John's story

Hi, I'm Phaselock. I have a friend whose name is John. He started playing Card Hunter recently and asked me an interesting question. So I thought I'd share it with everyone. John tells me that to play Card Hunter, he makes decks of cards with items. He also says:

a) A deck of a lvl 18 party character contains 36 cards.
b) John has a warrior character who has 26 attack cards and 10 non-attack cards.
c) John finds that pvp games are often decided in the early turns (approximately 5 turns)
d) in the 1st turn, 3 cards are drawn from the warrior's deck. Subsequent turns draw 2 cards from the deck per turn.

John wants to know the chances of drawing as many attack cards as possible in the first 5 turns. He also wants to know the chance of not drawing a single attack card in the first 5 turns.

I did some homework and came up with the answers:

For 5 turns, John would have drawn 3 + 2 + 2 + 2 + 2 = 11 cards from his deck.

The chance of drawing 11 attack cards straight out
= 26/36 * 25/35 * 24/34 * 23/33 * 22/32 * 21/31 * 20/30 * 19/29 * 18/28 * 17/27 * 16/26
= 1.29 %

The chance of not drawing a single attack card in 11 cards = 0 %

I went ahead and did a few more in-depth calculations and summarized them below.

Chance of drawing

11 attacks cards in 11 = 1.2860 %
10 attacks cards in 11 = 8.8410 %
9 attacks cards in 11 = 23.403 %
8 attacks cards in 11 = 31.2036 %
7 attacks cards in 11 = 22.9921 %
6 attacks cards in 11 = 9.65670 %
5 attacks cards in 11 = 2.29921 %
4 attacks cards in 11 = 0.29860 %
3 attacks cards in 11 = 0.01947 %
2 attacks cards in 11 = 0.00054 %
1 attacks cards in 11 = 4.32753E-06 %
0 attacks cards in 11 = 0 %

John was surprised by the results. The total chance of drawing 7 to 9 attacks cards in the 1st 5 turns is 77.6 % ! In other words, it was highly likely that there would be 1 - 2 turns out of 5 where he would draw no attack cards. I tell John not to fret. These numbers only refer to minimum chances. In other words, if John built his party right, he could have other party members help the warrior draw more cards per turn to offset the 1-2 turns of lull. John agrees and decides to invest more time into deck-building.

6 months later, John won the CardStock 2 tournament against finalist Melvin. Melvin ragequits. John opened a pizza shop with his winnings and lived happily ever after. End of story. Thank you for reading !

Web Reference: http://www.kibble.net/magic/magic10.php

 

Great post.

To elaborate further given the same initial conditions - deck composition, initial 3 card draw, dynamic of deck changes due to draws, and 4 rounds of drawing:

You should expect that 26.5% of your matches to have at least one round where you do not draw any attack cards.

 

But I ALWAYS get a move card when I NEED an attack card. EVERY TIME! EVERY TIME!

 

hello,

Your post is great but has one big error, in the first turn you draw 3 card from your deck and not 4( you draw 3 cards + 1 move default card)

So your calculus are wrong but the idea is here.

Friendly,
Platouf.

 

fixed, John thanks Platouf for catching the error.

John proceeds to bish Phaselock for epic fail...and John lives happily ever after. Phaselock has a friend whose name is skip_intro ... but that's another story for another day.

 

Care to do another sample but with a lower amount of cards? Don't forget that Traits and trait-like cards virtually don't count towards card count, because as soon as they're drawn they replace themselves with another card. (IE A 36 card deck with 3 Traits is basically a 33 card deck; When I say Trait-Like I refer to something like Forward Thinking or Spin Around). It's probably fair to say the average deck has about 3-5 Traits, counting drawback traits, although I'm sure somebody trying to take advantage of this mechanic could manage more than 10 at least.

 

With an exception: new players might not have many good Traits at all, and might also be too scared to play with bad Traits. It is perfectly possible that a "zero Trait" analysis (or just one Trait per character on a class skill) matches the experience of new players.

 

http://www.cardhunter.com/forum/threads/beta-feedback-on-rng.2386/

Might be interesting to you.

 

And there's also the issue that certain drawback traits make you drop attack cards.

 

We can keep things to one thread. I don't see a real need to have a separate one when the actual discussion is happening elsewhere.