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?