I've done some more math. I finally figured out the
Gilded Lotus thing and I can tell you it wasn't easy. Ultimately I wasn't able to answer the question I set out to but that's okay. I found other answers. I tried to ask "How often will
Gilded Lotus screw up your starting hand?" but that was really complicated to formulate into probabilities. Instead I got the answers to the following questions:
- How much does replacing a land with Gilded Lotus help you get a good hand?
- How much does replacing a ramp spell with Gilded Lotus help you get a good hand?
- What's the probability of being able to cast Gilded Lotus on curve given that your hand was reasonable otherwise?
- What's the proportion of games where you're able to cast Gilded Lotus on curve when you kept a reasonable hand?
Let's get into it. I've laid out the basic assumptions before already so I'm not going to through them again.
How much does replacing a land with Gilded Lotus help you get a good opening hand?The question formatting is very
deliberate. The math is P(good hands with
Gilded Lotus)-P(generically good hand). So for example if you've got 35 lands and 9 ramp spells the net effect of
Gilded Lotus on drawing a good hand is about -1% i.e. replacing a land with
Gilded Lotus decreases your chance of drawing a good hand. Having 37 lands and 15 ramp spells on the other hand is excessive from the perspective of drawing an ideal hand so replacing a land with
Gilded Lotus actually improves your chances of drawing a good hand by 0.5%. You're less likely to draw too many lands in your opening hand.
How much does replacing a ramp spell with Gilded Lotus help you get a good opening hand?The question formatting is very
deliberate. The math is P(good hands with
Gilded Lotus)-P(generically good hand). So for example if you've got 36 lands and 8 ramp spells the net effect of
Gilded Lotus on drawing a good hand is about -2% i.e. replacing a ramp spell with
Gilded Lotus decreases your chance of drawing a good hand. Having 37 lands and 15 ramp spells on the other hand is excessive from the perspective of drawing an ideal hand so replacing a ramp spell with
Gilded Lotus actually improves your chances of drawing a good hand by 1%. You're less likely to draw too many ramp spells in your opening hand.
What's the probability of being able to cast Gilded Lotus on curve given that your hand was reasonable otherwise?Here
Gilded Lotus doesn't replace anything. This chart assumes you always draw
Gilded Lotus in your opening hand. No mulligans. We do 5 extra draws to see if we can cast
Gilded Lotus on turn 5. The math is P(good hand) x (1-P(not drawing enough mana)). I actually went hand by hand so it takes into account the fact that 3 lands and 0 ramp needs to draw 2 additional mana sources whereas 3 lands and 1 ramp only needs to draw 1 additional mana source. For example the "ideal composition" of 36 lands and 12 ramp spells produces a 36% chance to draw a good hand
and into a situation where you can cast
Gilded Lotus on curve. This also means that if you've got a
really high mana curve (say average mana cost over 4) you might want to optimise your deck differently and add a lot more lands and ramp. The ideal amount of lands and ramp based on this chart would seem to be 43 lands and 16 ramp spells.
What's the proportion of games where you're able to cast Gilded Lotus on curve when you kept a reasonable hand?Here it's kind of the same math as the previous example except we divide out the probability of drawing into a good hand. So this here is the proportion games where you were able to cast
Gilded Lotus on curve given that you kept a good hand. For example with 36 lands and 12 ramp spells you've got an 86% chance to cast a 5-drop on curve. This actually applies to all 5-drops so if your commander costs 5 mana 1 game in 7 games you're not able to cast your commander on curve given that you kept a reasonable opening hand. I think this chart is the best one at describing how important it is to run enough lands and ramp in your deck. The differences are significant and even one land / ramp spell makes a difference in your ability to cast bigger spells.
Summary of results- If you're playing reasonable amounts of lands and ramp replacing a land with Gilded Lotus doesn't make much of a difference in terms of drawing a good hand. Mulliganing away a Gilded Lotus hand is always an option.
- Replacing a ramp spell makes a bigger difference but it's still not much. One could argue that 0.5%-1% difference is enough of a difference not to replace a ramp spell with a land but that's up to personal preferences. Mulliganing away a Gilded Lotus hand is always an option.
- The chance of being able to cast Gilded Lotus on turn 5 is less than half so if you do find a hand with Gilded Lotus in it it would make sense to keep it only if it has an abnormally large amount of mana sources.
- If your average mana cost is really high or your commander costs a lot you may want to up your mana source count significantly.