Deck Math

It’s been awhile since I've written an article! Sorry guys. I took a nice holiday vacation to the beach, and it was fabulous. But I’m back now, and ready to go. This article is going to be a bit more calculus than most, so be warned. There may be some math errors, but the information will be generally accurate, I promise!

One of the biggest choices made in Redemption deck building is the size of the deck you use. For years, small decks (53 or less cards) have been considered the best (with some people strongly holding that 56 is the way to go). Today I am going to show you the math behind why I always try to play at 50 or 51 cards (if I am using Haman’s Plot) if I am playing a conventional offense heavy or balanced deck.

Let’s examine some proportions in a 50 card deck. Since almost every deck should be playing the Hopper lost soul, that means there are 8 lost souls in this 50 card deck. They don’t really count for deck size, because if you draw them, they get replaced. While I should technically account for the chance of drawing a soul and distribute that across and proportional math I do, I’m lazy, and it’s much easier to simply ignore lost souls and treat this deck as 42 card deck, so that’s what I am going to do.

With the 42 card deck, your chance of drawing any one card in your opening hand looks like this:

1/42 + 1/41 + 1/40 + 1/39 + 1/38 + 1/37 + 1/36 + 1/35 = .2085328

That means that any one card has a chance of appearing in your hand about 20.85% of the time, or slightly more than 1 in 5 games. Let’s look at the same math for anyone card in a 56 card deck, which would have 48 non-lost soul cards:

(1/41) + (1/42) + (1/43) + (1/44) + (1/45) + (1/46) + (1/47) + (1/48)=.18025413

In this 56 card deck, your odds of drawing any one card in your deck have dropped to 18.03%, or slightly less than 1 in 5 games. The change equates to a 2.82% greater chance of drawing a single card in a 50 card deck rather than a 56 card deck. While this might not seem like much, let’s look at this size difference in terms of turns to deck out.

Since Son of God is often a card needed to win the game, suppose it is on the bottom of both decks in this scenario. How many turns will be needed to draw it out? The equation to find out is ((X-(LS+8))/3) where X is size of the deck. I will be assuming no drawing occurs via abilities for the purpose of this math.

In a 50 card deck: ((50-16)/3)=11.3
In a 56 card deck: ((56-16/3)=13.3

That’s a two turn difference! That’s a huge deal. That means the 56 card deck is going to need to outdraw the 50 card deck by a full two turns via abilities on cards in order to get to Son of God.

While the odds are not incredibly high that Son of God will be your bottom card, the principle of it remains. All other things equal, a 50 card deck is 2 turns faster than a 56 card deck. Often 56 card decks are said to have more endurance than a 50 card deck – that they have an advantage simply by having more cards. In reality, this couldn't be further from the truth. I would estimate that the average Redemption game takes 10 turns or less, which means each player will have access to, at most (assuming no draw abilities), 38 cards (8 for opening hand, drawing 3 every turn if you went second). Both a 50 and 56 card deck have more than 38 non-LS cards in their deck – which means the 56 card deck has received no advantage of the 50 card deck in terms of number of cards played. The difference is that 50 card deck has between 4-12 cards left in deck, while the 56 card deck has between 10-18 cards in deck. The 56 card deck receives absolutely no advantage to playing with a bigger deck until he draws the 43rd through 48th playable card in his deck. While this seems good in theory, in practicality, most games are over by this point, and rather than reaping this advantage, you have spent all game lowering your odds of drawing that one card you need to counter a certain hero or win a rescue attempt.

Math is why I play with a 50 card deck. I realize this won’t be applicable for all decks – some defensive heavy decks need more space and want more resources. But I’d be willing to bet that 90%+ of the time, 50 is better.

-Olijar

EDIT: The draw math is wrong, but the percentages play out relatively similarly and I'm slightly lazy. Sorry guys!