Draft simulators are widely used training tools in the Magic: the Gathering community. Many other draft simulators have somewhat limited features, so I designed and built a draft simulator with smart computer opponents, pick suggestions, and automatic deckbuilding. This simulator, draftsim, was quickly adopted by the community and is currently the leading free tool for draft preparation.
The draftsim model is designed to mimic the behavior of professional players and aims to maximize the quality of cards within a two color pair. Recommended picks are shown in a table on the site and there are computer draft opponents who always make the most recommended pick. Decks are automatically constructed by identifying the two colors with the best cards and playing the highest rated cards in those colors.
The valuation of cards is a sum of two components, a base rating, intrinsic to the card, and a color bonus, which provides an incentive to draft cards from a two color pair. The base ratings for each set can largely be derived from pick order lists, although some fine tuning can be done based on trends in professional draft viewers, community articles, or experience on the simulator. Generally speaking consistent cards like creatures and removal spells should be rated slightly higher and situational cards like combat tricks should be rated slightly lower than the professional pick order list to ensure the construction of functional decks. A complete list of draftsim card ratings can be found here.
The drafting process is broken down into two stages - the speculation stage and the committed stage.
During the speculation stage, the model searches for two open colors to play. When a player picks a card, that player's commitment to the card's colors is increased by (rating - baseline), where baseline=2.0. Thus, a replacement level card with rating=2.0 won't draw the model into new colors, but a bomb rare with rating=5.0 will.
As a player's commitment to a color grows from 0 to threshold=3.5, the color bonus for cards of that color grows linearly from 0 to max bonus=+0.9 before capping off. At that point, the player is considered committed to that color. To help find a second color, the bonus of the color with second highest commitment is increased to 0.8 * max bonus. When the player is either committed to two or more colors or the draft has progressed the fourth pick of the second pack, the model enters the committed stage.
During the committed stage, the model priotizes cards in the two color pair that the player is most committed to. These cards are given a large on color bonus=+2.0. Off color cards are assigned an off color penalty of -1 for each off color mana symbol beyond the first.
The above description holds for single-colored cards. Colorless cards are given a bonus equal to the largest bonus available to single-colored cards.
Multicolored cards are handled differently. During the committed stage, multicolored cards with 2-3 colors are either given an on color bonus=+2.0 or the off color penalty described above. During the speculation stage, these multicolored cards are assigned a bonus equal to the sum of color bonuses in the card's colors, minus the sum of color bonuses outside of the card's colors, and minus a multicolored penalty=-0.6. Multi-colored cards with 4-5 colors will not be played by the model and are assigned no bonuses or penalities.
The draftsim model is then used to automatically construct decks for the user and the computer opponents. First, the strongest color pair is identified as the two colors with the highest color commit. The highest rated on-color cards are added to the deck until there are 23 nonland cards. A total of 17 lands are then added to the deck, split as evenly as possible and favoring the color with greater color commit in the case of a uneven split.
Work is currently underway to consider the effect of additional factors such as curve and synergy. To train these parameters, drafting data will be collected from users on the site and from user uploaded drafts played on the official Magic Online client. This data can be used to train more sophisticated drafting models, allow users to play against a variety of opponents, and provide insights into the drafting stratgies employed by a wide range of users.