Monday, July 28, 2014

CLA Series - Part 1: What is Card Level Advantage?

Hello, my name is Gabriel Moreno though I'm known to the community as Gabo. I'm a video game developer living in Canada and a family man. I used to play paper Magic The Gathering until my life became too busy so I moved into its online counterpart, but then my life grew even more busy and I had to stop. Then I found Solforge which has bite sized games and an awesome and innovative system and so I became addicted.

One very interesting but polarizing aspect of the game is the leveling mechanic. I have been analyzing the random aspects of the leveling mechanic and how players can interact with it and I would like to share my thoughts on the matter. 

Defining Card Level Advantage

In the game of Solforge players duel each other by drawing 5 cards and playing or discarding 2 of them each turn. Those cards  "level up", that is, they are sent to a discard pile as a more powerful version of themselves. After every 4 turns the players themselves level up and at that point the full deck is reshuffled. During the turns after this, each player will usually draw a mix of leveled up and non-leveled up cards. In most cases, being able to play as many leveled up cards each turn will give an advantage because the cards are more powerful than their unleveled counterparts. Card Level Advantage (CLA), a term coined by Bobby2, can be used to measure this advantage. It is originally defined like this:

Card Level Advantage for a given player is equal the sum of the levels of all cards played by that player minus the sum of the levels of all cards played by that player's opponent.

I'd like to expand this definition to account for a few gameplay elements. First of all, sometimes it is better to play an underleveled card, but that doesn't mean that the player is at level disadvantage. It should also take into account that there are cards that can make a player draw and/or play additional cards but those extra cards and plays should be considered as effects of the two cards initially played. This is because CLA is meant to be a deck-agnostic measure of how randomness affects the cards drawn. Therefore, a more accurate definition would be:

Card Level Advantage for a given player is equal to the sum of the levels of the two cards of the highest levels initially drawn by that player each turn minus the sum of the levels of the two cards of the highest levels initially drawn by the opposing player.

Here is an example of CLA: After entering the second level of play (also written as turn 2.1 and 2.2) Player A drew and played a level 1 and a level 2 card in turn 2.1 and another level 1 and level 2 card in turn 2.2, for a total card level of 6 ((1 + 2 ) + (1 + 2)). Player B also played a level 1 and a level 2 card in turn 2.1 and at the beginning turn 2.2 has drawn three level 2 cards. This gives him a total card level of of 7 ((1 + 2) +(2 + 2)) since he only counts two of the level 2 cards in his hand. The total CLA at this point in the game is +1 for player B or, likewise, -1 for Player A.

Note that we can differentiate a "turn CLA", the CLA only for that turn, from the "game CLA", which is the sum of CLA for all turns.

Accumulated CLA

If suddenly you find yourself with game CLA of -2 but the next turn the CLA goes back to 0 because you are able to play 2 levels more than your opponent, there shouldn't be too much of a disadvantage even though your opponent got the positive CLA first. However, if a couple of turns go by before the game CLA recovers back to 0, then you will likely find yourself at a disadvantage. We can call this difference Accumulated Card Level Advantage (ACLA) and can measure it by accumulating the game CLA each turn.

For example, if player B gets a CLA of 1 after turn 2.1, then in the next turn both players draw a hand of 5 level 1 cards, the CLA for that turn would be 0, the total game CLA would still be 1, but the ACLA would now be 2.

Level Count and Distribution in a Deck

In any given game, CLA will usually be going up and down for both players from turn 4 onwards and it is highly unlikely that CLA stays at zero for the whole game. However, the higher it goes for one player, the less probability there is of it continuing to grow as it means that player has already drawn higher level cards and now the rest of their pool will have fewer of them, while the other player will have not drawn their higher level cards and will have a better chance of drawing them. 

Given this, if both players level cards the same number of times, we can expect CLA to trend towards 0. This changes if one of the players is able to level more times than the other, changing their level count. If that is the case, then the expected CLA will be a fraction above 0 for that player.

Besides the sum of all the levels in a deck there is one other measure that is relevant when discussing card level advantage:  the distribution of these levels among cards, which can be used to calculate the ratio of risk vs reward. A deck with its levels distributed among more cards will have a lower risk of having a big card level disadvantage, but a deck with fewer leveled cards of a higher level will have the possibility of a powerful turn with high CLA, but also runs the risk of getting a sequence of turns with low level cards, giving the opponent the advantage.

For example, if two players start a turn and Player A has 16 level 2 cards and no level 3 cards, while player B has 8 level 3 cards but no level 2 cards, the sum of the levels is the same but the number of leveled cards is different. Player A has a higher chance of seeing leveled cards but while Player B has a lower chance of seeing leveled card, there is the possibility of making more powerful plays.

Ending Comments

Card Level Advantage is a way to measure the relative advantage gained by a player being able to play higher level cards over the course of the game. CLA varies as the game plays out and the probability of getting a positive or negative CLA will usually be dependent on the number cards and the number of levels that each player has managed to gain for their decks. If all other things are equal, the player with who has the highest accumulated CLA will have an advantage in terms of random card draw over the other player.

However, in Solforge all other things are usually not equal. While its important to understand how the random elements of CLA work on Solforge in a quantitative sense, the qualitative effects vary greatly depending on the selection of cards and the way they are played in the game. In the following article I will take a look at how the effects of CLA on a given game can be very different depending on the situation.

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