SMIP Podcast # 88 - The "London" Mulligan in Vintage

This is excellent, @evouga! This was exactly the type of analysis I was hoping to see. Thank you so much for doing this!

@fsecco and @Protoaddct I think that view is a bit myopic. The 5% failure rate was always more of a talking point than a significant detriment for dredge. So the deck lost 1 in 20 games or 1 game every 7 to 10 matches (or basically once an event on average)? Yeah, the London mulligan eliminates the number of non-games, but that was the stated point of the rules change. The important aspect of the above figure is that restricting Serum Powder would have a non-negligible effect on the starting hand size of the Dredge opener. From my experience with and against Dredge, the hardest games to win post board are the games in which Dredge keeps 7-6 cards, which allows it to navigate the hate, and restricting Powder would lower the likelihood of that by it looks like 10-15% or so (for 7 cards). That honestly might be worth considering if the deck proves too strong if the new rule is implemented.

Edit: A 90% chance of keeping a 6-7 card hand with Powder means I'm not cutting Powders from my dredge list. I think they are well worth the increase from 75% (which includes one Powder from the chart).

last edited by ChubbyRain

@chubbyrain said in SMIP Podcast # 88 - The "London" Mulligan in Vintage:

Yeah, the London mulligan eliminates the number of non-games, but that was the stated point of the rules change.

I mean, it was to eliminate non-games, not increase the win percentage of some decks by a large magnitude.

Let's face it here, Dredge foregoes conventional deck building wisdom at its own risk, and it's a calculated risk that you accept when you play a deck with no mana and what is in effect an all in strategy. When WOTC says they are concerned with non-games, they are really referring to decks that play mana lands and spells and some sort of conventional ratio to them. I doubt they are really super concerned about 1 land beltcher and pitch dredge. These are the type of decks that made the no land mulligan rule non viable to begin with.

If you wanted to take a 17 land merfolk deck in legacy and cut it down to 10 lands, chances are you are building a bad deck in defiance of conventional wisdom. This rule is not being passed to accommodate people who want to spit in the eye of the science of these things, but to help the person who built a reasonable mana base to spell ratio from avoiding being crushed by variance too often.

@protoaddct

If you would address the entire post rather than one sentence, I would appreciate it. The entire point of my post was that the failure rate of Dredge currently has a very small effect on the deck's actual win rate.

@chubbyrain

It depends on your plan post sideboard. The gold line is overall higher, but the left tail that determines whether or not you have Bazaar is the most important one. Cutting Powder completely from a list potentially opens up the deck to be that much easier to transform into something that isn't Dredge post sideboard.

@vaughnbros Sure, but the vast majority of Dredge decks in the current metagame aren't running transformational sideboards. Transformational sideboards also have trouble persisting in metagames since they become less effective the more they are known and the larger share of the metagame they hold.

@chubbyrain

Currently, no, but that's because there isn't much advantage to doing so right now with Hollow One and the mulligan rule as it is. If this change is made, there is more incentive to work on that.

The Dark Depths transformation persisted for years as the best Dredge deck on MODO. I don't think its a question of your opponents response. You are always still a threat to not transform.

@vaughnbros If I remember correctly, it was a number of months. Adaptation included running more Pithing Needles, Wastelands, and leaving Swords in. Still, I would view opening up the Dredge archetype to more variants a positive. The new mulligan would certainly help the Dredge Shops deck with more consistent draws.

@chubbyrain

I think it opens up the deck quite a bit to new possibilities and opens up other deck to a potential willingness to run main deck hate, which would change the book on dredge completely.

The benefit to opponent's post board is also very noteworthy as it will much easier for them to find a hate piece, and a hate piece with a higher hand size. I'd love to see the graphic Evouga produced, but with 4,5,6,7,8,9 hate pieces from opponents mulliganing to hate (I mean I guess the 4 is kind of there and you can see someone could basically just lock in a leyline if they don't mind top decking the rest of the game).

@vaughnbros said in SMIP Podcast # 88 - The "London" Mulligan in Vintage:

(I mean I guess the 4 is kind of there and you can see someone could basically just lock in a leyline if they don't mind top decking the rest of the game).

Point is if you mull a 1 Leyline hand and they mull to a 1 Bazaar hand, they're winning that game.

@fsecco

Not necessarily. A mull to a 1 Bazaar hand against a 1 Leyline hand is pretty brutal.

@evouga said in SMIP Podcast # 88 - The "London" Mulligan in Vintage:

Here is the additional analysis you asked about in the podcast:

Probabilities of finding a Bazaar under the Vancouver system:

Bazaars\Powders 0 1 4
1 38.58% 41.45% 51.77%
4 86.50% 88.70% 94.18%

For the London system:

Bazaars\Powders 0 1 4
1 58.04% 62.14% 75.52%
4 97.18% 98.08% 99.57%

Methodology: I assumed you

  • keep any hand with at least one Bazaar
  • use Serum Powder whenever you draw it and do not have a Bazaar
  • under the London system, tuck any extra Serum Powders back in your deck before any use of Serum Powder.

Mathematica source code: https://www.dropbox.com/s/np0y0maooxln4cr/mulligan.nb?dl=0

If I am reading this table correctly, it says that the probability of finding a particular/specific restricted card in your opening hand under the London system and with 4 powders is 75.52%?

I'm assuming that Bazaar is the column, and Powder the row. That's pretty astounding.

But if I am reading that table correctly, it also means that with 0 Powder, you have a 97% chance of finding Bazaar. 1 more powder gets you to 98%. 4 get you to 99.57%. That basically eliminates a game loss a tournament from the mull to oblivion.

Separately, the point I made in the podcast is that the defining feature of Magic is variance. While lamented in some respects, by being non-deterministic, Magic actually introduces skill aspects that could otherwise not exist. For example, without variance, deck construction would look very differently.

My main point, though, is that different aspects of the game - deck construction rules, floor rules, the sideboard - are all attempts to manage variance in one direction or another.

The 4 card max/60 card min rule fixes variance at a certain rate (that is, create variance - a no minimum deck size could be entirely deterministic).

The best 2/3 match structure and the mulligan are two additional rules (generally floor rules) that try reduce variance in the other direction. That is, matches that are played as best 2 of 3 have less variance that best of one matches. It moves you closer to the statistical norm.

I am of the firm belief that you want to produce a balance of variance into a Goldilocks zone, not too much, but not too little variance either.

My overall fear is that the London rule reduces variance too much. I don't think that decks should have that kind of starting hand consistency. I wouldn't mind it as much if starting deck size were a bit larger, but I think it makes it too easy to find a single card, and also to assemble 2-card combos.

While I have this fear, I also like the fact that the rule should help non-tier one decks the most. The decks that stand to benefit the most are those that are not Xerox, PO or Shops (the three tier 1 decks).

So, for the short term, I think the London rule will be good for the metagame, in the sense of 1) increasing metagame diversity, 2) increasing metagame balance, and 3) increasing win rates for (some) lower tier decks. But the long term effects are harder to gauge, and I am less sanguine in the long run.

Anyway, that is a very brief synopsis of my remarks in the podcast, which were more elaborate and detailed.

last edited by Smmenen

@smmenen said in SMIP Podcast # 88 - The "London" Mulligan in Vintage:

If I am reading this table correctly, it says that the probability of finding a particular/specific restricted card in your opening hand under the London system and with 4 powders is 75.52%?

I'm assuming that Bazaar is the column, and Powder the row. That's pretty astounding.

This is quite exciting and scary. In addition to what you pointed out above, if you include tutors as additional copies of restricted cards, you can get access to any restricted card as a consistent gameplan. I wonder how much this opens up building around restricted cards. Of course it's already done to some degree, but this could catapult it even further.

last edited by Hrishi

@smmenen said in SMIP Podcast # 88 - The "London" Mulligan in Vintage:

My overall fear is that the London rule reduces variance too much. I don't think that decks should have that kind of starting hand consistency. I wouldn't mind it as much if starting deck size were a bit larger, but I think it makes it too easy to find a single card, and also to assemble 2-card combos.

Mechanically this is problematic for a number of reason. Larger decks in paper lead to longer shuffle cycles and are more cumbersome. I'm not saying 70 is substantially different than 60, but it depends where you set the limit.

Increasing deck size would increase variance yet again, which is counter to what they are trying to achieve. I don't think I need to explain the math to you but a 120 card deck that is literally just 2x of every thing in a 60 card deck will have wildly different hands because of how the odds change every time you draw a card.

If I draw a card from a 60 card deck with 30 lands, I have a 50% chance that my first card is a land, then if I drew a land a 49.1525% chance of another on my second draw from it. If I drew a non-land my chances of a land are now 50.8474%.

That same example, with 120 card deck with 60 lands, is 50% on the first card, 49.5798% on the second if I drew a land, and 50.4201% if I did not. The gamut between the numbers gets wider the more you go down the hyper geometric wormhole. I know the difference does not seem substantial but in the long run it does lead to a swingier range of possibilities. It also has the consequence of making tutors more powerful since they have a wider range of options, mill less viable (not really an issue but still) and cantrips better in some ways and worse in others.

That being said, if you want to increase variance without distorting proportions or increasing mechanical challenges, you could go to a 3 of a kind format. This does have the added bonus of limiting cards that cause issues when they compound upon themselves like spheres, as well as reduces the price point of the format. It still has some other consequences like making tutors more powerful by increasing the range of cards they inherently can find, but you can already build your deck that way if you so chose.

@smmenen I listened to the VSL analysis (good stuff, tough breaks in the games as well) and the initial part of the London Mulligan on reducing variance. I think it will actually benefit Shops and PO. A 58% chance of hitting a single restricted card without Powder is very high and both Shops and PO have powerful cards that they can mulligan to if their opener is not a typical Shops or PO opener. PO has potential access to Timetwister, Tinker, Ancestral, Tutors, Mentor, Balance, Wheel, Windfall (which could get much better), any 1 of which could eliminate the disadvantage of mulliganing. Shops has access to Trinisphere, Chalice, and to a lesser degree Thorn, Sphere, Strip Mine, and Workshop as powerful cards that can enable degenerate openings and win games with fewer cards. Dredge and Survival both benefit as Bazaar decks, though for Survival finding Bazaar is neither necessary or sufficient to win and so the rule's change won't help as much. The decks that get hit the most are the control decks that generally don't operate well on few cards. The only card that really saves them on mulligans is Ancestral. BUG Fish and Blue Aggro-Control are both going to be impacted by the new rules change.

@hrishi

Considering you have to mulligan all the way to a single card to get that probability, I'd say it doesn't open up much at all. Maybe Tolarian decks are slightly more viable, but its not like you can cut your cards that search for lands.

@chubbyrain said in SMIP Podcast # 88 - The "London" Mulligan in Vintage:

@smmenen I listened to the VSL analysis (good stuff, tough breaks in the games as well) and the initial part of the London Mulligan on reducing variance. I think it will actually benefit Shops and PO. A 58% chance of hitting a single restricted card without Powder is very high and both Shops and PO have powerful cards that they can mulligan to if their opener is not a typical Shops or PO opener. PO has potential access to Timetwister, Tinker, Ancestral, Tutors, Mentor, Balance, Wheel, Windfall (which could get much better), any 1 of which could eliminate the disadvantage of mulliganing. Shops has access to Trinisphere, Chalice, and to a lesser degree Thorn, Sphere, Strip Mine, and Workshop as powerful cards that can enable degenerate openings and win games with fewer cards. Dredge and Survival both benefit as Bazaar decks, though for Survival finding Bazaar is neither necessary or sufficient to win and so the rule's change won't help as much. The decks that get hit the most are the control decks that generally don't operate well on few cards. The only card that really saves them on mulligans is Ancestral. BUG Fish and Blue Aggro-Control are both going to be impacted by the new rules change.

I think you are missing the forest for the trees in the middle part of your analysis.

While it's true that Shops has a (growing) number of restricted lock parts, a Shops deck is unlikely to mulligan more aggressively (relative to other strategies) to find them, simply because modern Shops decks rely on cumulative pressure (both lock parts and damage) more than a single tactic to hold an opponent at bay, like it could do in the days of unrestricted Trinisphere.

Similarly, PO is not going to want to mulligan any more aggressively (relative to other strategies) to find the titular card. PO requires a density of mana rocks and other perms to make PO payoff. Thus, it needs a larger starting hand in general.

Your math is correct, but you are applying it in a way that does not properly account for the context in which the mulligan occurs.

What really matters is the relative rate of mulliganing in the assessment of 'who benefits?'. It's possible that all decks will be more likely to mulligan to 6 as a result of the rule change. But I think both PO and Shops (as well as Xerox) will have a lower mulligan rate increase relative to the other strategies described in the podcast.

So, if PO and Shops were to increase their mulligan rate by, say, 5% under the London rule (such as from 1 out of every 5 games to 1 out of every 4 games), then Survival and Eldrazi's will be even greater (say, 8%, from 1 out of every 4 games to 1 out of every 3), and that's accounting for any imbalance in starting levels of mulligan rates.

last edited by Smmenen

@smmenen said in SMIP Podcast # 88 - The "London" Mulligan in Vintage:

I think you are missing the forest for the trees in the middle part of your analysis.

While it's true that Shops has a (growing) number of restricted lock parts, a Shops deck is unlikely to mulligan more aggressively (relative to other strategies) to find them, simply because modern Shops decks rely on cumulative pressure (both lock parts and damage) more than a single tactic to hold an opponent at bay, like it could do in the days of unrestricted Trinisphere.

Similarly, PO is not going to want to mulligan any more aggressively (relative to other strategies) to find the titular card. PO requires a density of mana rocks and other perms to make PO payoff. Thus, it needs a larger starting hand in general.

The point of my post is that this dynamic potentially changes with the rule change. These decks can now potentially function as hybrids where "mulligan to restricted or broken cards (X,Y,Z)" is a much more viable plan B. You no longer have to keep a medium 6-7 on PO because you were a critical mass deck as now you can reasonably hope to mise a Timetwister, Tinker, Ancestral, or whatever. It's less true for Shops but I actually think that PO is a huge beneficiary of the new rule.

last edited by ChubbyRain

Has the new mulligan rule actually been implemented? I thought it was just an experiment?

@desolutionist said in SMIP Podcast # 88 - The "London" Mulligan in Vintage:

Has the new mulligan rule actually been implemented? I thought it was just an experiment?

It hasn't even been tested yet. Mythic Championship London is only at the end of April.

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