Card Pack Expected Value Calculator
Calculate the expected value (EV) of opening a card pack. Enter card rarities, pull rates, and market values to find if a pack is worth buying.
Calculate your new Elo or MMR rating after a match. Enter current rating, opponent rating, and K-factor for precise post-match rating.
The Elo rating system is the foundation of competitive matchmaking. Originally designed for chess, it's now used in countless games โ from League of Legends and Dota 2 to Overwatch and beyond. This calculator computes your new rating after a match.
The system works by comparing your actual performance against an expected performance derived from rating differences. If you beat a higher-rated opponent, you gain more points. If you lose to a lower-rated opponent, you lose more points.
The K-factor controls how volatile ratings are. Higher K values mean faster rating changes. New players typically have high K-factors (40) while established players use lower values (16-32).
Use the estimate as a planning baseline and adjust it once you have real session data from the game you are playing.
Understanding how Elo works helps you predict rating changes, understand matchmaking, and set realistic rank goals. Knowing that beating a higher-rated opponent gives bonus points while losing to a lower-rated one costs extra keeps your expectations grounded.
Expected score: E = 1 / (1 + 10^((opponent_rating โ your_rating) / 400))
New rating: R' = R + K ร (actual โ expected)
Where actual = 1 (win), 0.5 (draw), 0 (loss)Result: New rating: 1224 (+24)
Expected score: 1/(1+10^(200/400)) = 0.24. You won (actual = 1), so change = 32 ร (1 โ 0.24) = +24.3, rounded to +24. Beating a higher-rated opponent gives a large gain.
Arpad Elo, a Hungarian-American physics professor, created the Elo system for the United States Chess Federation in the 1960s. Its elegance and mathematical soundness led to worldwide adoption in chess and eventually in video game matchmaking.
Most modern games don't use pure Elo. Systems like Glicko-2 add rating deviation (confidence) and volatility parameters. Microsoft's TrueSkill handles team games with unknown teammate ratings. Despite modifications, the core expected-score formula remains.
A stable Elo rating doesn't mean you've stopped improving. It means you're improving at the same rate as your opponents. True rating growth requires deliberate practice that outpaces the general player improvement curve.
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K-factor controls rating volatility. Higher K means bigger swings per game. New players use higher K (32-40) for faster placement. Experienced players use lower K (16-24) for more stable ratings.
A 200-point Elo gap means the higher-rated player is expected to score 0.76 (win 76% of the time in a win/loss game). A 400-point gap corresponds to about 91% expected win rate.
Many team games use Elo-derived systems (like Glicko or TrueSkill), but they add complexity for team performance. The core concept is the same: rating adjusts based on expected vs actual performance.
In pure Elo, ratings never go up after a loss. Some game-specific modifications add performance-based adjustments that can occasionally cause this, but it's not part of standard Elo.
With a K-factor of 32, it typically takes 30-50 games to converge near your true skill level from a fresh start. With K=16, it takes roughly twice as many games.
Elo farming (intentionally losing to lower your rating then beating weaker opponents) is possible but detectable. Most competitive platforms have anti-manipulation measures including decay, placement matches, and behavior detection.
Calculate the expected value (EV) of opening a card pack. Enter card rarities, pull rates, and market values to find if a pack is worth buying.
Predict your future chess Elo rating based on games played and improvement rate. Project your rating over weeks and months of play.
Estimate the total cost to build a card game deck. Enter card names, quantities, and prices to calculate your full deck budget.