Fair enough, I was thinking along the lines of the previous standard decks that stole the opponent's 60 lands for landfall triggers. Waste has just been the default non-card. there have even been ideas for vintage decks where the only way to activate an Eldrazi is with the opponent's wastes.
Fair enough, I was thinking along the lines of the previous standard decks that stole the opponent's 60 lands for landfall triggers. Waste has just been the default non-card. there have even been ideas for vintage decks where the only way to activate an Eldrazi is with the opponent's wastes.
I was trying to aim for the cautious end with the rules in the original post, but alternatives are certainly also interesting to explore.
Speaking of alternatives, a recent Reddit post has gotten me thinking about another possible challenge. This one isn't really focusing on cards as a limit, but the restriction is big enough that this thread feels to me like it might be a better place than the 60-card one.
The original challenge was finding the best way to kill the opponent with a Legacy-legal deck that isn't able to cast spells. The original post suggested a turn 3 kill with Dark Depths, and it looks like a dredge strategy can win on turn 1.
So, to build off that, how much damage could we deal? (Perhaps switching from the Legacy card pool to Vintage, but it might not even matter.) One thing that could be helpful is Priest of Fell Rites, since it can get back arbitrary creatures without casting a spell. Angel of Glory's Rise can turn one reanimation into many, and reanimating creatures can turn into reanimating artifacts and enchantments.
I think I can now exceed Graham's Number in 8 cards!
The main improvement is that Renegade Doppelganger or Unstable Shapeshifter can serve the purpose of Doubling Season, without needing an extra card (which was Astral Dragon). The downside of this is lower initial growth rates; I brought the growth rate back up a bit with precise card selection.
Start with Black Lotus and Show and Tell to put Bolas's Citadel onto the battlefield.
Cast Boulderbranch Golem from library. (-7, +6; 19 life)
Cast Saw in Half from library, targeting Boulderbranch Golem. (-3, +6; 22 life)
Cast Inverter of Truth from library; it moves Black Lotus, Show and Tell, Boulderbranch Golem, and Saw in Half from graveyard into library. (-4; 18 life)
Cast Black Lotus, and cast Boulderbranch Golem. (-7, +6; 17 life)
Cast Saw in Half on Inverter of Truth. Two copies trigger. (-3; 14 life)
The first trigger exiles Show and Tell and sends Saw in Half and Inverter of Truth into the library.
Before the second trigger resolves, sacrifice Black Lotus for 3 mana, and cast Saw in Half targeting Boulderbranch Golem. (-3, +6; 17 life)
The second trigger exiles Inverter of Truth and sends Black Lotus, Saw in Half, and Boulderbranch Golem into the library.
Cast Black Lotus, and cast Boulderbranch Golem. (-7, +6; 16 life)
Cast Saw in Half on an Inverter of Truth. Two copies trigger. (-3; 13 life)
The first trigger sends Saw in Half into the library.
Before the second trigger resolves, sacrifice Black Lotus for 3 mana, and cast Saw in Half targeting Boulderbranch Golem. (-3, +6; 16 life)
The second trigger sends Black Lotus, Saw in Half, and Boulderbranch Golem into the library.
With enough mana now, cast Unstable Shapeshifter from hand, and then cast Black Lotus and Boulderbranch Golem (-7, +6; 15 life); Unstable Shapeshifter becomes a copy of Boulderbranch Golem.
Cast Saw in Half on an Inverter of Truth. (-3; 12 life) Two copies trigger, and Unstable Shapeshifter triggers twice; put the Inverter triggers on top.
The first Inverter trigger sends Saw in Half into the library.
Before the second trigger resolves, sacrifice Black Lotus for 3 mana, and cast Saw in Half targeting the Shapeshifter-Golem. (-3, +6; 15 life)
The second trigger sends Black Lotus, Saw in Half, and Unstable Shapeshifter into the library.
Cast Black Lotus one more time, then cast another pair of Saws on an Inverter and the original Golem (life-neutral). (Unstable Shapeshifter gets exiled.)
Cast Boulderbranch Golem. (-7, +6; 14 life) Both Shapeshifters trigger to become the full 6/5 Golem.
Let those triggers resolve one by one, and after each one resolves, cast another life-neutral Saw pair on an Inverter and the 6/5 Shapeshifter-Golem. There are now four Unstable Shapeshifters, two copying 3/3 Golems and two copying Inverters.
Now we can begin the full loop:
Cast a Saw pair on a Shapeshifter-Inverter and the original Golem.
Cast Boulderbranch Golem. (net -1 life) All Shapeshifters trigger.
After each of those Shapeshifter triggers resolve, cast a Saw pair on an Inverter and the 6/5 Shapeshifter-Golem. The first two times, it has to target a plain Inverter; each subsequent time can target a Shapeshifter-Inverter that does not have a waiting trigger to become a 6/5 Golem.
The net result is -1 life, and +1 and then *3-2 to the number of Shapeshifters, which works out to *3+1.
This can be repeated 7 times, ending with 7 life and 9841 Shapeshifters.
Cast the final card, Life of the Party, from hand. All the Shapeshifters turn into that.
Attack with all possible creatures, getting triggers from Life of the Party and the Shapeshifter copies of it; put the original's trigger on the bottom.
Cast a Saw pair on an Inverter and the original Golem, this time letting the triggers turning Shapeshifters into Inverters resolve first, so that afterwards they become Golems and get to stay Golems for a while.
A trigger from Life of the Party resolves, giving a big boost to the power of a Shapeshifter that is now copying a Golem. Start Sawing again with that one.
(As before, leave the high-value Shapeshifter triggers on the stack until they are ready to be consumed. Now that there is excess life being gained from the big Golems, it can be spent on extra Saws on small Golems. This should work out to a number of Knuth arrows somewhere around the base-2 logarithm of the starting power.)
Repeat with each Life of the Party trigger, until the final one resolves for the original Life of the Party, which is left to deal the big damage.
Cast a Saw pair on a Shapeshifter-Inverter and the original Golem.
Cast Boulderbranch Golem. (net -1 life) All Shapeshifters trigger.
After each of those Shapeshifter triggers resolve, cast a Saw pair on an Inverter and the 6/5 Shapeshifter-Golem. The first two times, it has to target a plain Inverter; each subsequent time can target a Shapeshifter-Inverter that does not have a waiting trigger to become a 6/5 Golem.
The net result is -1 life, and +1 and then *3-2 to the number of Shapeshifters, which works out to *3+1.
This can be repeated 7 times, ending with 7 life and 9841 Shapeshifters.
Are those numbers correct? The initial saw pair accounts for the +1, but after that we only cast one saw pair for each shapeshifter with a trigger. Each saw increases the number of creatures with the shapeshifter ability by -1+2 = 1. So I think we go from N to (N+1)*2-2 = 2*N instead of the N*3+1 you have.
That would result in 512 shapeshifters instead of 9841. That should still be enough to beat grahams number though.
I had another run in with the "oracle text" on mtgsalvation. It says "Whenever another creature enters the battlefield, Unstable Shapeshifter becomes a copy of that creature and gains this ability." That would lead to the combo not working, since the Saw in Half copies of a shapeshifter that has become a copy of the golem or inverter would just be that golem or inverter. The shapeshifter ability would not be transferred to the new copies since it was only gained later.
Fortunately the actual gatherer text is "Whenever another creature enters the battlefield, Unstable Shapeshifter becomes a copy of that creature, except it has this ability." It gives the shapeshifter ability by modifying the copy effect with an "except", so the ability gets copied properly onto the Saw in Half copies.
So as far as I can tell the combo should work. That's an amazing build!
Cast a Saw pair on a Shapeshifter-Inverter and the original Golem.
Cast Boulderbranch Golem. (net -1 life) All Shapeshifters trigger.
After each of those Shapeshifter triggers resolve, cast a Saw pair on an Inverter and the 6/5 Shapeshifter-Golem. The first two times, it has to target a plain Inverter; each subsequent time can target a Shapeshifter-Inverter that does not have a waiting trigger to become a 6/5 Golem.
The net result is -1 life, and +1 and then *3-2 to the number of Shapeshifters, which works out to *3+1.
This can be repeated 7 times, ending with 7 life and 9841 Shapeshifters.
Are those numbers correct? The initial saw pair accounts for the +1, but after that we only cast one saw pair for each shapeshifter with a trigger. Each saw increases the number of creatures with the shapeshifter ability by -1+2 = 1. So I think we go from N to (N+1)*2-2 = 2*N instead of the N*3+1 you have.
What you're missing is that the Shapeshifter count is increased both by Sawing Shapeshifter-Golems and by Sawing Shapeshifter-Inverters.
Ah, I misunderstood the procedure after attacking. I thought we'd go through the main loop described earlier again to turn life into more shapeshifters. That one includes the golem cast for efficiency. But it is of course enough to turn life into shapeshifters less efficiently using only Saw in Half.
What you're missing is that the Shapeshifter count is increased both by Sawing Shapeshifter-Golems and by Sawing Shapeshifter-Inverters.
I still count only two Saws for each Shapeshifter ability that is around when we cast the golem. And both of those Saws destroy 1 and create 2 creatures with the ability, whether it's an inverter or golem. I still don't see how you get the *3.
I still count only two Saws for each Shapeshifter ability that is around when we cast the golem. And both of those Saws destroy 1 and create 2 creatures with the ability, whether it's an inverter or golem. I still don't see how you get the *3.
That makes it a change of +2; to get the final number, the change has to be added to the initial number.
Wow this combo seems insane. I really like how we need to mulligan to have cards start in the library.
So the main 'engine' of the combo is that we cast Saw on an inverter for 3 life to get two inverter triggers, the first needs to immediately get Saw back, then in response to the other we cast saw again for 3 more life on a bolderbranch golem to gain 3+3 life and the second inverter trigger puts the saw back in the library again.
We can repeat this until we run out of 6 power golem-shapeshifters.
This then gets supercharged in combat because we now have a lot more power and therefore life to work with and can gain life 12, 24, 48 ... or (MUCH) more at a time. We now have a more 'normal' saw in half stage.
I think there might be some clever trigger stacking we can do to do a bit better than those combos, but not enough to change the big O.
I wonder what other applications there might be for these strategies. I imagine they could add at least a layer to 9-card, although I haven't found a method yet. Extending to multiple stages seems trickier.
I guess using one of the ones that needs to hit the opponent could work? though I don't think we can actually attack with small creatures like that... and Karlach, Fury of Avernus is unfortunately legendary
I think World at war works? Instead of exiling black lotus we keep it in play through combat, then after combat we use it to cast world at war from hand, and then use the excess life to cast it as part of the Saw loop.GAH rebound will exile it from the first cast
Edit: yeah I think all of the extra combat cards don't work. They either need to be activated in combat, go infinite, or are legendary. World at War would work if we could get it into the yard post combat.
Speaking of alternatives, a recent Reddit post has gotten me thinking about another possible challenge. This one isn't really focusing on cards as a limit, but the restriction is big enough that this thread feels to me like it might be a better place than the 60-card one.
The original challenge was finding the best way to kill the opponent with a Legacy-legal deck that isn't able to cast spells. The original post suggested a turn 3 kill with Dark Depths, and it looks like a dredge strategy can win on turn 1.
So, to build off that, how much damage could we deal? (Perhaps switching from the Legacy card pool to Vintage, but it might not even matter.) One thing that could be helpful is Priest of Fell Rites, since it can get back arbitrary creatures without casting a spell. Angel of Glory's Rise can turn one reanimation into many, and reanimating creatures can turn into reanimating artifacts and enchantments.
The difference between Legacy and Vintage is actually significant for this. In Vintage, we can get started relatively easily: reveal four Chancellor of the Tangle, play Bazaar of Baghdad and activate it and discard two Chancellors and a Golgari Grave-Troll, cycle Street Wraith and dredge the Golgari Grave-Troll, exile a Simian Spirit Guide for one more mana, exile two Jack-o-Lantern from the graveyard to fix mana, and unearth a Priest of Fell Rites with three remaining non-fixed cards in the graveyard and one in hand (or four in graveyard by discarding one instead of a Chancellor).
In Legacy, it's harder to get started. The Geier Reach Sanitarium method you mentioned in the linked post doesn't leave enough cards to get the mana to unearth a Priest of Fell Rites. Starting with Dakmor Salvage + cycle Edge of Autumn does a bit better; continuing similarly to above does allow unearthing a Priest of Fell Rites on the draw only, with four remaining non-fixed cards in the graveyard. But to do it on the play, I needed to use a more complicated method. Start by revealing two Chancellor of the Tangle and putting three Leyline of Anticipation onto the battlefield. Play Nykthos, Shrine to Nyx and activate it for 6 blue mana. Use the last card -- Waker of Waves -- to put a Golgari Grave-Troll in the graveyard and a Vizier of Tumbling Sands in hand. Cycle that, untapping Nykthos, activate Nykthos again for another 6 blue mana, and dredge the Golgari Grave-Troll with the draw. Then, as before, exile two Jack-o-Lantern from the graveyard to fix mana, and unearth a Priest of Fell Rites with three remaining non-fixed cards in the graveyard.
Speaking of alternatives, a recent Reddit post has gotten me thinking about another possible challenge. This one isn't really focusing on cards as a limit, but the restriction is big enough that this thread feels to me like it might be a better place than the 60-card one.
The original challenge was finding the best way to kill the opponent with a Legacy-legal deck that isn't able to cast spells. The original post suggested a turn 3 kill with Dark Depths, and it looks like a dredge strategy can win on turn 1.
So, to build off that, how much damage could we deal? (Perhaps switching from the Legacy card pool to Vintage, but it might not even matter.) One thing that could be helpful is Priest of Fell Rites, since it can get back arbitrary creatures without casting a spell. Angel of Glory's Rise can turn one reanimation into many, and reanimating creatures can turn into reanimating artifacts and enchantments.
The difference between Legacy and Vintage is actually significant for this. In Vintage, we can get started relatively easily: reveal four Chancellor of the Tangle, play Bazaar of Baghdad and activate it and discard two Chancellors and a Golgari Grave-Troll, cycle Street Wraith and dredge the Golgari Grave-Troll, exile a Simian Spirit Guide for one more mana, exile two Jack-o-Lantern from the graveyard to fix mana, and unearth a Priest of Fell Rites with three remaining non-fixed cards in the graveyard and one in hand (or four in graveyard by discarding one instead of a Chancellor).
In Legacy, it's harder to get started. The Geier Reach Sanitarium method you mentioned in the linked post doesn't leave enough cards to get the mana to unearth a Priest of Fell Rites. Starting with Dakmor Salvage + cycle Edge of Autumn does a bit better; continuing similarly to above does allow unearthing a Priest of Fell Rites on the draw only, with four remaining non-fixed cards in the graveyard. But to do it on the play, I needed to use a more complicated method. Start by revealing two Chancellor of the Tangle and putting three Leyline of Anticipation onto the battlefield. Play Nykthos, Shrine to Nyx and activate it for 6 blue mana. Use the last card -- Waker of Waves -- to put a Golgari Grave-Troll in the graveyard and a Vizier of Tumbling Sands in hand. Cycle that, untapping Nykthos, activate Nykthos again for another 6 blue mana, and dredge the Golgari Grave-Troll with the draw. Then, as before, exile two Jack-o-Lantern from the graveyard to fix mana, and unearth a Priest of Fell Rites with three remaining non-fixed cards in the graveyard.
For 3 cards with unlimited mana: Mondrak, Glory Dominus, Ratadrabik of Urborg, Twinflame making two copies of each; have the originals and one copy of each die to the legend rule, generating six Ratadrabik triggers for Mondrak and four Ratadrabik triggers for Ratadrabik. Resolve the triggers for Mondrak first, getting >2^^6 nonlegendary copies of Mondrak, then resolve the rest for >2^^7 nonlegendary copies of Ratadrabik. Now activate one of the Mondrak tokens, sacrificing the two remaining legendary tokens and getting >2^^7 Ratadrabik triggers for each. Again, resolve the triggers for Mondrak first for >2^^2^^7 copies of Mondrak, and then resolve the rest for >2^^2^^7 copies of Ratadrabik. Those tokens have haste and can attack.
(Cadric, Soul Kindler would have been better if its haste were copiable.)
The total mana consumption is 16, so this can also become a 6-card solution with Black Lotus, Channel, and Chromatic Orrery.
For 3 cards with unlimited mana: Mondrak, Glory Dominus, Ratadrabik of Urborg, Twinflame making two copies of each; have the originals and one copy of each die to the legend rule, generating six Ratadrabik triggers for Mondrak and four Ratadrabik triggers for Ratadrabik. Resolve the triggers for Mondrak first, getting >2^^6 nonlegendary copies of Mondrak, then resolve the rest for >2^^7 nonlegendary copies of Ratadrabik. Now activate one of the Mondrak tokens, sacrificing the two remaining legendary tokens and getting >2^^7 Ratadrabik triggers for each. Again, resolve the triggers for Mondrak first for >2^^2^^7 copies of Mondrak, and then resolve the rest for >2^^2^^7 copies of Ratadrabik. Those tokens have haste and can attack.
(Cadric, Soul Kindler would have been better if its haste were copiable.)
The total mana consumption is 16, so this can also become a 6-card solution with Black Lotus, Channel, and Chromatic Orrery.
Awesome find! I wonder if there's any other deck sizes that would want Mondrak.
For 4 cards with unlimited mana, we can do Mondrak, Glory Dominus, Ratadrabik of Urborg, Cadric, Soul Kindler, and... something. Junji, the Midnight Sky would be ideal if not for the life loss. The best I could find is Colfenor, the Last Yew, which adds 2 layers (because the stack has to clear to recast cards) to the 4 from the other cards for a total of 6. (How to do it: Sacrificing each Colfenor token gets multiple triggers to return all the other cards. Cast Ratadrabik and Cadric first and get copies of them. Then, cast Mondrak and get a bunch of Cadric triggers. After each of those triggers resolves and gives a bunch of legendary Mondrak tokens, sacrifice a single legendary Ratadrabik token to get a bunch of Ratadrabik/Ratadrabik triggers, and alternate resolving those triggers with sacrificing legendary Mondrak tokens, so that the Ratadrabik count is boosted for each sacrifice of a legendary Mondrak token.)
Unfortunately, adding Black Lotus, Channel and Lich's Mirror for the no-mana-given version doesn't work with these cards, because it is possible to set off the Lich's Mirror reset with Ratadrabik triggers still on the stack, giving a higher starting point, and repeat to go infinite. If we weren't constrained to Vintage legality, 2x Black Lotus and Auriok Salvagers would work as an alternative way of getting infinite mana.
For 5 cards with unlimited mana, I think we can add Kodama of the East Tree to Mondrak, Glory Dominus, Ratadrabik of Urborg, Cadric, Soul Kindler, and Colfenor, the Last Yew. Ratadrabik can now be the starting point; the Mondrak count doesn't get increased at that point, but we still get a multiplication for each legendary Ratadrabik token, and then an exponentiation for each sacrifice of a Mondrak token getting back Ratadrabik and Cadric, for a layer-1 foundation. After that, Mondrak, Kodama, and Colfenor each add 4 layers above that, for a total of 13 layers.
(Correction) Mondrak doesn't get re-increased enough to count for a layer from multiplying its own nonlegendary tokens, dropping it to 3 layers; thus Mondrak ends up at layer 4 whether you use this procedure or the other procedure from above, and the total is 12 layers.
For 4 cards with unlimited mana, we can do Mondrak, Glory Dominus, Ratadrabik of Urborg, Cadric, Soul Kindler, and... something. Junji, the Midnight Sky would be ideal if not for the life loss. The best I could find is Colfenor, the Last Yew, which adds 2 layers (because the stack has to clear to recast cards) to the 4 from the other cards for a total of 6. (How to do it: Sacrificing each Colfenor token gets multiple triggers to return all the other cards. Cast Ratadrabik and Cadric first and get copies of them. Then, cast Mondrak and get a bunch of Cadric triggers. After each of those triggers resolves and gives a bunch of legendary Mondrak tokens, sacrifice a single legendary Ratadrabik token to get a bunch of Ratadrabik/Ratadrabik triggers, and alternate resolving those triggers with sacrificing legendary Mondrak tokens, so that the Ratadrabik count is boosted for each sacrifice of a legendary Mondrak token.)
Unfortunately, adding Black Lotus, Channel and Lich's Mirror for the no-mana-given version doesn't work with these cards, because it is possible to set off the Lich's Mirror reset with Ratadrabik triggers still on the stack, giving a higher starting point, and repeat to go infinite. If we weren't constrained to Vintage legality, 2x Black Lotus and Auriok Salvagers would work as an alternative way of getting infinite mana.
For 5 cards with unlimited mana, I think we can add Kodama of the East Tree to Mondrak, Glory Dominus, Ratadrabik of Urborg, Cadric, Soul Kindler, and Colfenor, the Last Yew. Ratadrabik can now be the starting point; the Mondrak count doesn't get increased at that point, but we still get a multiplication for each legendary Ratadrabik token, and then an exponentiation for each sacrifice of a Mondrak token getting back Ratadrabik and Cadric, for a layer-1 foundation. After that, Mondrak, Kodama, and Colfenor each add 4 layers above that, for a total of 13 layers.
Ooh, that's neat. I like the idea of a way to get infinite mana without Lich's Mirror, although that's true that the second Lotus doesn't fit the Vintage legal restriction.
Hmm yeah I don't see a way to get infinite mana with just three cards, Mishra's workshop is I think the only other card that is +3 mana from nothing like black lotus, but it doesn't cast salvagers.
Hmm yeah I don't see a way to get infinite mana with just three cards, Mishra's workshop is I think the only other card that is +3 mana from nothing like black lotus, but it doesn't cast salvagers.
For 4 cards with unlimited mana, we can do Mondrak, Glory Dominus, Ratadrabik of Urborg, Cadric, Soul Kindler, and... something. Junji, the Midnight Sky would be ideal if not for the life loss. The best I could find is Colfenor, the Last Yew, which adds 2 layers (because the stack has to clear to recast cards) to the 4 from the other cards for a total of 6. (How to do it: Sacrificing each Colfenor token gets multiple triggers to return all the other cards. Cast Ratadrabik and Cadric first and get copies of them. Then, cast Mondrak and get a bunch of Cadric triggers. After each of those triggers resolves and gives a bunch of legendary Mondrak tokens, sacrifice a single legendary Ratadrabik token to get a bunch of Ratadrabik/Ratadrabik triggers, and alternate resolving those triggers with sacrificing legendary Mondrak tokens, so that the Ratadrabik count is boosted for each sacrifice of a legendary Mondrak token.)
Unfortunately, adding Black Lotus, Channel and Lich's Mirror for the no-mana-given version doesn't work with these cards, because it is possible to set off the Lich's Mirror reset with Ratadrabik triggers still on the stack, giving a higher starting point, and repeat to go infinite. If we weren't constrained to Vintage legality, 2x Black Lotus and Auriok Salvagers would work as an alternative way of getting infinite mana.
For 5 cards with unlimited mana, I think we can add Kodama of the East Tree to Mondrak, Glory Dominus, Ratadrabik of Urborg, Cadric, Soul Kindler, and Colfenor, the Last Yew. Ratadrabik can now be the starting point; the Mondrak count doesn't get increased at that point, but we still get a multiplication for each legendary Ratadrabik token, and then an exponentiation for each sacrifice of a Mondrak token getting back Ratadrabik and Cadric, for a layer-1 foundation. After that, Mondrak, Kodama, and Colfenor each add 4 layers above that, for a total of 13 layers.
(Correction) Mondrak doesn't get re-increased enough to count for a layer from multiplying its own nonlegendary tokens, dropping it to 3 layers; thus Mondrak ends up at layer 4 whether you use this procedure or the other procedure from above, and the total is 12 layers.
It doesn't work for this combo since you need so much mana of different colors to get set up, but in other token-making combos you may be able to use Salvage Scout duplicates to cycle Black Lotus for cheaper.
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Speaking of alternatives, a recent Reddit post has gotten me thinking about another possible challenge. This one isn't really focusing on cards as a limit, but the restriction is big enough that this thread feels to me like it might be a better place than the 60-card one.
The original challenge was finding the best way to kill the opponent with a Legacy-legal deck that isn't able to cast spells. The original post suggested a turn 3 kill with Dark Depths, and it looks like a dredge strategy can win on turn 1.
So, to build off that, how much damage could we deal? (Perhaps switching from the Legacy card pool to Vintage, but it might not even matter.) One thing that could be helpful is Priest of Fell Rites, since it can get back arbitrary creatures without casting a spell. Angel of Glory's Rise can turn one reanimation into many, and reanimating creatures can turn into reanimating artifacts and enchantments.
I don't think there's a way to use Saw in Half or Artificial Evolution under these conditions, but I think we could still hit Graham's Number with the help of Toralf, God of Fury.
The main improvement is that Renegade Doppelganger or Unstable Shapeshifter can serve the purpose of Doubling Season, without needing an extra card (which was Astral Dragon). The downside of this is lower initial growth rates; I brought the growth rate back up a bit with precise card selection.
Start with Black Lotus and Show and Tell to put Bolas's Citadel onto the battlefield.
Cast Boulderbranch Golem from library. (-7, +6; 19 life)
Cast Saw in Half from library, targeting Boulderbranch Golem. (-3, +6; 22 life)
Cast Inverter of Truth from library; it moves Black Lotus, Show and Tell, Boulderbranch Golem, and Saw in Half from graveyard into library. (-4; 18 life)
Cast Black Lotus, and cast Boulderbranch Golem. (-7, +6; 17 life)
Cast Saw in Half on Inverter of Truth. Two copies trigger. (-3; 14 life)
The first trigger exiles Show and Tell and sends Saw in Half and Inverter of Truth into the library.
Before the second trigger resolves, sacrifice Black Lotus for 3 mana, and cast Saw in Half targeting Boulderbranch Golem. (-3, +6; 17 life)
The second trigger exiles Inverter of Truth and sends Black Lotus, Saw in Half, and Boulderbranch Golem into the library.
Cast Black Lotus, and cast Boulderbranch Golem. (-7, +6; 16 life)
Cast Saw in Half on an Inverter of Truth. Two copies trigger. (-3; 13 life)
The first trigger sends Saw in Half into the library.
Before the second trigger resolves, sacrifice Black Lotus for 3 mana, and cast Saw in Half targeting Boulderbranch Golem. (-3, +6; 16 life)
The second trigger sends Black Lotus, Saw in Half, and Boulderbranch Golem into the library.
With enough mana now, cast Unstable Shapeshifter from hand, and then cast Black Lotus and Boulderbranch Golem (-7, +6; 15 life); Unstable Shapeshifter becomes a copy of Boulderbranch Golem.
Cast Saw in Half on an Inverter of Truth. (-3; 12 life) Two copies trigger, and Unstable Shapeshifter triggers twice; put the Inverter triggers on top.
The first Inverter trigger sends Saw in Half into the library.
Before the second trigger resolves, sacrifice Black Lotus for 3 mana, and cast Saw in Half targeting the Shapeshifter-Golem. (-3, +6; 15 life)
The second trigger sends Black Lotus, Saw in Half, and Unstable Shapeshifter into the library.
Cast Black Lotus one more time, then cast another pair of Saws on an Inverter and the original Golem (life-neutral). (Unstable Shapeshifter gets exiled.)
Cast Boulderbranch Golem. (-7, +6; 14 life) Both Shapeshifters trigger to become the full 6/5 Golem.
Let those triggers resolve one by one, and after each one resolves, cast another life-neutral Saw pair on an Inverter and the 6/5 Shapeshifter-Golem. There are now four Unstable Shapeshifters, two copying 3/3 Golems and two copying Inverters.
Now we can begin the full loop:
- Cast a Saw pair on a Shapeshifter-Inverter and the original Golem.
- Cast Boulderbranch Golem. (net -1 life) All Shapeshifters trigger.
- After each of those Shapeshifter triggers resolve, cast a Saw pair on an Inverter and the 6/5 Shapeshifter-Golem. The first two times, it has to target a plain Inverter; each subsequent time can target a Shapeshifter-Inverter that does not have a waiting trigger to become a 6/5 Golem.
The net result is -1 life, and +1 and then *3-2 to the number of Shapeshifters, which works out to *3+1.This can be repeated 7 times, ending with 7 life and 9841 Shapeshifters.
Cast the final card, Life of the Party, from hand. All the Shapeshifters turn into that.
Attack with all possible creatures, getting triggers from Life of the Party and the Shapeshifter copies of it; put the original's trigger on the bottom.
Cast a Saw pair on an Inverter and the original Golem, this time letting the triggers turning Shapeshifters into Inverters resolve first, so that afterwards they become Golems and get to stay Golems for a while.
A trigger from Life of the Party resolves, giving a big boost to the power of a Shapeshifter that is now copying a Golem. Start Sawing again with that one.
(As before, leave the high-value Shapeshifter triggers on the stack until they are ready to be consumed. Now that there is excess life being gained from the big Golems, it can be spent on extra Saws on small Golems. This should work out to a number of Knuth arrows somewhere around the base-2 logarithm of the starting power.)
Repeat with each Life of the Party trigger, until the final one resolves for the original Life of the Party, which is left to deal the big damage.
Some other things I found:
Also attaining F_{w+1}, but not as high, and only on the draw: Black Lotus, Channel, Chromatic Orrery, Unstable Shapeshifter, Mycoid Shepherd, Saw in Half, Soulfire Grand Master, Life of the Party
Some cards with dual-purpose potential: Conclave Mentor, Packsong Pup, Swiftgear Drake
That would result in 512 shapeshifters instead of 9841. That should still be enough to beat grahams number though.
I had another run in with the "oracle text" on mtgsalvation. It says "Whenever another creature enters the battlefield, Unstable Shapeshifter becomes a copy of that creature and gains this ability." That would lead to the combo not working, since the Saw in Half copies of a shapeshifter that has become a copy of the golem or inverter would just be that golem or inverter. The shapeshifter ability would not be transferred to the new copies since it was only gained later.
Fortunately the actual gatherer text is "Whenever another creature enters the battlefield, Unstable Shapeshifter becomes a copy of that creature, except it has this ability." It gives the shapeshifter ability by modifying the copy effect with an "except", so the ability gets copied properly onto the Saw in Half copies.
So as far as I can tell the combo should work. That's an amazing build!
EDIT: Wait. How are we casting Boulderbranch Golem for the loop with Unstable Shapeshifter triggers on the stack? Or in combat?
We're not. Boulderbranch Golem is only cast after each batch of Shapeshifter triggers is finished, and is no longer cast once we attack.
I still count only two Saws for each Shapeshifter ability that is around when we cast the golem. And both of those Saws destroy 1 and create 2 creatures with the ability, whether it's an inverter or golem. I still don't see how you get the *3.
So the main 'engine' of the combo is that we cast Saw on an inverter for 3 life to get two inverter triggers, the first needs to immediately get Saw back, then in response to the other we cast saw again for 3 more life on a bolderbranch golem to gain 3+3 life and the second inverter trigger puts the saw back in the library again.
We can repeat this until we run out of 6 power golem-shapeshifters.
This then gets supercharged in combat because we now have a lot more power and therefore life to work with and can gain life 12, 24, 48 ... or (MUCH) more at a time. We now have a more 'normal' saw in half stage.
I think there might be some clever trigger stacking we can do to do a bit better than those combos, but not enough to change the big O.
I guess using one of the ones that needs to hit the opponent could work? though I don't think we can actually attack with small creatures like that... and Karlach, Fury of Avernus is unfortunately legendary
I think World at war works? Instead of exiling black lotus we keep it in play through combat, then after combat we use it to cast world at war from hand, and then use the excess life to cast it as part of the Saw loop.
Edit: yeah I think all of the extra combat cards don't work. They either need to be activated in combat, go infinite, or are legendary. World at War would work if we could get it into the yard post combat.
Edit: Hmm, maybe something before combat then? Maybe an X cost pump effect like Exponential growth or Finale of devastation?
I have done some looking into that challenge.
The difference between Legacy and Vintage is actually significant for this. In Vintage, we can get started relatively easily: reveal four Chancellor of the Tangle, play Bazaar of Baghdad and activate it and discard two Chancellors and a Golgari Grave-Troll, cycle Street Wraith and dredge the Golgari Grave-Troll, exile a Simian Spirit Guide for one more mana, exile two Jack-o-Lantern from the graveyard to fix mana, and unearth a Priest of Fell Rites with three remaining non-fixed cards in the graveyard and one in hand (or four in graveyard by discarding one instead of a Chancellor).
In Legacy, it's harder to get started. The Geier Reach Sanitarium method you mentioned in the linked post doesn't leave enough cards to get the mana to unearth a Priest of Fell Rites. Starting with Dakmor Salvage + cycle Edge of Autumn does a bit better; continuing similarly to above does allow unearthing a Priest of Fell Rites on the draw only, with four remaining non-fixed cards in the graveyard. But to do it on the play, I needed to use a more complicated method. Start by revealing two Chancellor of the Tangle and putting three Leyline of Anticipation onto the battlefield. Play Nykthos, Shrine to Nyx and activate it for 6 blue mana. Use the last card -- Waker of Waves -- to put a Golgari Grave-Troll in the graveyard and a Vizier of Tumbling Sands in hand. Cycle that, untapping Nykthos, activate Nykthos again for another 6 blue mana, and dredge the Golgari Grave-Troll with the draw. Then, as before, exile two Jack-o-Lantern from the graveyard to fix mana, and unearth a Priest of Fell Rites with three remaining non-fixed cards in the graveyard.
For 3 cards with unlimited mana: Mondrak, Glory Dominus, Ratadrabik of Urborg, Twinflame making two copies of each; have the originals and one copy of each die to the legend rule, generating six Ratadrabik triggers for Mondrak and four Ratadrabik triggers for Ratadrabik. Resolve the triggers for Mondrak first, getting >2^^6 nonlegendary copies of Mondrak, then resolve the rest for >2^^7 nonlegendary copies of Ratadrabik. Now activate one of the Mondrak tokens, sacrificing the two remaining legendary tokens and getting >2^^7 Ratadrabik triggers for each. Again, resolve the triggers for Mondrak first for >2^^2^^7 copies of Mondrak, and then resolve the rest for >2^^2^^7 copies of Ratadrabik. Those tokens have haste and can attack.
(Cadric, Soul Kindler would have been better if its haste were copiable.)
The total mana consumption is 16, so this can also become a 6-card solution with Black Lotus, Channel, and Chromatic Orrery.
Unfortunately, adding Black Lotus, Channel and Lich's Mirror for the no-mana-given version doesn't work with these cards, because it is possible to set off the Lich's Mirror reset with Ratadrabik triggers still on the stack, giving a higher starting point, and repeat to go infinite. If we weren't constrained to Vintage legality, 2x Black Lotus and Auriok Salvagers would work as an alternative way of getting infinite mana.
For 5 cards with unlimited mana, I think we can add Kodama of the East Tree to Mondrak, Glory Dominus, Ratadrabik of Urborg, Cadric, Soul Kindler, and Colfenor, the Last Yew. Ratadrabik can now be the starting point; the Mondrak count doesn't get increased at that point, but we still get a multiplication for each legendary Ratadrabik token, and then an exponentiation for each sacrifice of a Mondrak token getting back Ratadrabik and Cadric, for a layer-1 foundation.
After that, Mondrak, Kodama, and Colfenor each add 4 layers above that, for a total of 13 layers.(Correction) Mondrak doesn't get re-increased enough to count for a layer from multiplying its own nonlegendary tokens, dropping it to 3 layers; thus Mondrak ends up at layer 4 whether you use this procedure or the other procedure from above, and the total is 12 layers.
Edit: I guess if we allow un cards, black lotus into mana screw gets us there with any of Energy Refractor/Gemstone Array/Chromatic Orrery/prismite etc.
If we're using un cards, you may as well just go Black Lotus, Channel, Mox Lotus
It doesn't work for this combo since you need so much mana of different colors to get set up, but in other token-making combos you may be able to use Salvage Scout duplicates to cycle Black Lotus for cheaper.