0ā otherwise. That RNG follows a Bernoulli distribution, which is a special case of binomial distribution. Its mean is 0.2 and its variance is 0.16 (see Variance). You can also verify that by typing āoutput 1d100 < 21ā on AnyDice.com. The OPās sample has a size of 300 and a mean of 0.08. Those are the values I have put in the site I linked above.

Note that due to the nature of randomness, non-randomness cannot be proved with 100% certainty. It is possible that the OPās sequence is the result of very bad luck.

I once read an essay on writing automated tests for a pRNG. I was hoping to find some really clever analysis.

But really what it boiled down to was the naive approach:

1. Define what you think random data should look like.
2. Decide how much variance from that you can tolerate as āwithin expectationsā.
3. Generate huge data sets many thousands of times.
4. Decide if your millions of tests satisfy (1) within the bounds of (2).

By definition, some oddball results that definitely violate (2) should happen. But you probably expect, in most distributions, that they appear with a predictable rarity. That āpredictable rarityā is only a certainty in the presence of a lot of samples. So that was basically what they did: test thousands of distributions with millions of data points and make sure the oddball results appeared with the expected probabilities.

(For the record Iāve been lazy at testing this so far but Iām at 5 total āeligibleā casts, 1 Vorpal activation, and 4 no-activations. Testing this is tricky because as has been pointed out, if the things that happen before Vorpal triggers will kill the troop, that cast is ānot eligibleā.)

I my experience if you kill the troop you Vorpal the second troop. So it should be eligible

While youāre at itā¦

This lands way closer to 100% for the AIā¦ It must land 10% of the time for the player.
Easy counter to just match brown gems right? RFG makes sure it gets brown gems during Cascades. Ridiculous.

Thanks for reminding me that the variance of a binomial distribution is well-defined (dāoh!). I now see that the data shown have a z-score of -5.2, meaning they are more than 5 standard deviations away from expectation. So you are right that the result is significant at the 1% level. It is also significant at the 0.1% level, and the 0.01% level, and possibly also the 0.001% level.

The Higgs boson was announced, and the Nobel Prize awarded, at a lower threshold. Yes, Venarās results could be simple bad luck, but he would have to be really unlucky (or he misinterpreted how the weapon is supposed to work). Thus why I, and perhaps others, will now see if it behaves similarly.

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(Data analyst here) Not gonna do the calculations myself right now but that data set clearly says to me that the underlying % to kill is much less than 20%. Sample size of 300 may not be enough to nail down the exact percent, but itās near-certain to be in the 8-10% range.

Also, thanks so much for breaking it down into chunks. 3 trials of 100 are way more significant than 1 trial of 300.

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U guys are still looking at it slightly wrong in my opinion.
Your only sample size is one.
Every time u go, itās 20%.
Itās not 20% over a certain amount of tries, hopefully leveling out to 1 out of 5
Itās rng based on single chance probability.
I just canāt understand why anyone thinks keeping track of results is worth their time
But thatās it from me so do ur thing

In a quick test, Vorpal failed to trigger on 27 consecutive attempts where the initial damage killed the first enemy. This should only happen 0.24% of the time if Vorpal targets the second slot in such cases. I am now leaning toward the explanation that the Vorpal affix does not shift to the next enemy when the initial damage was already lethal.

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Each attempt is 20%, but the law of probability says the more attempt you do, the closer you should get to the statistical value.

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Yeah but look at it from another angle.

Weāre well aware a coin should land on either side 50% of the time. Now imagine you flip one ten times and get nine heads. Interesting, right?

Now imagine you flip it 100 times and only see tails twice. Interesting, right?

Now imagine you flip it 1,000 times and only see seven tails. More and more interesting.

Now, imagine if (like in the example Iāve already made) you start flipping a different coin. You get 5 heads. Then 62 heads. Then 498 heads. Huh. That sounds like what we expected.

So you pick up the original coin again and flip 10 times with 9 heads. 100 times with 98 heads. Huh.

The more āinterestingā that one particular coin gets the more likely itās not a fair coin. Even if the results are independent, we donāt expect a very consistent 98% output from a coin. It gets more suspicious as you find that the āluckā only happens if youāre using that one coin. Luck doesnāt work like that.

Wondering how the testers are doing.
On my part I see even less insta kill going onā¦

Played some in sets of 25 casts.

1. 25-5, 25-2, 25-3, 25-2, total 100-12.
2. 25-0, 25-1, 25-3, 25-1, total 100-5.
3. 25-6, 25-2, 25-1, 25-2, total 100-11.

I tried to avoid all questionable situations on the last 4 sets and only cast if enemy could survive a cast+skull drop or if it would die (and instakill would move to the next one, which did happen a couple of times).

Does look fishy.

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Sometimes I forget how much I enjoy statistics .

Well, I finally had Vorpal trigger for me, on my 68th cast. @Saltypatra, this would be an exceptionally unlucky streak on my part if the odds are really 20% as written.

Edit: the post is two hours old, but oh well. This trigger did take out the next troop in line after killing the top troop. So my earlier supposition, that Vorpal doesnāt shift to the next target, was wrong. It does.

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In fact, since the update, I have not seen a single Vorpal, and it is my main weapon.

Any Devs want to look into it?

As far Iām aware we havenāt made any changes to these spells or troops, so they are working as intended. We have spoken about statistics at great length on these forums over the years.

Iāll be moving this thread to Feature Requests and Game Feedback, as it is not a bug.

First iāll Confirmed that I did chop 2 heads today, so it works.

As for the Ā« working as intended Ā» and statistic, iāll say this:

This is the only weapon with this effect, so itās unique.

Also, it never worked ever at 20 %.

I actually think that the spell came out at 7% and is wrongly worded at 20%, itās just that no one ever check it.
I mean, yes, statistic were talked about a lot on these forums. Butā¦
No player has come close to the 1/5 effect. Not one. I hardly consider this Ā« fixed Ā» or resolved.

Also, some info, like, does it pass impervious and does it work on any troop, would be useful.

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