Merir

05-21-2013, 01:30 PM

I'm sure we've all seen the Head Games card spoiled in today's The Guild Experience article. For those of you who don't remember the mechanic:

Secretly choose 5 or 10. Target opposing champion guesses which number you chose. If they guess incorrectly, deal damage to them equal to the number you chose. If they guess correctly, deal damage to you equal to the number you chose.

When I saw this I thought that it's a pretty cool idea for a card, adds a bit of randomness, risk vs. reward and all that, but something troubling occurred to me after a few moments. I would like to preface this by saying I'm not very good at math, and if this turns out to be a silly mistake on my part I'll be only happy to be proven wrong.

Now let's imagine a situation where you play the Head Games card, and your opponent defends based on a coin-toss. Heads, he picks 5, tails, 10. So he has a 50/50 chance of picking either one, but leaves no recognisable pattern for you to exploit.

What is your expected value in terms of damage dealt (positive) and damage taken (negative) when you secretly choose 5 against this opponent?

0,5 * 5 [you deal 5 damage 50% of the time when he chooses 10] + 0,5 * (-5) [take 5 damage when they choose 5] = 2,5 - 2,5 = 0

When choosing 5 against an opponent who is making their choice based on a coin-toss, you can expect to deal exactly zero damage over the long run - or, the damage you deal will be exactly offset by the damage you take. The same is true when choosing 10 against this opponent:

0,5 * 10 [deal 10 damage when he picks 5] + 0,5 * (-10) [take 10 damage when he picks 10] = 5 - 5 = 0

What ever you choose, as long as your opponent defends 50 / 50 without a repeating pattern your expected value for playing Head Games is exactly zero. This leads me to the conclusion that Head Games is a waste of resources to play, and a waste of space in your deck. Even worse, having a Head Games in your deck actually benefits your opponent: every time you play it, you use four resources for zero gain, and having this card in your deck makes it less likely for you to draw cards that actually benefit you.

As I said before, I'm not good at maths and might have made a mistake in thinking about this scenario. Please prove me wrong, since the concept is interesting and it would be nice to be able to play this card without it hurting you.

Secretly choose 5 or 10. Target opposing champion guesses which number you chose. If they guess incorrectly, deal damage to them equal to the number you chose. If they guess correctly, deal damage to you equal to the number you chose.

When I saw this I thought that it's a pretty cool idea for a card, adds a bit of randomness, risk vs. reward and all that, but something troubling occurred to me after a few moments. I would like to preface this by saying I'm not very good at math, and if this turns out to be a silly mistake on my part I'll be only happy to be proven wrong.

Now let's imagine a situation where you play the Head Games card, and your opponent defends based on a coin-toss. Heads, he picks 5, tails, 10. So he has a 50/50 chance of picking either one, but leaves no recognisable pattern for you to exploit.

What is your expected value in terms of damage dealt (positive) and damage taken (negative) when you secretly choose 5 against this opponent?

0,5 * 5 [you deal 5 damage 50% of the time when he chooses 10] + 0,5 * (-5) [take 5 damage when they choose 5] = 2,5 - 2,5 = 0

When choosing 5 against an opponent who is making their choice based on a coin-toss, you can expect to deal exactly zero damage over the long run - or, the damage you deal will be exactly offset by the damage you take. The same is true when choosing 10 against this opponent:

0,5 * 10 [deal 10 damage when he picks 5] + 0,5 * (-10) [take 10 damage when he picks 10] = 5 - 5 = 0

What ever you choose, as long as your opponent defends 50 / 50 without a repeating pattern your expected value for playing Head Games is exactly zero. This leads me to the conclusion that Head Games is a waste of resources to play, and a waste of space in your deck. Even worse, having a Head Games in your deck actually benefits your opponent: every time you play it, you use four resources for zero gain, and having this card in your deck makes it less likely for you to draw cards that actually benefit you.

As I said before, I'm not good at maths and might have made a mistake in thinking about this scenario. Please prove me wrong, since the concept is interesting and it would be nice to be able to play this card without it hurting you.