Every match begins with one single choice that sets the tone for the entire game. This is the decision to keep or to mulligan the opening hand of seven cards. Professional players often say that the mulligan phase is the most important part of any match. If a player starts with a bad hand, they may lose before the first turn. However, if they throw away a good hand, they lose a card for no reason. To make the right choice, we must look at the math behind the cards. This article explores the mathematical thresholds that define a keepable hand of seven cards. We will look at probability, mana needs, and how the rules of the game affect these odds.
A deck of sixty cards is a large set of data. When a player draws seven cards, they are taking a small sample of that data. The goal is to find a sample that allows the player to execute their plan. Most players look for a balance of lands and spells. Lands provide the mana needed to play the spells. If there are too many lands, the player has nothing to do. If there are too few lands, the player cannot play their cards. This balance is the first thing we must measure using statistics. We use a tool called the hypergeometric distribution to calculate these odds. This formula tells us how likely we are to see a certain number of successes in a small sample.
The Statistical Foundation of the Opening Hand
To understand a keepable hand, we must first define what we want to see. In a standard deck with twenty-four lands, the most likely outcome is drawing two or three lands in the first seven cards. Specifically, the math shows there is a thirty percent chance to draw exactly two lands. There is also a thirty percent chance to draw exactly three lands. This means that sixty percent of the time, a player will have a fair mana base. However, the game does not just require any lands. It requires the right colors of mana at the right time. This adds another layer of math to the decision. If a deck has two colors, the player must calculate the odds of having both colors in the first seven cards.
A keepable hand must also have a clear path to the middle of the game. A hand with three lands and four spells that cost five mana is usually a bad hand. This is because the player will have nothing to do for the first four turns. To fix this, we look at the mana curve. The mana curve is the distribution of spell costs in the deck. A keepable seven-card hand should usually contain at least one or two cards that can be played in the first three turns. If the math shows a low chance of drawing a cheap spell, the player should consider a mulligan. The threshold for keeping is often tied to the ability to make a play by turn two or turn three.
The Role of Hypergeometric Calculations
Calculators for the hypergeometric distribution help players build better decks. They also help players make better mulligan choices. For example, if a player needs a specific card to win, they can find the odds of it being in their hand. In a sixty-card deck with four copies of a key card, the chance of having one in the opening hand is about forty percent. This is a high number, but it is not a guarantee. If a hand has everything else but lacks that key card, the player must decide if the risk is worth it. Mathematical models suggest that keeping a functional hand is better than chasing one specific card in most cases. This is because every mulligan reduces the total number of resources available to the player.
The Impact of the London Mulligan Rule
The rules for how players mulligan have changed over time. The current rule is known as the London Mulligan. Under this rule, a player always draws seven cards when they mulligan. After they decide to keep, they put one card back for each time they have mulliganed. This rule has a big impact on the math of the game. It allows players to see more cards even when they go down in hand size. This makes it easier to find specific combo pieces or land counts. Because the player sees seven cards every time, the quality of a six-card hand is much higher than it used to be. This changes the threshold for keeping a hand of seven.
Before the London Mulligan, players were more afraid to throw away a hand of seven. Now, the math shows that a mediocre hand of seven is often worse than a strong hand of six. If a hand of seven has no clear plan, a player can safely mulligan. They know they will still see seven cards to choose from. This has led to a more aggressive style of play. Players now look for hands that are high in power rather than just functional. The threshold for keeping a seven has moved up. A hand that was once a keep is now often a mulligan in a competitive setting. The math supports this shift because the penalty for the first mulligan is lower than it was in the past.
Variance and Risk Mitigation
Variance is the natural swing of luck in the game. Even with perfect math, a player can still lose to a bad draw. The goal of a keepable hand is to reduce this variance. A keepable hand acts as a safety net. It provides enough resources to survive the early game while the player waits for the rest of the deck to arrive. Professional players look for hands that can win even if the next few draws are bad. This is called a floor. If the floor of a hand is high, it is a keep. If the hand requires a perfect draw on turn one to work, it is a high-risk hand. Mathematicians suggest that players should avoid high-risk hands when they are holding seven cards.
Archetype Specific Thresholds
Not every deck uses the same math for keeping a hand. Aggressive decks need to start fast. They need low-cost creatures and enough mana to play them immediately. For an aggro player, a hand of seven cards with four lands is often a mulligan. They would rather have two lands and more threats. The math for these decks focuses on the first three turns. If the hand cannot deal a certain amount of damage by turn four, it is not keepable. The threshold here is based on speed and pressure. The player must weigh the loss of a card against the gain in speed. Often, a fast hand of six is better than a slow hand of seven for an aggro deck.
Control decks have a different set of rules. These decks want to go long. They need land drops more than anything else. A control player might keep a hand with four or even five lands. Their goal is to ensure they never miss a land play. The math for control decks focuses on the late game. They need to survive the early turns using only a few spells. For them, a keepable hand of seven is one that has mana and at least one piece of interaction. Interaction can be a counterspell or a removal spell. If the hand has no way to stop the opponent, the control player is in trouble. Their threshold is based on stability and survival.
Combo Decks and Piece Density
Combo decks are the most mathematical of all. These decks need specific cards to work together. A combo player looks for those pieces in their opening seven. If they have the pieces, they keep. If they do not, they often mulligan until they find them. The London Mulligan is a huge benefit for these decks. It allows them to dig deep into the deck. The math of a combo hand is a simple yes or no question. Do I have the pieces? If the answer is no, the player moves to six cards. The threshold for a seven-card keep in a combo deck is very strict. They rarely keep a hand just because it has a good land count.
Conclusion on Keeping Strategies
Deciding to keep a hand of seven cards is a balance of logic and probability. A player must know their deck and the odds of their draws. The math shows that a hand with two to four lands is usually the safest start. However, the specific needs of the deck archetype must come first. Aggro needs speed, control needs mana, and combo needs pieces. The London Mulligan has made the choice easier by giving players more information. Even so, a player must be careful not to mulligan too often. Every card lost is a resource that could have been used. By understanding the mathematical thresholds, players can make better choices and win more games. The secret to a good start is knowing when the math is on your side.