Like Poker, Magic is a game of probabilities. This is because we start with only a limited number of random cards from our deck and do not have knowledge of exactly what we will draw in a game or in what order. It is this aspect of the game which can be the most frustrating but is also what has allowed the game to become as popular as it is and thus appeal to players of various levels of play skill.

In my last article, I talked about the most common probability related fallacies players tell themselves and how knowledge of probability can prevent us from making the wrong decisions.

However, even if you have a good grasp on basic probability you can occasionally just be blown out by variance. Sometimes despite the odds being against it you can draw 8 non-land cards in a row when a single land would have allowed you to win by casting [card]Sorin's Vengeance[/card].

While variance is common in both Magic and Poker there is one major difference between the two games in this regard. In Poker, the players have no control over what cards are in the deck. The deck is always the same 52 cards, while in Magic, every deck is different. The composition of a deck is entirely up to each player, providing it adheres to deck construction rules.

Today’s article covers an idea which as far as I know has never actually been addressed before. The issue is that we should be sideboarding lands in or out during limited matches depending on whether or not we are on the play or draw. For this article I will limit the discussion to limited decks because in limited the sideboard is, for want of a better term, unlimited and as such there is no detriment to having lands in the sideboard.

However I will discuss the same principle in relation to specific constructed decks in a few weeks time.

So, let’s begin.

In order for a deck to function it needs to be able to play a land each turn up until a certain point. This point varies for each individual deck. In constructed this point can be as low as turn 2 (Aggressive combo decks) or as high as turn 6 (control decks). However, in limited this point on average tends to be either turn 3, 4 or 5.

When considering our chances of hitting n lands by turn n, not many players bother considering the math involved when deciding how many lands to run. We take the shortcut of using what is a generally accepted number of lands; 16-18 depending on curve and alternate mana sources and we stick with that.

Now this method is mostly fine as a starting point for game 1 of a match, but can and should be improved upon in games 2 and 3.

The difference between being on the play and the draw is one extra card. Most players understand the importance of drawing cards in a game but fail to realise the significant impact one extra card has on your capability to hit your early land drops.

When a player complains about mana problems they are invariably met with the question “how many lands are you running?

Now of course this is important but as can be seen from the tables below, the appropriate number of lands actually differs depending on whether the player is on the play or draw.

*Note that the percentages I am using are assuming that we mulligan any opening hand with 1 or less lands or 6 or more, any 6 card hands with 5 or more or 1 or less and any hands below this point without any lands. While in reality the numbers will be slightly different based on the amount of hands where we have more than 2 lands but mulligan anyway, it is impossible to take all such situations into account when dealing with a theoretical deck.

Looking at the results from two Limited GPs, GP Montreal and GP Santiago, we can see that 7 out of the top 8 decks in both events had 17 lands and the two that didn’t were running early mana acceleration or card draw. On that basis we can assume that in M12 and Innistrad limited, 17 lands is the consensus of where you should be unless you have a particularly high or low curve. As such I have used 17 as the midpoint when calculating the percentages in the tables below.

As you can see from the percentages, depending on what number of lands you are aiming to hit by the corresponding turn, being on the draw can actually improve your chances of doing so by more than 10%. What percentage we should be aiming for precisely, is different for each deck and how to determine this is a discussion for another day.

The point I want to make with this article is that considering how important consistency is to having a winning decklist it makes no sense to have the accepted percentage vary so much between games 2 and 3.

So how do we figure out what percentage we should be aiming for in games 2 and 3?

Well, going into a match we have no definitive knowledge about whether we will be on the play or draw. Assuming that there is a 50-50 chance between being on the play or draw the chance of having n lands on turn n in game 1 is the midpoint.

For example, if we want to play our 4th land on turn 4 and we are running 17 lands, on average we will do this 73.7% of the time according to the above table.

68.9% + 78.5% = 105.6

105.6 / 2 = 73.7%

Sticking with these figures, this means that in game 1 it is generally accepted that ~73.7% is an acceptable probability of hitting 4 lands on turn 4.

Knowing this and being mindful of the difference that being on the play or draw makes, there is no reason for us to not adjust the land count of our decks so that the chance of hitting 4 lands on turn 4 remains ~73.7% in games 2 and 3. By doing this we reduce the amount of variance in the deck by maintaining the same percentage throughout the match.

This will allow you to get manascrewed less often on the play, and manaflooded less often on the draw.

Looking at the table, if our aim is to have 4 lands on turn 4 we can see that to achieve closest to the equilibrium percentage we would need to take out a land when on the draw (72.2%) and add a land when on the play (75.3%).

Therefore, in this situation being on the draw increases your chances to almost the same amount as if you were running an additional 2 lands.

Will this actually affect my draws?

Yes.

However, whether you will actively notice it is another thing. The effect that doing this will have is not large. If we stick with the example above of trying to hit 4 lands on turn 4 you will be 6.4% more likely to make your 4th land drop if you sideboard in an 18th land than if you had stuck with the original 17.

Are there any downsides with doing this?

While there is no disadvantage to having lands in your sideboard in limited, because your sideboard is technically infinite, there are a couple of other potential downsides with doing this.

The first and biggest issue is if you incorrectly guess whether or not you will be on the play or draw or your opponent deliberately chooses the other option after seeing you sideboard in or out a land. Most players will tell you whether or not they are choosing to play or draw while you are sideboarding. Ultimately for this to really be a risk your opponent would have to actually know what you’re doing and then be a big enough jerk that they attempt to mana screw you in this way.

The second issue is the hassle involved in having to figure out which card to interchange with the land. This however shouldn’t be a big issue and can actually be good when you are having trouble figuring out which is the last card to cut while deckbuilding as you know that the card you cut will at least be coming in when you’re on the draw.

Conclusion

While sideboarding lands in and out between games will not have a huge effect on reducing mana screw, it will have some effect for what is a very minimal cost. As such, while the difference may not be great it is still correct to harness that small advantage and increase consistency.