to start, I want to say that I'm using numbers from Frank Karsten and extrapolating from there, in addition to basic combinatorial work that anyone can do themself in excel.

The london mulligan has people discussing playing dredge without 4 serum powder, and even testing it during the mtgo test period and in paper events with the new rules. In my opinion, playing dredge without serum powder is a mistake. the following is an anecdote and then some numbers.

Anecdote: I played in TSI this weekend with dredge under london rules. List was similar to @ChubbyRain and others recent lists, with hogaak, force of vigor, and field/salvage as only nonbazaar lands main, playing ghast and ichorid over narcomoeba. I went 2-4 in games where I mulled to 4 or less and 8-0 in games where I kept 5 or more cards. I sleeved up a list with powders over the 4 worst cards for an eternal weekend trial the next day, but it ended up not firing.

Dredge probably has a better win rate when it keeps 2-4 card hands than any other deck in any format with such hands, but given how often we mull it leads to a significant portion of our game losses. But first, the math if all we care about is finding bazaar:
Vancouver Mulligan, no powder has an 86.5% chance of finding a bazaar if you're willing to mulligan to one card, discounting the scry. miss every 7 games.
Vancouver Mulligan, with powders has a 94.17% chance, a miss every 17 games, again discounting scry.
London Mulligan, no powders, has a 97.2% chance to find a bazaar, a miss every 36 games.
London Mulligan, with powders, has a 99.3% chance to find a bazaar, a miss every 143 games.
(As a refresher, the powder-London interaction is that you put back the number of cards as if you've kept the hand, exile the hand to powder, draw that many, then have the option to mulligan to another 7 if you don't like what you drew and keep going.)

of course, bazaar isn't actually everything, and mulling so low that you don't have the ability to keep counterspells, hollow one, unmask, cards to pitch to counterspells/unmask/FoV, or lands to trigger ghast in hand after you activate bazaar, or having cards to discard as you dig for these things. This is my primary point in favor of the continued use of serum powder- not the 2% increase in finding bazaar, which is significant, but the average hand size at which you find bazaar.

Playing serum powder increases the average hand size you keep by over half a card. The proportion of hands kept that are 5 or more cards goes up over 11%, from 78.2% to 89.6%.
By the mulligan to what will if kept be a hand of three Powder-London has a higher chance of finding bazaar than pure-London has if willing to go to one. London has to be willing to mulligan to 2 to have equivalent odds to Vancouver-Powder, while London-Powder only has to be mulliganing to 4 to have chances better than what dredge has had under the old rules. We are of course going all the way down, but I think these are useful comparisons.

This glosses over a few bits, such as assuming that what you powder from your deck is a cross-section of its components and thus doesn't change its strength, but this isn't the case. Powder exiling non-bazaar cards leads to a higher proportion of kept hands with double bazaar, for example, and there's some other changes once you've mulliganed and have some choice over what you're exiling(this probably also changes the powder math slightly as you can put excess powders back before powdering the hand). This is all hard to sim, as is figuring out exactly how much higher win rate you get with double bazaar over single and stuff like that, so maybe another time.

to sum up main points, powder is still worth playing in dredge, partially for the raw percentage chance of hitting bazaar but moreso for the larger portion of games in which it allows the player to keep a hand with enough cards to do something.

does anyone have a large dataset of dredge starting hand size vs game win rate?

In the 90 games that I was recording hand size, I didn't win any with a hand under 5, while I had a well over 60% win % in games with 5 or more. A larger sample would be nice, but I think that given the large disparity that I saw in the small sample, this would probably mostly hold up. 11% more hands with 5 or more cards is a dramatic difference that makes Serum Powder worth it. It also helps that there are simply no other options.

My key points of experimentation post London are

1. powder vs no powder
2. mana vs manaless (Pitch vs nonpitch)
3. combo vs noncombo

I hypothesize that mana less and combo are better able to cut powder than pitch variants as hand size is more important to pitch. The utility of pitch is dependent on the exact metagame post London and the concept of sacred cows outside of bazaar is pretty patently false given recent graveyard centric printings, so it should be an exciting time for Dredge innovators.

@chubbyrain when you say combo, do you just mean dread return? because if we mean stuff like fatestitcher lists, hand size is important for at least keeping a mana source in hand(so ideally 4 cards to be able to bazaar and then bazaar on upkeep and still have rainbow land in hand, or 3 cards to bazaar and have the sapphire/lotus/petal remain.

Transformative sideboards are the versions that wouldn't want to run Powder. I'm not sure if there is a transform that actually works in the current meta though.

@blindtherapy Perhaps Aggro is the better term. There was a 2nd place list in the trial period that cut powders to run street wraiths and probes. I think there was still a pitch component though. And fatestitcher just needs a single mana source, right? That’s less than Force + Card. If you gain half a card on average, then depending on the deck, you might not need that half a card if you eliminate the pitch component. That’s my rationale.

it isn't exactly like we are adding half a card to every hand.

Powder lets you keep 7 54% of the time instead of 39.9%. The percent of time you keep 6 is about the same, as going to 6 is more likely to result in keeping 6 but we are going to 6 less of the time; the chances of keeping 6 once you have mulliganed once are 53%. This means that that 14% increase in times you keep 7 is coming from 3% hands of 5, down from 14 to 11%; 9% hands of 4 or less, down from 19% from 10%; and 2% from games where you previously would have mulliganed. It's not that half of your 2 card keeps become 3 card keeps, half of your 3s become 4s, etc; It's that half of the times that you kept 4 or less or mulliganed out you instead keep 7. These scenarios were previously 21.8% of games and are now 10.4%.

Can someone do the math on effective hand size treating Powder as a blank?

If I keep half a card more on average but I also keep a Powder half the time it starts to look like not so much of a benefit

There's a reason normal decks like Workshops don't usually run Serum Powder even though they would also like to keep a larger hand.

Edit: And of course you have to include the odds of drawing Powder in the first few draws.

@blindtherapy yes, but the math is more complicated as you can assemble some pretty unbeatable 3-4 card hands out of the London mulligan. The quality of your powder hands is not improved as you just draw x cards with no selection (though if this is a subsequent powder, then you do have more control over what you exiled). I don’t know how to weigh this, but in my experience control decks still want to preserve the quantity of cards in their hand while aggro and combo decks can mulligan more often into explosive draws that can win with less cards. Dredge variants have similar philosophical differences in my experience and can exploit Powder and London in different ways. The whole point of cutting narcomoeba and other core components was to demonstrate that the evolving metagame and recent printings make such alterations possible. “Oh no, you are going to be weak against fast combo...” Oh, crap, that’s really going to hurt my win rate against...the literal 0 PO and ritual decks in the top 32 of the challenge.

The point is the Dredge archetype has a ton more depth than its ever had before and even the rules are facilitating more freedom in deck design. I plan on exploring it more in a couple of weeks.

@ajfirecracker It isn't actually a blank, as discarding to bazaar and letting you keep force/hollow one/etc is still very relevant, but this is worth adressing.
In hands below 7 that you keep with bazaar powder is pretty much always going to be one of the cards you bottom, but even here we can say that had it been something else we would have had the option to keep it and bottom something else. Hard to quantify this.
You're not going to have a powder half the time; the chance of it being in a given keepable 7(with 1 bazaar) is 35.7%; the chances of having 2 powders in such a hand is 4.8%(45.1/8.5 with bazaar activation on the play, 49.4/10.6 on the draw). mulligans mean that you get to put powders back if you don't need them, so it's not a dead card in hand. You will on average about half a powder in a hand+ top 2/3, even when keeping 7, so just comparing to the increase in average hand size(.59) to the number of 'dead' cards(~.5 when you keep 7 and much less at all other hand sizes) it seems to be worth it.

@chubbyrain not every 4 you keep in a powder list is a 4 you powdered into; by my quick math about 20% are, the rest being hands you chose which 3 to put away. you are always free to throw the hand you powdered into back; it is supplemental to the mulligan. Exiling random cards from your deck in 7s and then somewhat pruned cards in 6s and lower has neutral and minor positive effects on deck quality respectively, if not in the hand the powder draws but in the hand you then mulligan into after if the powder hand doesn't suffice.

While I understand the discussion as to who can exploit powder better, it seems to me like talking about which blue deck best takes advantage of ancestral recall. The value of the card may vary depending on how much a deck is attempting to assemble, say, bazaar+blue card vs bazaar alone, but it is definitely worth it in either case. I admittedly have never played the counterspell lists, so I might be missing something here, but the math seems pretty convincing. Might brush up on python and dive into the simulations.

@blindtherapy I'm assuming you keep every hand with Bazaar in it, which might not continue to be the case. I agree that exiling non-bazaars improves the odds of finding bazaars but is a 6 card hand from Powder with a Bazaar better than 5 of 7 without another mulligan? 4 of 7? 3 of 7? What about at 5 cards from Powder and having to keep Powders that you might find? I don't have a certain answer for that and I'm not sure a simulation would answer qualitative measures like this.

For the record, I agree with you. My take on seeing initial data from @evouga was that dredge would value the greater starting hand size afforded by Powder. The 3 week London trial left a lot of unresolved questions about the format, including this about Powder. There was only one deck that really sought to omit Powder in a more aggressive shell during Week 2 and finished second in the challenge. This isn't anywhere close to a significant enough sample size to draw a conclusion from.

That's an interesting point - probably there's no way to get around really doing the math and comparing the distribution of number of useful cards in the final hands.

@ChubbyRain After watching a few VoDs of the deck, thinking about it, and testing a bit on MTGO with a similar list I have a few questions and comments.

First of all my questions:

1. How did you come about making the deckbuilding decisions you did? What prompted you? What was your reasoning behind some of the decision?
2. What changes did you make during testing? What cards were you really impressed with or were unimpressed with?
3. What are the strengths and weaknesses of this version of Dredge in your opinion?

Now, through my testing, thinking and watching I have found Dakmor Salvage, Creeping Chill, Force of Vigor, Vengeful Pharaoh to be insanely impressive. While I have not had a chance to test Hogaak and Bloodghast I think the Hogaak seems very powerful and Bloodghast seems mediocre.

I think Dakmor Salvage is the card I have been most impressed with and it single handedly won me a game against a G1 T1 Priest when I had no other outs and I came very close to winning games 2/3 because of it. Dakmor allows you to consistently and reliably get to three mana with the help of Riftstone Portal, allowing you to hardcast Stinkweed Imp and Shambling Shell. Hardcasting these cards with a priest out can win you the game since it ignores their hate completely and can still generate insane value from saccing Shell to put a +1 on Imp and generate a few zombies. Combined with Creeping Chill just one Imp with a single +1 counter can be a 3 turn clock not counting the zombies you may have just produced. I have even been able to hardcast Pharaoh because of the amount of lands I had out.

Vengeful Pharaoh has also really impressed because of how it can allow you to really slow down and control the game, allowing you to find what you need while making it really hard for them to put a clock on you.

Creeping Chill is nice because it dodges a lot of the common hate and allows you to win while committing fewer resources. It also makes the hardcast beatdown much more viable. The same can be said for Hogaak except he is just so much better it seems like.

Interestingly/strangely I have lost quite a few post board games to decking and I think adding an anti-decking card like Progenitus or Emrakul could really help combat GY wipes and help you prevent from decking, allowing you to not only reuse certain cards but also give you enough cards to continue the hardcast beatdown plan.

Let me know of your thoughts or comments!

@rat3de said in Dredge, The London Mulligan, and the continued use of Serum Powder:

Interestingly/strangely I have lost quite a few post board games to decking and I think adding an anti-decking card like Progenitus or Emrakul could really help combat GY wipes and help you prevent from decking, allowing you to not only reuse certain cards but also give you enough cards to continue the hardcast beatdown plan.

Perhaps Gaea's Blessing is a better option since you can cast it if you need; e.g. when it got stuck in your hand and you don't mind shuffling Narcomoeba's back into the library.

@Rat3dE

Hardcasting creatures to beat other decks off of salvage is definitely a line that exists, but it isn't the main one. Dakmor Salvage exists to trigger bloodghast most of the time, and the card is amazing, like a narcomoeba you can use turn after turn. Hardcasting pharoah sounds harder than hardcasting Troll, given the color requirments, and troll is bigger. the hardcast plan has always existed(I have cast ichorid, i have cast dread return on ichorid with spell pierce mana up, I have cast ashen rider) but it shouldn't be high on the strategy list. If one is seriously concerned with maindeck priest, then play crippling fatigue, or a loam/pit package. Hardcasting dredgers seems most relevant to then casting Hogaak off them.

I'm interested to hear that pharoah has been good for you; what has it been good against?

Chill dodges priest and cage, falling victim to everything else. Dredge doesn't generally need much help beating priest and cage in my opinion, as the yard is still there once you remove the hate.

progenitus just shuffles itself, so no reuse there. Emrakul/Blessing/Other shuffle everything as soon as they hit the bin; they don't really counteract, for example, crypt effects, unless you are discarding emrakul in response to the crypt. Shuffling your yard into your deck is pretty close to crypting yourself in tempo terms, if not in total resources available over the game. Losing games to decking happens, but it's possible you're bazaaring too aggressively when you could afford to not do so. Usually you should only be losing to decking in games where you fight through multiple crypts and don't have the time to slow roll through them, throwing 15ish cards into each crypt.

This is all fairly off topic from the serum powder discussion i think, but those are my thoughts. Matt has played Chill more than I have, I'm curious as to his take.

@BlindTherapy My point with winning G1 against Priest was more that it was possible whereas with most lists it would not be.

bloodghast most of the time, and the card is amazing, like a narcomoeba you can use turn after turn.

When you put it that way it actually makes it sound much better than I initially thought.

Hardcasting pharoah sounds harder than hardcasting Troll, given the color requirments, and troll is bigger.

It was because I was low on cards in library and I happened to draw a Pharaoh, also black is easier to get than green because of Dakmore.

I'm interested to hear that pharoah has been good for you; what has it been good against?

Against things like Eldrazi it can really slow them down as it essential comes down to a topdeck war of can they draw 20 power worth of castable creatures before you find your anti-hate.

Chill dodges priest and cage, falling victim to everything else. Dredge doesn't generally need much help beating priest and cage in my opinion, as the yard is still there once you remove the hate.

While in general I would agree I think it is a bit more complex than that as the games where they have the resources to maintain their GY nearly continuously it allows you to take advantage of weak points or mistakes much more effectively and efficiently since they are already at a lower life. In the Hogaak version I would imagine this is even more amplified by the inclusion of HO, Bloodghast and Hogaak as these all become much better at crossing the finish life as a one to four turn clock then a three to ten turn clock.

@rat3de said in Dredge, The London Mulligan, and the continued use of Serum Powder:

black is easier to get than green because of Dakmore.

my point was that it is generally easier to get 5 lands(including bazaar) in play with a portal in the bin than to get 5 lands, 3 of which make colored(black) mana. 5 mana is usually portal territory, so troll can be case off stuff like 2 bazaar 1 field 2 dakmor while pharoah can't. but yeah, casting pharoah isnt plan A for sure, though I think i've done it off lotus in the past.

can they draw 20 power worth of castable creatures before you find your anti-hate.

was the eldrazi player not aware of how pharoah works, or did you have multiple pharoahs? it can only hit 1 creature a combat, so they only really need to get to 12ish and swing twice.

It's worth noting that Pharoah can kill a creature that was blocked, so if their guys are different sizes and you throw a Narcomoeba or a zombie token in front of the larger one you can still kill it

@ajfirecracker yes, as well as the first strike trick, where you use the trigger from a first striker hitting you to destroy the other creature before it deals damage