What It Is, What It Ain't
Here is a short definition for reference, sourced from Wikipedia:
The gambler's fallacy, also known as the Monte Carlo fallacy or the fallacy of the maturity of chances, is the mistaken belief that if something happens more frequently than normal during some period, then it will happen less frequently in the future (presumably as a means of balancing nature).
I will rephrase it to focus more precisely on the part that actually trips people. Gambler's Fallacy, is the mistake of believing that the probabilities of two completely separate events are, in fact, linked. Although, it is not strictly speaking correct to do so, I also refer to making the opposite error using the same moniker. That is to say, to me at least, making a mistake about whether or not the probabilities of two events are linked is the essence of the Gambler's Fallacy. Let's look at an example both inside and outside of the game of Magic.
- You are playing Roulette. Standard wheel, no cheating or trickeration, or what have you. The last three spins have resulted in a Red, so you put your money on Black because you think that the 'Red streak' can't last forever. This is incorrect logic. The results of previous Roulette spins are not related in any scientifically valid way to the results of this spin. For all intents and purposes, that ball has an equal chance to land in any slot and that is true on every spin.
- You are playing some kitchen table Commander. You have a fetch land in play that you would like to crack, but you also NEED to hit a land in your next couple draw steps in order to win. You should not crack your fetch land because it will then thin a land out of your deck, reducing the likelihood of drawing a land next turn by 1/the number of cards left in your library. In this case these two events ARE linked because your choice in the first affects the probability of a favorable outcome in the second event.
And Now For Something Completely Different
Those examples were simple and left out a critical assumption be must make based on the context in which we play the game of Magic. That assumption being that the physical laws of our universe MUST apply and, in fact, do. Let's look at another example and I will stop to illustrate where I think people really commit to incorrect thought patterns.
You're playing a game of Magic. You have drawn three lands in a row, but you would really like to draw some action. What are the chances you're going to draw that crucial spell? Well, you are a savvy mathmagician so you know that drawing all those lands is increasing your chances of drawing action in the future because now there are fewer lands in your deck going forward. You might even know the exact proportional composition of your deck. Say you have 32 lands left in 70 cards so you know you have a roughly 50-50 shot of drawing a spell, with a slight edge favoring spell over land. Now aren't you smart? You figured out you have a 55% chance of drawing a spell, except you are wrong. Don't think so? Let's switch gears and talk about physics.
Once your deck is shuffled it just sits on the table. It is not in a random order, it is in a specific one. In the physical universe we occupy the deck is never going to be truly random. Moreover, according to the rules of the game, you draw the card from the top of your deck NOT a random card. The rules say that each time you shuffle your deck it must be sufficiently randomized such that no player has any knowledge about the specific position of any single card within the deck.
Let's assume for the moment that you and your opponent are master shufflers and actually get a truly random shuffle every time. Then all of the possible orderings of the cards in the deck are equally likely, but only one of them actually gets chosen. Once you stop shuffling there is only one order in which you will draw those cards. As a result of this you can pull fifty lands in a row off the top, IT STILL DOESN'T CHANGE WHAT THE NEXT CARD IS. You can predict the probability, you can model it with numbers, you can cross your fingers and hope, but none of that changes the facts. Fallacy or not, fact is, no matter how you think about it the truth is immutable. The point is that you shouldn't let those pieces of false evidence affect your decisions in the game.
The only thing you can do to change this is to shuffle your deck more often. You can't do it all willy-nilly because that is against the rules, but you can consciously include more shuffle effects in your decks which will make your draws more random...in a good way. See, when you use those probability models that assume your draws are random, your expectations will more closely match reality. You will draw better because shuffling frequently prevents you from having to play 10 turns with the same chunk of bad cards stuck on top. It refreshes the order in which your cards are physically stacked. You will also, and this is the important part, draw more closely to your expected results. If you are crunching the numbers and doing the predictions, then you will be playing the odds in your favor. Maximizing your shuffles per game maximizes the extent to which you can count on your draws truly being random. You will get a more normal distribution, a more even mix of your cards, which is what you generally want...if your deck is good at least.
Try to think about the gambler's fallacy when you play. Do you catch yourself making mistakes like this? How often do unrealistic expectations about your draws cause you to lose games or, at the very least, be disappointed?
-GG
