Post your deck's land count, mana cost distribution, and the number of turns you want to play your cards efficiently, and I'll tell you how good your mana curve is.
How does it work? I wrote a program that simulates deck play literally millions of times to determine the most efficient mana curve given land count, whether you're on the play or not, and how many turns you want to play efficiently. If you want to play the first 8 turns as efficiently as possible, then just specify "8 turns." The simulator considers mulligans and even makes decisions about how to play cards in hand intelligently (should I play two 2-drops on turn 4 or a 3-drop and a 1-drop?). Then I use a hill climbing algorithm to find the best mana curve possible, and divide average mana spent of your mana curve by the average mana spent by the best mana curve. This gives you how good your mana curve is as a fraction of the best mana curve possible.
Note: Unfortunately I can't incorporate ramp spells and card draw with the program I've written, but I've still found my algorithm useful for rough checks on my mana distributions. It has also guided my taste in how to craft a good mana distribution.
2nd Note: If your highest cost card is 5, then a good choice for turn count is 5. If your highest cost card is 7, then a good choice for turn count is 7. But non-equal numbers can work too.
I think there is more to mana curves than meets the eye. I think good mana curves are related to the Rayleigh distribution, NOT the normal distribution. Also there seems to be some hidden but simple arithmetic rules for a good mana curve that no one knows about. Mana curves haven't been studied by serious mathematicians that I know of, so it's up to hobbyists to pick up the slack.
Example:
5 Turns (On the Play)
Lands: 24
1drop - 4
2drop - 8
3drop - 12
4drop - 8
5drop - 4
Score: 98.76% (excellent)
Example:
5 Turns (On the Play)
Lands: 24
1drop - 12
2drop - 6
3drop - 6
4drop - 6
5drop - 6
Score: 92.88% (mediocre)
How does it work? I wrote a program that simulates deck play literally millions of times to determine the most efficient mana curve given land count, whether you're on the play or not, and how many turns you want to play efficiently. If you want to play the first 8 turns as efficiently as possible, then just specify "8 turns." The simulator considers mulligans and even makes decisions about how to play cards in hand intelligently (should I play two 2-drops on turn 4 or a 3-drop and a 1-drop?). Then I use a hill climbing algorithm to find the best mana curve possible, and divide average mana spent of your mana curve by the average mana spent by the best mana curve. This gives you how good your mana curve is as a fraction of the best mana curve possible.
Note: Unfortunately I can't incorporate ramp spells and card draw with the program I've written, but I've still found my algorithm useful for rough checks on my mana distributions. It has also guided my taste in how to craft a good mana distribution.
2nd Note: If your highest cost card is 5, then a good choice for turn count is 5. If your highest cost card is 7, then a good choice for turn count is 7. But non-equal numbers can work too.