Opening P/F vs. S/S

[taliesin]

Sorry, my bad, some sloppy analysis there. Not sure what I was thinking. Always throwing SWD at the para-man reduces you effectively to two 50-50s though. I agree that including "nobody" in the targets does confuse things more than a little, since it opens up the possibility of an instant loss. (SWD at self and para at nobody is as fatal as SWD at nobody and para at you). Will need to think as to how to randomise that correctly, but always going SWD at the para-man is obviously weak.

Now, with the DSF:
DSF and FFF countering both give you another 50-50.
DSF on your opponent while he paralyses you gives you an escape.
DSF on yourself while he self-paralyses also gives you an escape, though he may get a fireball - you can safely clap.
In short, it's a proper 50-50, as is the DPP/clap after it.

So you've got 1/4 with predictably casting Fear at Paraman all of the time, if he knows what you'll do.

Let's weigh up the options beyond that though.

Casting SWD at him: 50-50 chain continues if he self-paralyses, escape if he paralyses the ogre, escape if he paralyses you.
50-50 chain gives you a 75% chance of escape.

Casting SWD at self: escape if he self-paralyses, outright loss if he paralyses the ogre, 50-50 chain continues if he paralyses you.

Casting SWD at nobody:
escape if he self-paralyses, 50-50 chain continues if he paralyses the ogre, outright loss if he paralyses you.

This is going to require a bit of math-crunching. It's above 75%, but exactly how much above 75% will take a chunk of working out. You'll want to select SWD at nobody/yourself sometimes, but I don't know how often yet.

Incidentally

PWPPWP
FFFFFF

SWPPWPPSDF
WPSFWFFFF
gives a fairly clean 1/8 with good strong 50-50s. Our defender can para himself or his opponent with impunity, and the clap/charm 50-50 at the end is likewise safe. I think the continuation is perhaps a little weaker against PWPPS than PS/FW, but not critically so.

Double Ogres
Not sure why you have a W in your analysis vs the double ogres. This looks potentially fatal against your line:


12345678901
PWPPWPFSSSD
FFFFFFFFFPP

SWPPSFW>>
WPSFWPPSDD


Turn 5: first damage of game, paraman down to 13.
Turn 7: Paraman paralyses new ogre (why not? you're countering yourself/the old ogre after all and can't cover it) - down to 11
Turn 8: The "50-50" with the Invis. You get away if he paralyses you and you go PS, or if he paralyses the ogre and you go Pw.
However if you go Pw and he paralyses you, he drops to 7, and 3 the turn after. You have a double death with


12345678901
PWPPWPFSSSD
FFFFFFFFFPP

SWPPSFWWDDC
WPSFWPPWPPC


If he paralyses the ogre and you go PS/>, he drops to 8. You squeeze out 6 damage the turn after, but he jams you into PSDD preventing the clap and kills you.

I think you've a better option though in:

SWPPSFWP
WPSFWPPS


If he paralyses you:
takes 4 damage turn 8, 3 turn 9 - dropping him to 4, and he has to protect the charm, which requires a para on himself he can no longer afford.

If he paralyses an ogre:
He drops to 9 health turn 8. You then get another 50-50 - if you go WPP and he paralyses you, he takes 5 damage turn 9 and cannot defend the charm. If you go WPF and he paralyses the ogre, he drops to 7 health and then has to defend the charm and WPFD on turn 10. In all other cases you die, but it gives you double the survival chances of the PSD/W>> defence.

A reward for those of you who've stuck out reading this all the way to the end:

It's also worth mentioning that

PWPFSSSD
FFFFFFF

SWPPSDD
WPSDF
looks pretty nasty for S/W. If S/W gets caught dummying the initial fear, it gets ugly pretty fast, with just one 50-50 between him and oblivion. I would suggest for this reason that you don't get predictable about trying that particular dummy....

[mikeEB]

I believe that targeting fear at yourself one time in five is correct. If your opponent paralyzes you, you will escape 80% of the time. If your opponent paralyzes himself, you will escape outright 20% of the time, and there is an additional 6 out of 8 chance that you will escape in the subsequent 50-50s, giving a net 80% chance of escape.

I stand by my earlier 80% figure.

As far as I can tell, the only advantage to hitting yourself with fear as opposed to nobody is the ability to surrender cleanly next turn.

EDIT:Hold on, I'm not taking into account the additional edge you get if you mix up targeting yourself with targeting nobody.

You should target him with fear 5/7ths of the time, yourself with fear 1/7th of the time and nobody with fear 1/7th of the time to maximize your chances of escape. If you prefer surrender to death, you should fear self slightly more often. This defense escapes just over 82% of the time.

[taliesin]

If no-one was choosing to aim at nobody, Fear at yourself would be as good as Fear at your opponent. If your opponent self-paralyses, he can't keep the Para and FoD both going and you'll still be able to pull out a DPP or SWD to kill the FoD bit. It would be a true 1/8 for the FoD to go through.

That is to say, your maths are wrong on this, given the assumptions you made. If you cast fear at yourself, and your opponent tries to paralyse you, you get out 3/4 of the time (two 50-50s left). If you cast fear at your opponent and he tries to paralyse you, you escape 100% of the time. If you cast fear at yourself and he tries to paralyse himself, you escape 100% of the time. If you cast fear at your opponent and he tries to paralyse himself, it's back to 3/4 escape. Net result is 2 in 16 of the FoD going through, or 1 in 8.

However, if your opponent aims at nobody (or the ogre), Fear at yourself is fatal, while Fear at nobody leads you down the same procession of 50-50s as the neutralisation of spells would get you. This complicates matters seriously.

[mikeEB]

The 5-1-1 split does take the possibility of aiming at nobody into account. The result is slightly worse than 1 in 8.

[taliesin]

Dec 29, 2008 10:20:44 GMT -5 mikeEB said:

You should target him with fear 5/7ths of the time, yourself with fear 1/7th of the time and nobody with fear 1/7th of the time to maximize your chances of escape. If you prefer surrender to death, you should fear self slightly more often. This defense escapes just over 82% of the time.

You're very nearly right, mike.

Rycchus and I crunched the numbers last night. Rycchus noticed that an extra factor was involved - the DSF "50-50" is also vulnerable to a nothing target. That is to say, if the paralyser aims FFF at nobody and the defender targets DSF at himself, he's screwed. So, only the last 50-50 is a true 50-50, and both the DSF and SWD outcomes can be represented by the following table:

Outcomes are represented as scores for the Attacker first and the defender second. They represent the defender's chance of escape represented as a probability from 0 to 1.
N is the chance of escape assuming the disruptions cancel, and will also be a probability from 0 to 1.

Att/Def	Self	None	Opp
Self	0.0/1.0	0.0/1.0	1-N/N
None	1.0/0.0	1-N/N	0.0/1.0
Opp	1-N/N	1.0/0.0	0.0/1.0

For the DSF case, N is 0.5 - there is a single true 50-50 remaining after cancellation. For the SWD case, N is the final DSF probability.

This can be converted into 3 planes in 3D space and solved for intersection; we did this and extracted the following formulae:

x = ( 1 - N ) / ( 4 - 3N )
z = ( 2 - N² ) / ( 4 - 3N )

x is the frequency with which you should pick nobody, or yourself, instead of targetting your opponent. That is to say, if you're randomising with an RNG which gives you a value between 0 and 1, the band 0 -> x represents picking nobody, x -> 2x represents picking yourself, and 2x -> 1 represents picking your opponent.
z is the guaranteed win percentage - this is the point at which your spellflow absolutely cannot be exploited to lower your odds of success.

Applied to DSF with 0.5, this yields a nice neat 0.2 for x and 0.7 for z.
Applied to SWD with 0.7, this yields a slightly less neat 0.3/1.9 for x, or 0.158, and 1.51/1.9 for z, or 0.795.

Guessing that you'd assumed two 50-50s, I plugged in 0.75 to get your figures of 1/7 and 0.821.

In any case, this seems quite a powerful general-purpose result for "50-50s" in which targetting nobody makes a difference.

Edited: brackets added to disambiguate formulae.

[taliesin]

As the defender, you should target yourself exactly as often as you target nobody. Both win equally against an attacker targeting himself, and are symmetrical in payoff against an attacker targeting you or nobody. The rest of the time you must target your opponent; this will be not less than one-half the time, varying with N.

As the attacker, you should target your opponent exactly as often as you target nobody, and target yourself the rest of the time.

Of course, if you're facing an opponent who is not making use of the ability to target nobody, you don't need to worry about them exploiting your spellflow. As the attacker, if you know the defender will never target nobody, you can use that to exploit their spellflow by solely targeting them or nobody; as a defender, you don't gain anything from targeting nobody unless they're following the strategy just mentioned - i.e. never targeting themselves.