We’re on a long tangent away from the Lotus, but it’s an interesting question how widely Vintage decks would replace duals with “painless City of Brass,” if that were printed.
My guess is that in many decks the fetch lands and duals have value beyond mana fixing (source of shuffling; wasteland resistance; fuel for Gush and Mystic Sanctuary, etc) so that the duals would still be heavily used.
I highly doubt people will actually pay 17-19 lives for this on turn 1. You'd need a god draw with 3-4 mana floating after the wheel to have a somewhat reliable kill. If you don't win that turn, you're pretty much dead to anything.
You can also cast a mini-Tendrils to gain the life needed to cast the second Wheel. Presumably you are running the Wheel in a TPS shell (since if your deck is based around artifact acceleration only, PO is just better than even a one-sided Wheel of Fortune, no?).
They are definitely replacement effects:
614.1d Continuous effects that read “[This permanent] enters the battlefield . . .” or “[Objects] enter the battlefield . . .” are replacement effects.
The real question is whether they are self-replacement effects:
614.15. Some replacement effects are not continuous effects. Rather, they are an effect of a resolving spell or ability that replace part or all of that spell or ability’s own effect(s). Such effects are called self-replacement effects. The text creating a self-replacement effect is usually part of the ability whose effect is being replaced, but the text can be a separate ability, particularly when preceded by an ability word. When applying replacement effects to an event, self-replacement effects are applied before other replacement effects.
From a strict reading of the comp. rules, the Guildgate replacement effect that causes it to enter the battlefield tapped cannot be a self-replacement effect, since lands are not spells and don't enter the battlefield as a result of "a resolving spell or ability." There is a slightly stronger case for the "enters the battlefield tapped" abilities of permanent spells being self-replacement effects (replacing the permanent's own effect of entering the battlefield on resolution) but since 614.1d seems to clearly label these abilities "continuous effects" and self-replacement effects are "not continuous effects," I think this case is also flimsy.
So: we will get an official ruling before the set releases (including, potentially, clarification in the comp. rules themselves) but right now I'd bet on the controller of the permanent choosing whether it enters tapped or untapped.
This card has no Vintage implications, but is a notable printing nonetheless as the closest replica yet to MtG's most iconic card:
Jeweled Lotus 0
T, Sacrifice Jeweled Lotus: Add three mana of any one color. Spend this mana only to cast your commander.
I don't play a lot of Commander, but naively I expect this card to dramatically increase the variance and power level of that format...
This card looks like great fun. I agree with Protoaddict that it will be a real skill-tester. I think like all "punisher" cards this one is much weaker than it looks in decks that try to play it "fairly," while preserving some life for fetchlands, Force of Will, Mana Crypt flips, etc. I think it's stone busted in decks specifically build to bid 19 life and combo off that turn.
@john-cox I'm leaning more towards mono-red than UR as a shell though. Besides the obvious Ancestral Recall and Time Walk, blue doesn't bring much to the table: getting your own Force of Will, Treasure Cruise, etc. remanded is clearly terrible, and even double-Preordain for UU is not that great because you will quickly run out of blue mana to chain them together.
On the other hand a mono-red shell can fuel itself with rituals (which are great since Krak amplifies the net mana you gain from them), which I think ends up more consistent even if the individual red spells are weaker than the blue cantrips.
(Either way Gitaxian Probe is an auto-include, of course.)