Do we have a dirty trick handbook?

[JaronK]

Callix and JaronK, what build are we trying to get a probabilistic bound on number of attacks for? And Callix, have you tried computing the variance on it?

The basic build, IIRC, was Fighter 2/Warblade 10/Disciple of Dispater 8 with a pair of Aptitude Kukris, using TWF, ITWF, GTWF, Weapon Focus (Light Mace) Lightning Mace, Improved Unarmed Strike, Roundabout Kick, and Improved Critical (Kukri), plus the prerequisites for DoD.  Because of the Aptitude enchantment, Lightning Mace and Roundabout Kick apply to your Kukris, so you critically hit on a 9-20, and every critical threat gives you an extra attack, plus every confirmed critical gives you an extra attack.  As such, you've got a 55% chance with each attack to get an extra attack from the critical threat, and then if that triggers you've got a 95% chance to get a second additional attack, assuming you hit on a 2+ (which, with Blood in the Water, is extremely likely).  Using Dancing Mongoose helps a bit as well.

Now, this particular mathmatical problem is already notorious for screwing with summations.  A similar problem is the doubling quarter flip game.  Let's say I make a gambling game, and I tell you that you have to give me some money, and then you flip coins.  If you get tails, game over and you lose.  If you flip and get heads and then get tails, I give you $1.  If you flip and get heads, then heads, then tails I give you $2.  If you get three heads and then tails I give you $4.  If you get four heads and then tails I give you $8, and so on.  How much money would you expect to win, and thus what's the most amount of money you should give me and still expect to come out ahead?

Well, if you do it the normal way, you have a 1/2 chance to win nothing.  You have a 1/4 chance to win $1, a 1/8 chance to win $2, a 1/16 chance to win $4, etc... that comes out to 25 cents + 25 cents + 25 cents, etc all the way to infinity, suggesting that your average pay out is infinite, and thus you should happily give me $100 play my game, and if we play enough times you'll be rich indeed.  However, the actual average payout is around $11, IIRC, if you just run it in simulations.  It's a really interesting mathmatical thing.

JaronK

[Callix]

Callix and JaronK, what build are we trying to get a probabilistic bound on number of attacks for? And Callix, have you tried computing the variance on it?

The build is JaronK's "potentially endless attacks" one at Gleemax: Swashbuckler 1/Warblade 2/Lion Totem Barbarian 1/Fighter 8/Disciple of Dispater 8 with Roundabout Kick, Lightning Mace, Improved Critical, TWF, ITWF, GTWF, and a few other feats, using Blood in the Water and the Whirling Frenzy variant. Use a pair of aptitude kukris, and you generate two attacks per attack 52.25% of the time, one attack per attack 2.75% of the time, and you don't generate 45% of the time.

We're all fairly sure that the mean is infinite, so finding the variance is not an option. We're looking for a proof as to whether the median is finite or infinite. Series calculations show that the number of attacks should diverge the majority of the time, while there's some theorem or other about random walks that claims it's impossible for this to diverge. IIRC, Omen of Peace said that any average velocity on a random walk would make the system transient, meaning that the probability of divergence would be non-zero, but I really don't know much about random walks.

Also, JaronK, if you use that coin-flipping example and sum the probability of termination, you get the sum of (1/2) x (1/2)^H from H=0 to infinity. This is (1/2)/(1-(1/2)) = 1. So for a fair distribution, series and random walks agree. The question is whether it's supposed to apply when it isn't a fair distribution.

[JaronK]

Ah yes, that was the exact build I used... I had forgotten.

But yeah, it's weird, and if we could get the calculations exactly right it should be possible to get a median that's high but non infinite by making just the right build.

JaronK

[EjoThims]

And Eco: I was saying we can't increase the attacks much more, precisely because the goal is to avoid going infinite.  Increasing much over this definitely results in infinity, which you get with the Warmind version of this.

Why not go infinite? You'd at best have a set average number of triggered attacks each round, while your granted would still be super low.

[JaronK]

Well, going infinite means it's just a more complicated version of doing something that's already trivially easy (doing infinite damage).  The trick is to get the maximum possible average finite attacks... that's actually a challenge.

JaronK

[Omen of Peace]

Omen of Peace said that any average velocity on a random walk would make the system transient, meaning that the probability of divergence would be non-zero.

Indeed. At this point you mostly have to trust me except if you want to pick up a book on Markov chains & random walks. Perhaps I can point you to some online course notes at some point.

Using the numbers you gave (52.25, etc...), I can bound the probability P that the sequence will end :
(0.45/0.55)^A < P < (0.475/0.525)^A
where A is the initial number of attacks. (It probably wouldn't be too hard to figure out the exact proability but I don't really want to spend time on it.)

By choosing a low A (1, 2 or 3) you can get a finite median, but since the mean is always going to be infinite I personally don't see the point.

[JaronK]

In the end, it's a thought excercise that's fun to play with, really.  That's the point, in the end.  After all, if we just wanted infinite damage or something, Crusader gets us there.

Speaking of which, has the Crusader infinite damage trick been mentioned in this thread yet?

JaronK

[Prime32]

Minor dirty trick:

Play a druid. Craft a club or quarterstaff out of livewood (Eberron CS). Enchant it as a +1 sizing weapon. Get drawmij's instant summon or a similar effect on it.

When things get rough, turn the club Colossal, drop it, then cast transport via plants. When you arrive at your destination, summon the stick after you.

[Archmage Joda]

How did that psionic sandwich thing go again?

[Kuroimaken]

In the end, it's a thought excercise that's fun to play with, really.  That's the point, in the end.  After all, if we just wanted infinite damage or something, Crusader gets us there.

Speaking of which, has the Crusader infinite damage trick been mentioned in this thread yet?

JaronK

I believe it was, but I already forgot about it.

What about dirty tricks with spells? Not necessarily the shady ones, but the regular, core spells, for instance. I know there's a lot of shit one can do with Gate, for example...

[PhaedrusXY]

Minor dirty trick:

Play a druid. Craft a club or quarterstaff out of livewood (Eberron CS). Enchant it as a +1 sizing weapon. Get drawmij's instant summon or a similar effect on it.

When things get rough, turn the club Colossal, drop it, then cast transport via plants. When you arrive at your destination, summon the stick after you.

to a plant of the same kind in a single round

How would that work? Is Livewood a species of plants? Would you only be able to transport to another Collossal Livewood +1 Sizing Quarterstaff?

[Sunic_Flames]

Even if it did, leave one at home.

[Omen of Peace]

How did that psionic sandwich thing go again?

In short : have an arcanist cast Polymorph Any Object on a sandwich to change into a creature (one not immune to mind-affecting effects), manifest Mind Switch to get the creature's body, have the mage dismiss PAO and destroy your old body.
(You lose a level, so typically you want to take extra steps to get it back.)

[Kuroimaken]

In short : have an arcanist cast Polymorph Any Object on a sandwich to change into a creature (one not immune to mind-affecting effects), manifest Mind Switch to get the creature's body, have the mage dismiss PAO and destroy your old body.
(You lose a level, so typically you want to take extra steps to get it back.)

Use something better than a FREAKING SANDWICH!

[Vidar]

In short : have an arcanist cast Polymorph Any Object on a sandwich to change into a creature (one not immune to mind-affecting effects), manifest Mind Switch to get the creature's body, have the mage dismiss PAO and destroy your old body.
(You lose a level, so typically you want to take extra steps to get it back.)

Use something better than a FREAKING SANDWICH!

I'm affraid you are talking nonsense, good sir!

[Kuroimaken]

I'm affraid you are talking nonsense, good sir!

Original idea involved becoming a sandwich. There was a pretty big thread at Failmax on how many better things you could become, including a working template for being Alphonse Elric.

[Callix]

In short : have an arcanist cast Polymorph Any Object on a sandwich to change into a creature (one not immune to mind-affecting effects), manifest Mind Switch to get the creature's body, have the mage dismiss PAO and destroy your old body.
(You lose a level, so typically you want to take extra steps to get it back.)

Use something better than a FREAKING SANDWICH!

That was the one thread I got in the SurrealDex. It was literally titled "Improvements on a Sandwich". The main trick was to turn yourself into armor and be worn. It's virtually impossible to destroy worn armor in 3.5.

The best build was Telepath, using the Telepathy ACF and Mindsight, and using Astral Seed to make the mind switch permanent.

[Vidar]

I'm affraid you are talking nonsense, good sir!

Original idea involved becoming a sandwich. There was a pretty big thread at Failmax on how many better things you could become, including a working template for being Alphonse Elric.

Yes, but think about it. We're talking about what's best. Full Sandwich Alchemist with a sandwish as brother instead of an armor would have been at least 10 times as good as a show!

[Omen of Peace]

There was a pretty big thread at Failmax on how many better things you could become, including a working template for being Alphonse Elric.

None of which had as much impact as becoming a sandwich. That's the stuff of legends.

edit: +1 to Vidar's post, I guess.

[Kuroimaken]

None of which had as much impact as becoming a sandwich. That's the stuff of legends.

edit: +1 to Vidar's post, I guess.

Except for a really, really sucky grapple modifier, or defense versus bites!

On the upside, sandwiches do not need sleep. (They might need refrigeration, though.)