I've been a huge fan of using Hypergeometric calculators for deckbuilding, mostly as a tool for establishing likelihood of drawing lands and whatnot. I recently stumbled upon a Binomial Probability Calculator, which calculates the odds of success over a number of trials. I combined the two to calculate some odds of winning games in the long run. I have always found that opening hands with at least 3 lands gives me the most confidence in winning a game. If we assume a 3 land opening hand is a Winning hand then we can calculate the odds of consistently Winning in the long run. Using the Binomial Probablity calculator I ran the numbers for the likelihood of having Winning hands in 200 out of 300 games, which would just be having a record of winning 100 matches over 300 games. Now, this doesn't actually mean anything because the premise is so vague, but I thought it was an interesting exercise in looking at deckbuilding. What I found was pretty surprising. While adding 1+ land to the list had little effect on the likelihood of drawing 3+ lands each opening hand, the cumulative effect on consistently seeing those 3 lands over hundreds of games increased significantly with each land added. What I found , if we're assuming having 3+ lands in our opening hand is the benchmark for winning a game, then it takes running 27 lands in a 60 card deck to consistently see those results in the long run. What I'm wondering now is if anyone else has things they look for in opening hands that give them the most confidence in winning a game, and how we can build to maximize that likelihood.
Number of Lands in a 60 card deck Probability of 3+ lands in 7 (A Winning Hand) Probability of 200+ Winning Hands in 300 games
22 0.509838301 < 0.000001
23 0.549341464 0.0000231
24 0.587929496 0.003075374
25 0.625348194 0.077150495
26 0.661372406 0.449759624
27 0.695807315 0.876423503