This is going to be one of those mathy articles again.
A note on the probabilities on this article: Obviously, the probabilities should change dynamically as we see certain cards. After drawing or looking at each card, we know more about what exactly we have in the deck, but I’m trying to keep this simple, so we use simpler, although not as accurate probabilities. I think they work well enough to make the point.
Lets suppose you have Thassa, God of the Sea in play. You have scry 1 for each of your turns, just before the draw phase. You are in need of land and will put on the bottom any and all cards that are not lands. If you have 16 lands in your 40 card deck (you got Thassa, in your pool – nice one), that means you have (on average) a 40% chance of drawing land, leaving you with a 60% chance of drawing something else.
This means that your chances of drawing a land are (the probability of the top card being a land) + (the probability of you drawing the next card instead) * (the probability of the next card being a land) or .4 + .6 * .4 = .64. That’s pretty good. Far from certain, but if you are desperately looking for lands, finding three among the next five is much better than finding two.
On the other hand, after we have the lands we need, we are not in the business of drawing more. Therefore, with the same deck, our chances of drawing gas are .6 + .4 * .6 = .84. Drawing a land only once in six cards is great when you don’t need one.
Worldclass players do their best to conserve even the smallest differences in probabilities to their advantage. After all, in a game of high variance, even the small edges will add up over time. You don’t know when you manage to eke out a win through them, but any one win can mean the difference between Gold and Platinum levels (the difference being free flights and accomodations, plus much better appearance fees for the Platinum level pro, all in all benefits of maybe around $15,000 a year, maybe more), as those who manage to get just around the number of points they need for the Platinum level (45 pro points per season)
Scry can be hard to use. This is a simplified example, but sometimes you need something other than land or nonland. Sometimes you scry, put the card on the bottom and then draw a card that would work very well with the card on the bottom. These situations can’t be avoided, but knowing your deck helps. Also, this is where math skills come in handy. This is after all something where experiences can leave impressions in our minds, which are not necessarily right, since we don’t necessarily see what would have happened had we done something different.