Puzzle:Single-handed gesture density

[mikeEB]

Definition:A gesture sequence's density is the average number of spells each gesture in the sequence is part of.

For example, PSDF by itself has a gesture density of 1.75. P is in shield and charm, S and D are each in magic missile and charm, and F is only in charm.

An easier way to find the density is to sum up the gestures of all spells cast and divide by the total number of gestures, although for single-handed sequences this requires special treatment for two-handed spells to be consistent with the definition.

The challenge: Excluding the degenerate case of a paralysis chain, find the repeating sequence of gestures that maximizes the spell density for one hand. Rules:
1)The other hand doesn't 'count' although it can still contribute, for example by completing a blindness to mix in with a main-hand D.
2)Paralysis may be used, as in the sequence DSFFFCWPF. However, sequences of four or more F's are forbidden, as is the paraFDF equivalent where allowed.
3)WDDC is not allowed, as it only works the first time through the sequence. Unfortunately, this spoils the rather elegant CWSSWDD with blindness on the second D.
4)Time-stopped turns still count as turns.
5)Other normal Warlocks rules apply. e.g. no surrendering in mid-sequence.

So now for my actual sequences:
PSDDP =10/5=2.0 : Amnesia(3)+Magic Missile(2)+Charm Monster(4)+Shield(1) [This is the baseline sequence. Don't post anything worse.]

SDWSSSPFP = 21/9 = 2.333 :Magic Missile(2)+Permanency(7)+Invisibility(2)+Delay Effect(6)+Anti-spell(4) [Good sequence in general that requires cooperation from the other hand]

DFWF =11/4 =2.75 :Blindness(5)+Paralysis(3)+Cure Light Wounds(3) [ParaFDF only!]

[Slartucker]

The math doesn't add up for me for DFWF. D is part of 3 spells, F is part of 3 spells, W is part of 2 and F is part of 2. That's an average of 2.5. The problem is that you counted both the first and last D for blindness, but you only counted one D for the gesture count. This is a relevant imbalance because it means that spells that overlap beyond one iteration of the string end up being worth more than they really should be, according to your initial description.

[Slartucker]

Also, technically WDDc can be cast more than once, it just doesn't have any effect after the first time.

Also, if WS can count for invis as you used it in the 2nd example, presumably that means D can count for blindness if you leave room on the other hand. right? and a clap could count for things before and after it...

[mikeEB]

Nov 9, 2008 0:31:51 GMT -5 Slartucker said:

The math doesn't add up for me for DFWF. D is part of 3 spells, F is part of 3 spells, W is part of 2 and F is part of 2. That's an average of 2.5. The problem is that you counted both the first and last D for blindness, but you only counted one D for the gesture count. This is a relevant imbalance because it means that spells that overlap beyond one iteration of the string end up being worth more than they really should be, according to your initial description.

The D is part of two different blindness spells.

Also, if WS can count for invis as you used it in the 2nd example, presumably that means D can count for blindness if you leave room on the other hand. right? and a clap could count for things before and after it...

Yes. I mention this in Rule 3 where I say "CWSSWDD with blindness on the second D."

[Slartucker]

Counting 2 blindness spells in that D seems a bit weird since 4 gestures is not even enough to complete a single blindness... eh, whatever.

[mikeEB]

Think of it as this equivalent sequence:
DFWFDFWF
It has the same density as the abbreviated version DFWF, since they're identical. But if you'd rather use the long version, go ahead.

[succat]

what is the meaning of this nonsense?

[Slartucker]

Right, the problem is that in the abstract it works, but only if you ignore the initial and terminal DFWF sequences which would have to exist were an actual warlock doing this in an actual game.

Anyway, I don't see anything better than DFWF that doesn't use para chains.

[toyotami]

I like this: in a more simplified form it could be a valuable exercise for new warlocks to acquire a good concept of efficient spell flow.

Say: how many spells can one hand get out of 10 moves.

and all sorts of other jedi training meditations.

EDIT: If only we had some MASTERS to come up with a good training regiment.

[awall]

Parafdf allows for all kinds of stupid; FD was never intended to be a starting sequence for spells. I find the challenge much more interesting without it. That said, getting anything better than 2.0 is hard.

WSSCWPP = 14/7 = 2.0: Ice Storm(4) + Magic Mirror(2) + Shield(1) + Counterspell(3) + Invisibility(4)
(throwing an extra W after the mirror also gives you 2.0 density, replacing Shield with Protection)
DSFWS = 10/5 = 2.0: Maladroitness(3) + Summon Goblin(3) + Invisibility(2) + Magic Missile(2)
DWPP = 8/4 = 2.0: Counterspell(3) + Blindness(1) + Remove Enchantment(4)
DSFFFC = 12/6 = 2.0: Maladroitness(3) + Paralysis(3) + Disease(6)
WPPSDF = 13/6 = 2.16: Shield(1) + Counterspell(3) + Magic Missile(2) + Charm Person(4) + Cure Light Wounds(3)

Edit: Wow, I started this response before any replies occured. ^^;;
I personally think that the challenge makes plenty of sense. I figure that you just stretch the spell string out indefinitely; with enough iterations, the constant overhead at the beginning goes away. But I'm a programmer, so I'm used to thinking this way.

[mikeEB]

Nov 9, 2008 1:17:11 GMT -5 Slartucker said:

Anyway, I don't see anything better than DFWF that doesn't use para chains.

DFWF only works for ParaFDF. I'm looking mainly for non-FDF sequences, but it was too good an example to pass up.

Nov 9, 2008 1:20:38 GMT -5 awall said:

WWPPSDF = 15/7 = 2.14: Protection(3) + Counterspell(3) + Magic Missile(2) + Charm Person(4) + Cure Light Wounds(3)

Try WPPSDF = 13/6 = 2.167 :Cure Light Wounds(3)+Shield(1)+Counterspell(3)+Magic Missile(2)+Charm Person(4)

[Rycchus]

The only one I got higher than 2.0 apart from PSDDP was PSDFWP = 13/6 = 2.1(6), but this has been mentioned...

Interesting thread though!

Editted once to put in another example and again to take it out as I realised it too had already been mentioned.

[Rycchus]

Nov 9, 2008 0:54:38 GMT -5 Slartucker said:

Counting 2 blindness spells in that D seems a bit weird since 4 gestures is not even enough to complete a single blindness... eh, whatever.

It's meant to be the average over an infinite string, I believe.