What were the Odds?

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A pretty rare occurrence tonight of a Secret Hunter with five secrets up at only two mana. I mean, that’s pretty crazy, Paladins were scary last year with five secrets on turn six, remember?

On the spot I noticed it (hence the screenshot), but it’s only after the game (won, by the way) that I realised how rare this was.

img_0096As you can see, this deck contains six different secrets: Cat Trick, Explosive Trap, Freezing Trap, and Snipe in two copies, while Bear Trap and Snake Trap were present only once.

The card log on the left shows that the one not in play was Explosive Trap.

Now, let’s look at the situation closely: for this to happen, it is imperative to play second, as without coin it would be impossible to play the Cloaked Huntress on turn two. That alone has a 0.5 probability of happening in a given game.

I don’t remember the order in which I received the secrets, but I remember that I had four of them from the scratch, which is what inspired me to keep them. In all honesty, I was hoping to draw first a Secretkeeper, then the Cloaked Huntress, instead I drew first the fifth secret, then the Cloaked Huntress.

We start with 30 cards. I played my coin first, then all cards from right to left, starting of course with the Cloaked Huntress which reduces the cost of the secrets to 0, so I received the cards in the opposite order (left to right).

There is a total of 10 secrets in this deck meaning that when I drew my first card, the odds of drawing a secret were 1/3 or 0.333333333

Once Cat Trick was in my hand, 29 cards were remaining, but only 8 would do it for the second secret, as a second copy of the first wouldn’t work. So probability of drawing a second secret different from the first was 8/29 or 0.275862069. After drawing Snipe, we are down to 6/28 or 0.214285714 then 4/27 or 0.148148148 for the following one. The fourth one was Snake Trap, one copy only, so the odds for the fifth secret I got on tour one were 3/26 or 0.115384615.

Finally, the Cloaked Huntress I drew on tour two: 2/25 or 0.08

1/2 x 10/30 x 8/29 x 6/28 x 4/27 x 3/26 x 2/25 = 0.0000134731169214

In the end, the chances for such a combination were pretty low: 1 in 74,222

One could argue that it’s not that low, but considering I have been playing for about 16 months, and I played a total of 250 games with the Hunter, that still represents about 400 years of playing hunter at my current pace, which suddenly gives a better idea of the rarity of the event.

Author: Paolo Belcastro

As a true European nomad, and after Italy, France, and Switzerland, Paolo currently lives in Vienna, from where he leads the WordPress.com Spectrum Division for Automattic and the WordCamp Europe 2017 crew. When not thinking about WordPress, he is usually absorbed by his other passion, photography. Paolo lives online at paolo.blog

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