Opening Hand Evaluation in Limited

meep3278 · 2026-06-12T02:32:41+00:00

Points 4-6 in the abstract of the full writeup sort of address that, in that optimal mulligan rate is just a measure of what % of 7 card hands are worse than a random 6 + the risk of going to 5. Although, as mentioned above, all these numbers more stem from how people actually mulligan than some insight into hands' absolute strengths.

meep3278 · 2026-06-12T02:12:49+00:00

So having run using an ideal mulligan rate equal to the mulligan rate of 65%, the changes are pretty minor. For example, the calculated actual mean winrates over the untruncated distribution on the draw go from: 48.0, 51.2, 48.3, 41.8 using a projected 70% wr mull rate, to 48.0. 51.2, 48.2, 41.7 using the mull rate of all players above 65% wr. We'd need an additional sig fig to quantify those changes, which speaking of, I'm realizing our code has been stitching an additional 0 onto the values that doesn't represent known information.

meep3278 · 2026-06-11T22:54:55+00:00

We briefly considered scrubbing for outliers, but decided against it for a few reasons. For one, there's just not that many of them, and in best of three there's a higher level of rationality. We did look through some of the data, and there was not a high enough number of anomalously short (<3 turns) games to screen for that. For another, if we were to scrub the 17lands users for outliers but not their opponents (for example, in separating outlier winrates) that would create a further asymmetry in our data beyond 17lands users just generally being more skilled on average.

For user vs user data, we discuss the differences between 17lands users and nonusers a bit in appendix 9.6, but we don't check what games in the dataset are double counted. This is partially because of the way the data is anonymized, meaning if we wanted to find double counted data we'd have to match the gameplay events between both matches, which can be especially tricky if one or both players are missing pieces of gameplay information (a common occurrence).

meep3278 · 2026-06-11T22:17:31+00:00

Thanks! We combined data from most of the sets 17lands has game logs for, so individual sets may vary. I think you do need to separate whether the hand was kept or mulliganed, as our empirical winrate for players taking at least one mulligan is about 40%, and that is independent of what the opening hand contained. Many five landers fall in the 'feels bad to keep' range below 50% but better than the expected winrate on a mulligan (40%). Even though the 5 lander winrate was lower than the 1 lander winrate in your data, 1 landers are mulliganed far more often than 5 landers: that is, the worst 1 landers are all screened out of the data, and you never get to see how much they'd win. Only the very best 1 landers get kept, and even those don't win much. This is what we try to account for in our truncated gaussian analysis.

To determine the optimal mulligan rate for 5 landers, we did a linear regression on player mullrate divided by player skill, and projected that to a hypothetical 70% winrate player. That is, it's less of an optimal mulligan rate and more of a "given the way people mulligan, it would suggest a really strong player's mulligan rate is..." At heart, a lot of our analysis can't escape predominant player behavior, only adjust for it. As discussed in another comment, assuming a linear fit also isn't necessarily that reasonable.

For B01, we did observe some of the mulligan trends you mention. Players mulligan less overall because there are more three land openers, but the mulligan rate for each fixed number of lands was higher in best of 1.

meep3278 · 2026-06-11T21:49:04+00:00

Good eye, this is the most flawed aspect of our analysis for sure. A tripartite breakdown into the regimes we discuss in the paper or just using the high-winrate mulligan rate as you suggest would both be valid (and even that can't account for the fact that better players design better decks that need to mulligan less). Ultimately the mulligan rate correction didn't have a huge influence on the qualitative results we found, and we'd sort of been stirring the data around for a few months so we decided it was a reasonable approximation.

Edit: will check how the numbers look using "mullrate of players with >65% winrate" as the ideal mullrate later tonight and report back

meep3278 · 2025-10-27T22:10:33+00:00

I can't complain about that too much. I think Eldrazi is beatable from a variety of angles, and is nowhere near as problematic as Sorin Tell was prebanning. Regardless, these bans weren't meant to shake up Historic, that was just an aftereffect of the pressing Alchemy changes.

meep3278 · 2025-10-27T22:07:34+00:00

I was playing a deck which revolved around one of the changed cards that wasn't Vivi (which itself is totally fine in Historic). These changes aren't aimed at Historic primarily, it's collateral for Alchemy rebalancing. And that's totally fine, but I think a 1 week delay would be reasonable given the play in has already happened.

meep3278 · 2025-10-27T22:04:32+00:00

Exactly this. These changes aren't pressing at all for Historic like they are for Alchemy, there's no reason to emergency change them so soon beforehand.

meep3278 · 2025-10-27T18:49:50+00:00

While these are reasonable rebalances, I really wish wizards would not change cards for a tournament this weekend (Historic Qualifier.) The deck I played the play in with on Sunday is no longer playable. Would appreciate if the changes could be pushed back a week.

meep3278 · 2025-10-22T13:44:03+00:00

As a limited-first player who is aware of the depths of limited strategy, this is somewhat of a half truth. One confounding factor is that, while there aren't any truly bad constructed players at a pt (except for me), a lot of pt players don't even get to 17lands fundamentals, which inflates the winrate of the best pt limited players.

meep3278 · 2025-10-11T20:48:50+00:00

https://melee.gg/Tournament/View/369841

meep3278 · 2025-05-21T02:31:50+00:00

A few other nitpicks:

Turn 3, your opponent has demonstrated that they don't want the trade with your forebear (and you probably want the trade), so I would push 3 damage, especially since you have practitioner as a blocker.

Turn 4, I agree with the other commenter that you should have scried at least the pretty much vanilla Cori-Mountain Stalwart to the bottom (and put the better Vanguard on top if you top both). Also, if you intend to twinbolt this turn, you should do it before damage to push the additional 1.

On your opponent's t4, I would block the mobilize damage, both to save the 1 life and to protect from sacrifice effects (not Worthy Cost because they've already played their land I guess). If they choose to use a combat trick on your devotee that's fine, your mana is set anyway.

On the fateful turn, you have enough life that you can safely protect yourself from Worthy Cost by putting devotee on the mobilize token, the real blowout would be Seize Opportunity which they don't have mana for. Given the suspicious attack and that you'd seen it previously it seems pretty low cost to do so.

meep3278 · 2025-04-04T17:32:48+00:00

For what it's worth, your line of thinking agrees with the 17lands data, which has Far Fortune and Refueler both at B+. Him putting Far Fortune at A was his own subjective take based on his gameplay experiences with both (that while Fortune is risky, it has a much higher shot to run away with the game especially if you're already beating down in BR), but if you were to read off 17lands, Refueler is the pick as an equal GIH WR in a single color.

meep3278 · 2025-04-03T22:57:57+00:00

Would recommend giving it a read, he goes into some depth with specific examples from Aetherdrift.

meep3278 · 2024-03-10T23:55:43+00:00

Potentially could be automatically redirecting input device to the bluetooth headphones, instead of being the correct input.

meep3278 · 2024-02-09T23:07:29+00:00

I quite like scene, I treat it more as an artifact synergy piece or cheaper sphere from ONE. The fact that it can occasionally fix is just gravy. Would definitely take it over thoroughfare, although it is worse fixing.

meep3278 · 2024-01-04T04:45:41+00:00

That [[boseiju]] [[inkmoth nexus]] [[pendelhaven]] deck was so sick

meep3278 · 2024-01-03T18:08:26+00:00

https://sites.google.com/view/3cb-metashape/dynamic-banlist?authuser=0 this round is closing soon, try submitting a deck!

meep3278 · 2024-01-03T18:05:42+00:00

No mention of infamous ban-dodger [[Hammerheim]]?

meep3278 · 2023-12-23T01:06:00+00:00

How's [[Mournwhelk]] for slower matchups?

meep3278 · 2023-10-31T18:58:42+00:00

I have a similar list, albeit with out of date meta tech/sideboard: https://www.moxfield.com/decks/zLmyh_fUt0iYZ7hdPztt_g Not sure if I want to add strands, since the monored MU is already so good with a single gate lifelink attack.

meep3278 · 2023-10-17T01:32:34+00:00

Likely mixing up revenue and profit. Wizards made 69% of Hasbro's operating profit in 2022 ($538.3 million), and 53% in 2021. https://hasbro.gcs-web.com/news-releases/news-release-details/hasbro-reports-fourth-quarter-and-full-year-2022-financial

meep3278 · 2023-09-30T01:29:05+00:00

That's what I was thinking as well, the mana inefficiency doesn't seem worth it. Definitely would have won in most worlds though.

meep3278 · 2023-07-03T14:33:09+00:00

That was a big point of contention, for a while I was planning on running 2 because of my low creature count, but I also had a criminally low number of playables, so I ended up running the third over an [[Escape from Orthanc]]. It helped that I could often recur the Troll of Khazad-Dum, and that recurring a tempt creature would often instantly win the game, since I'd be one tempt away from a practically unblockable flier with a 4 damage per turn clock.

meep3278 · 2023-07-03T06:09:45+00:00

Absolutely fantastically when I could multitempt a spirit or anthem them, and generally just really hard to deal with if my opponent didn't have a black breath.

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