So, what do you think A. should do?

reroll the die with a value of 6? or capture my 8 sided die with a value of 7? The latter
clearly increases the chance I have to reroll my 20-sided die; but if I *do* have to reroll my die, the former has a much better expected value of the lower die.

Or am I giving it away even by phrasing it this way?

(oh, let me point out the previous post was only published today, even though it says "October 30" -- the draft was dumped onto the site way back then, but I didn't get around to reviewing it until just today!)


Viewing Game #621844
This game was last modified on Mon Dec 17, 2007 16:13:27

* Next Turn * Player: Anders *ONE MILLION POINTS* *Fanatic* * Next Turn *
Button Man: Yuranosuke Score: 10 (-22 sides) Rounds Won/Lost/Tied: 1 / 1 / 0 (out of 3 round(s))
Captured Dice: Poison 16-sided die, X Swing 6-sided die

Dice	12-sided die	Focus 12-sided die
Value	6	10
Dice	8-sided die	8-sided die	20-sided die
Value	2	7	20

Player: ElihuRoot *Dead Dude* *Fanatic*
Button Man: Shepherd Score: 43 (22 sides) Rounds Won/Lost/Tied: 1 / 1 / 0
Captured Dice: X Swing 13-sided die, 8-sided die, 4-sided die

Results from last turn:
ElihuRoot is performing a power attack with a 8-sided die showing 2,
targeting Anders's 4-sided die showing 2.

The 8-sided die is rerolled and the new value is 7.

I don't have an absolute answer to this one

I mean, it seems clear to me that G. should either take my speed die, or my 20-sided die showing 11 (is there a case for taking my 12-sided die? I think we can rule out capturing the 20-sided die showing 2.)

I know what I would do, but I'm not sure it's right. I'm sure there *is* a right answer, but can anyone come up with a good bit of reasoning, short of working out the full details?


Viewing Game #613092

Tournament #9596: NFI 1838 - 2 Current Round: Round 6. (organized by kev)

This game was last modified on Tue Oct 30, 2007 21:55:26

Player: ElihuRoot *Dead Dude* *Fanatic*
Button Man: Hale Score: 40 (5.3 sides) Rounds Won/Lost/Tied: 4 / 4 / 0 (out of 5 round(s))
Captured Dice: None

Dice	Speed 8-sided die	12-sided die	20-sided die	20-sided die	S Swing (with 20 sides)
Value	7	12	2	11	15
Dice	6-sided die	6-sided die	Speed 12-sided die	20-sided die	20-sided die
Value	1	1	1	4	6

* Next Turn * Player: Gryphon *Rage* *Fanatic* * Next Turn *
Button Man: Sonia Score: 32 (-5.3 sides) Rounds Won/Lost/Tied: 4 / 4 / 0
Captured Dice: None

Results from last turn:
Rolling Dice...
Determining Initative...
It is Gryphon's turn to go first.

OK, Anders is kicking my butt again... but this still amuses me

I changed the value of one of ander's dice to make this problem more interesting.
which of his dice should I take?

Button Men Game #613905 [MODIFIED]
Tournament Legal challenge, copying communication from game 613499

Skills in this game: X Swing, Speed
Player: ElihuRoot *Dead Dude* *Fanatic*
Your Button Man: Dirgo (20 20 20 X) Score: 26 (-34.6 sides) Rounds Won/Lost/Tied: 0 / 1 / 0 (Out of 3 wins)
Your Captured Dice: 12-sided die, 4-sided die

X Swing (with 20 sides)		20-sided die
13		3 Captured last turn
8-sided die	8-sided die	Speed 20-sided die
3	4	17

Opponent: Anders *ONE MILLION POINTS* *Fanatic*
Button Man: Tamiya (4 8 8 12 z20) Score: 78 (34.6 sides) Rounds Won/Lost/Tied: 1 / 0 / 0
Captured Dice: 20-sided die, 20-sided die, 20-sided die

A similar situation to the last one...

Normally, I'd prefer to wait a while before posting a similar problem -- on the other hand, both of these came up in my games very recently (I do play a lot of Lot5R games). Anyhow:

Should D. use his focus dice to gain the initiative? if so, how?

Viewing Game #613143
Reverse Battle From Game 612932
This game was last modified on Fri Oct 12, 2007 08:26:51

* Next Turn * Player: Desdinova * Next Turn *
Button Man: Naga Score: 25 (8 sides) Rounds Won/Lost/Tied: 2 / 0 / 0 (out of 3 round(s))
Captured Dice: None

Dice	Focus 6-sided die	8-sided die	8-sided die	8-sided die	Focus 20-sided die
Value	3	1	2	8	12
Dice	6-sided die	6-sided die	6-sided die	X Swing (with 4 sides)	X Swing (with 4 sides)
Value	6	6	1	4	1

Player: ElihuRoot *Dead Dude* *Fanatic*
Button Man: Sylvia Branham Score: 13 (-8 sides) Rounds Won/Lost/Tied: 0 / 2 / 0
Captured Dice: None

One of those things I love about Crab

I'm reconstructing this from memory, and the format is not the one usually used with focus-die at the start of the game -- but I think it's clear enough...
[UPDATE: it has been pointed out that, despite the post title, Crab is not one of the buttons in this game! The theme in this position is one I associate so strongly with Crab that, in writing this post, I wound up reflexively invoking her.]

this is from #612930 -- my opponent has the initiative, but I could use my focus dice to seize it. Should I? how? what specifically should I do with my focus dice?

Skills in this game: Focus, X Swing
Player: ElihuRoot *Dead Dude* *Fanatic*
Your Button Man: Naga (f6 8 8 8 f20) Score: 25 (6 sides) Rounds Won/Lost/Tied: 1 / 0 / 0 (Out of 3 wins)

Focus 6-sided die	8-sided die	8-sided die	8-sided die	Focus 20-sided die
5	8	8	3	18
4-sided die	6-sided die	8-sided die	10-sided die	X Swing (with 4 sides)
2	6	7	9	3

Opponent: Desdinova
Button Man: Kitty Cat Seven (4 6 8 10 X) Score: 16 (-6 sides) Rounds Won/Lost/Tied: 0 / 1 / 0

wow, it has been a long time... but here's one.

Sorry, work and life has intruded, and will probably continue to do so.
Still, this position caught my eye, though not because I have any interesting choices --
I'm dead in the water right now, with my shadow dice stuck -- but does Anders have an interesting choice to make? or is it automatic?

Viewing Game #609050
This game was last modified on Mon Oct 8, 2007 21:31:33

* Next Turn * Player: Anders *ONE MILLION POINTS* *Fanatic* * Next Turn *
Button Man: Tonase Score: 26 (1.3 sides) Rounds Won/Lost/Tied: 1 / 2 / 0 (out of 3 round(s))
Captured Dice: 8-sided die, Shadow X Swing 4-sided die

Dice	4-sided die	20-sided die	Focus X Swing (with 4 sides)
Value	2	14	2
Dice	Shadow 4-sided die	8-sided die	Shadow 12-sided die
Value	4	7	11

Player: ElihuRoot *Dead Dude* *Fanatic*
Button Man: The Effster Score: 24 (-1.3 sides) Rounds Won/Lost/Tied: 2 / 1 / 0
Captured Dice: 8-sided die, 4-sided die

Results from last turn:
ElihuRoot is performing a power attack with a 8-sided die showing 7,
targeting Anders's 4-sided die showing 2.

The 8-sided die is rerolled and the new value is 7.

ElihuRoot takes Anders's die.

I botched it here

and I don't mean by playing against Anders! I mean I didn't use Crab's wonderful focus dice correctly. Did I have a better move? or should I have passed?
Viewing Game #607020

Tournament #2440: Samurai! (organized by AdmanB)

I love Samurai, let's play them.

This game was last modified on Tue Sep 4, 2007 10:52:48

Player: ElihuRoot *Dead Dude* *Fanatic*
Button Man: Crab
Score: 35 (0 sides)
Rounds Won/Lost/Tied: 0 / 0 / 0 (out of 3 round(s))
Captured Dice: None

Dice	8-sided die	10-sided die	12-sided die	Focus 20-sided die (dizzy)	Focus 20-sided die
Value	7	9	11	1	19
Dice	8-sided die	10-sided die	12-sided die	Focus 20-sided die	Focus 20-sided die
Value	2	5	12	12	17

* Next Turn * Player: Anders *ONE MILLION POINTS* *Fanatic* * Next Turn *
Button Man: Crab
Score: 35 (-0 sides)
Rounds Won/Lost/Tied: 0 / 0 / 0

Captured Dice: None


Results from last turn:

The Focus 20-sided die showing 14 is turned down to 1.
ElihuRoot turned down his focus dice.
ElihuRoot gained the initative with his Focus Dice.


Anders can now respond with his dice.

not seeing the X for the Y

where X is perhaps trees and Y might be forest; but really what I mean is getting the algebra right, but overlooking the point the algebra is meant to support.


For example, in this basic, algebraic summary of swing die theory, a formula is given. I'm copying it verbatim -- except for adding the bullet points to make the definitions easier to read, adding one clarification, and adding some emphasis on a phrase that I think is mistaken:

Ax<=Bx-Di+3/2*(An)-1/2 where:

• Ax: Player A's swing die size,
  
• Bx: Player B's swing die size
• Di: Player A's initial hand size minus Player B's initial hand size (greater than -1 by definition), [clarification: the intention in this formulation is that this does not include the swing dice of either player]
  
• An: The size of one of Player A's dice which must be kept for him to win. This value can vary from Player A's smallest to largest die, including his swing die. Optimally, Player A wants An to equal his smallest die, while Player B wants An to equal Player A's largest die. However, in practice one must vary An to find the optimal swing die that fits in one's swing range

The formula is certainly a correct, if somewhat ungainly restatement of the familiar two-thirds rule. While the author excludes poison dice, it's not that hard to add them into this (treat them as worth (-1/2) their size, as if captured, for the purpose of computing Di). And "An" could be the sum of two dice just as easily as a single die.

Everyone playing buttonmen should know the basic algebraic relationship between the total number of sides each player starts with and the victory conditions on the game, though you don't necessarily have to phrase it this formally. But the real unanswered question is:

WHAT SHOULD YOU CHOOSE "An" TO BE?

All things being equal (and maybe later I'll discuss the many exceptions to this), you'd like to be able to make Ax (your swing die) as large as possible, so long as you satisfy the inequality. Picking an unrealistically low value for An will needlessly restrict your value for Ax.

Example: if I'm playing slamkrypare (t1 10 10 z12 Y -- I've never actually had the pleasure of playing this button, but it illustrates my point)
vs. say, Kitty Cat Seven (4 6 8 10 X if you prefer, you can think of this as Ngozi)
and let's KCS has set her X swing to x=8 and soundly thrashed you, so you get to reset your
swing die.

if you believe "Optimally, Player A wants An to equal his smallest die", then you'll set An to equal 1 and the above formula (with Bx=8, Di=5) yields Ax <= 8 - 5 + 3/2 - 1/2 = 4. And it IS true that if you set s.'s swing die to X=4 in this matchup, you'll win the game if you capture all of KCS's dice and have at least 1 die uncaptured, whereas, if you picked anything higher for your swing, you would still lose if you captured all of KCS's dice, but had only your 1 sided die left at the end. BUT HOW LIKELY IS THAT TO ACTUALLY OCCUR? In order to win the game with ONLY your 1 sided die left uncaptured, on the penultimate move, your opponent would have had to capture your second-to-last die and rolled a 1 [actually, since your 1 sided die is a trip die here, there are some other possibilities, I suppose -- but the basic point is still valid == the idea that you'd lose all your mid-to-large dice and yet manage to strike the death blow with your littlest die is somewhat unlikely. You are much MORE likely to have one large die left uncaptured after the first few moves that you try to protect and avoid rerolling to keep it out of
range of your opponent. So, if you do the calculation with An = 10 [your next largest die, aside
from the swing die itself], you come up with Ax <= 8 - 5 + 30/2 - 1/2 = 17.5 and setting the swing equal to 17 gives a much more powerful button -- and you still win if you manage to keep any one of your dice (except the 1-sided die). If you are lucky, the 17 will be out of reach of KCS in the beginning; and even if not, she'll have to take it out early and expose herself to your speed die or at least give you a chance to get one of your 10 or 12 sided die out of reach. This example is muddied a bit since the t1 doesn't count for initiative... and setting your Y to 4 will increase your chances of getting initiative from "unlikely" to "somewhat unlikely" [though if someone does a computation or simulation to get hard numbers here, I'll stand corrected]. Anyhow, the same basic principle holds for other buttons; while it's certainly true that I'd like to be able to win with as few dice-sides as possible, I ought to stop to consider what a realistic endgame between these buttons is likely to be. If I'm playing Yeti (10 20 30 30 X) vs. Crab (8 10 12 f20 f20) , the formula above (modified just to account for the fact that Crab has no swing die), tells me I want my X to be <= -20 +(3/2)*An - 1/2 but what is realistic? An = 10 doesn't work, X would have to be negative. An=20 yields X>=9.5, i.e. X=9 is best. An=30 would permit Xn<=24.5, i.e. X=20 would be work. So there are really two options here: set X=9 and try to protect any one of the three big dice 20 30 30; or set X=20 and try to either protect the two big dice 30 30, or keep ANY two dice at the end. It isn't obvious to me which is the better game, though I personally feel more comfortable with the second option.

Max vs. Bluff update

No puzzle here...

irilyth and I played two games of : Max (p12 p12 p20 p20 p30 p30 pX pX)
vs. Bluff (ps6 ps12 16 20 X) to illustrate the subtleties of Swing die choice for Max. When irilyth played Max, he chose X=20. When I played him, I chose... well, what would you pick?

I didn't choose Bluff at random for this test, I thought it would make a good illustration --
I wanted a button that was worth 35 sides or fewer when captured, and Bluff (worth 31 points when fully captured by Max) might actually be easier for Max than a pure vanilla (non-poison) button with that many sides -- Bluff has the offensive capability of 58 sides, which makes it a little easier to get him to swallow big poison. Also Max could find ways to take advantage of the shadow dice, with some effort.

After starting the rounds, I noticed -- to my surprise -- that on the buttonmen.com statistics pages, out of the 11 previous Max vs. Bluff games played on the buttonmen.com website, Max had lost ALL of them -- had I picked a hopeless example?

As it turned out -- and as is so often the case with Max -- the previous statistics were not a good measure of his true capabilities. [Of course, our two games don't constitute absolute proof of anything, either, but I think it was clear from the playing that, while Bluff probably has an advantage over Max, with reasonable play, it's not an overwhelming, green-highlighted-in-the-statistics kind of advantage.]

In our games, Max lost 3-0 when playing with X=20, but won a squeaker when playing with X=... (oh, right, maybe I'll tell you later).

I'm happy to try this one again with anyone -- feel free to challenge me to either side of Max vs. Bluff!

More Max puzzles -- a SINGLE best move in the endgame:

I'm pretty sure I have exactly ONE move that ensures victory here. [other moves may also make victory pretty likely, but there's only one that guarantees it..]

Button Men Game #602955
This game is 'for fun' and does not count for player rankings.
Max has NEVER played Space Girlz? Let's fix that! (and you can challenge me to a reverse match if you like)

Skills in this game: Twin, Weak, Mighty, Ornery, Plasma, Poison, S Swing, Shadow, X Swing
Player: ElihuRoot *Dead Dude* *Fanatic*
Your Button Man: Max (p12 p12 p20 p20 p30 p30 pX pX) Score: -109 (-73 sides) Rounds Won/Lost/Tied: 1 / 1 / 0 (Out of 4 wins)
Your Captured Dice: Plasma {Mighty} Poison 12-sided die, 12-sided die

Poison 12-sided die	Poison 12-sided die	Poison 20-sided die	Poison 30-sided die	Poison 30-sided die	Poison X Swing (with 11 sides)		Poison 20-sided die
9	9	2	1	6	9		4 Captured last turn
Ornery 6-sided die	20-sided die	S Swing (with 6 sides)
6	4	5

Opponent: Gryphon *Rage* *Fanatic*
Button Man: Maya (o6 12 P{hs,H}p12 20 S) Score: 0.5 (73 sides) Rounds Won/Lost/Tied: 1 / 1 / 0
Captured Dice: Poison X Swing 11-sided die, Poison 20-sided die

This is from a current game with Max

But I wanted to wait until the round was over before talking about it.


Note I need G. to swallow 39+ sides of poison in the next two turns in order to win.
He has four choices right now... he must capture with his 20-sided die, but he could capture
either my poison 12-sided die, or either of the poison 20-sided dice, or my poison 30
-sided die [Val 5].

Most people would instinctively take the poison 12-sided die. If he does this, and rolls
anything between 5 and 10, he definitely loses. [I'll capture his 6 sided die with my OTHER 30-sided die, and he'll have to eat the first 30-sided die.]



If he rolls 12 or higher, probably my best chance is again to capture his 6-sided die with my large-valued 30-sided die, and hope it rolls low enough that, after he captures one of my 20-sided dice, he rolls too high and needs to capture ANOTHER. It's not much of a chance [I should calculate these odds!], but it's something


if he rolls an 11, I could either do the same thing as above for 12 and higher, or... and probably a little more likely, I could capture his 6 sided die with my
20-sided die with val 11 and hope to roll ABOVE 11, thus forcing to capture my 30-sided die
this has a 45% chance of success.

if he rolls 1-4, I'm in a bad spot... take the die with one of my 30-sided dice and hope to roll 1-4 myself so his 6 sided die must capture me. only 4/30 of a chance 13.33%
---------------------------
overall, he's in a pretty good position, around 65% chance of victory, maybe a hair less -- but is this best he can do? what if he took a different approach? Presumably he wouldn't take my 30-sided die, but could he do better by taking one of my 20 sided dice? and does it matter which one he takes?


Player: ElihuRoot *Dead Dude* *Fanatic*
Button Man: Max Score: -100 (-64 sides) Rounds Won/Lost/Tied: 1 / 0 / 0 (out of 4 round(s))
Captured Dice: Plasma {Mighty} Poison 12-sided die, Ornery 6-sided die, 12-sided die

Dice	Poison 12-sided die	Poison 20-sided die	Poison 20-sided die	Poison 30-sided die	Poison 30-sided die
Value	9	11	12	27	5
Dice	20-sided die	S Swing (with 6 sides)
Value	12	4

* Next Turn * Player: Gryphon *Rage* *Fanatic* * Next Turn *
Button Man: Maya Score: -4 (64 sides) Rounds Won/Lost/Tied: 0 / 1 / 0
Captured Dice: Poison X Swing 11-sided die, Poison X Swing 11-sided die, Poison 12-sided die

Another endgame position...

Am I better off with the speed attack, or trying to reroll my 12-sided die?

Skills in this game: S Swing, Speed
Player: ElihuRoot *Dead Dude* *Fanatic*
Your Button Man: Hale (z8 12 20 20 S) Score: 50 (-13.3 sides) Rounds Won/Lost/Tied: 1 / 1 / 0 (Out of 5 wins)
Your Captured Dice: 20-sided die, 20-sided die

Speed 8-sided die	12-sided die		20-sided die
5	2		2 Captured last turn
Speed 8-sided die	12-sided die	S Swing (with 6 sides)
8	1	4

Opponent: gauen
Button Man: Hale (z8 12 20 20 S) Score: 70 (13.3 sides) Rounds Won/Lost/Tied: 1 / 1 / 0
Captured Dice: 20-sided die, S Swing 17-sided die, 20-sided die

No news is ... well, no news

Ack, sorry, real life has intruded and it may be hard to keep this up for the next week or so -- but I am quite interested in accepting submissions -- either positions that came up in a game that you found particularly interesting, or particular aspects of the game about which you have something to say, or about which you'd like to see if I have anything to say.

I notice, by the way, that Max has never played the Space Girlz buttons on buttonmen.com [except for the one game I am currently playing]. I think these could actually be potentially interesting games. For example: Max vs. Maya [which is the game currently going on] -- how do you think Maya should set her plasma die? and what about Max's Swing die? You can see the choices we are currently trying at the link above..

I still think Max is much stronger than his statistics give him credit for being (though I might not go so far as to call him "strong" in an absolute sense -- but way better than 30%). There are certainly specific buttons he can't possibly beat, and there are some buttons to which he can't possibly lose, but for most of the middle, he could do better than people think if he's played correctly -- but it's subtle!

[Not so subtle part] In almost every game, Max will sweep the other button's dice off the field, the real question is how much poison he can make it eat before it goes -- so the object of the game is to set the swings properly so the amount of poison is achievable, then, make moves to force a sufficient amount of poison to be eaten.

In some sense, this is no different than any other matchup -- Buttonmen is always about knowing your victory conditions, and making moves most likely to push the game towards those conditions -- but with Max, that tends to mean finding ways to force your opponent to take at least one large poison die -- and that seems very different than the usual buttonmen plan:
if you take his small dice first and his big dice roll LARGE, they'll have too much choice and can take your smallest poison before they die -- but if you take his big dice first, his small dice may roll too low and get to pass alltogether!

Almost always, you want to have at least one of your larger dice roll lower than at least one of your small dice. With so many big poison, there's a good chance at least one of them will roll moderately low; then it's a matter of forcing its capture.

But this is all pretty vague, illustrative game positions would help -- and I don't have time to construct them right now, maybe I should set up a lot of challenges with Max to try to generate a few.

another messy position

I don't think I can prove my next move right -- and I'm prepared to believe I'm wrong -- but I do think it's an interesting choice.

Button Men Game #591452
This game is 'for fun' and does not count for player rankings.
Arena Game: Random BM from Majesty

Skills in this game: X Swing

Player: ElihuRoot *Dead Dude* *Fanatic*
Your Button Man: Yeti (10 20 30 30 X) Score: 36 (-16 sides) Rounds Won/Lost/Tied: 2 / 2 / 0 (Out of 3 wins)
Your Captured Dice: None

10-sided die	20-sided die	30-sided die	X Swing (with 12 sides)		30-sided die
5	16	10	10		11 Captured last turn
4-sided die	4-sided die	12-sided die	X Swing (with 20 sides)	X Swing (with 20 sides)
4	3	7	9	9

Opponent: kleric *Ninja Boy* *Fanatic*
Button Man: Nerni (4 4 12 X X) Score: 60 (16 sides) Rounds Won/Lost/Tied: 2 / 2 / 0
Captured Dice: 30-sided die

Once again, I'm in trouble...

Is there *ANY* way to win this round? What would have to happen? Is there something I can do to maximize even the remote possibility of it happening?

Skills in this game: Doppleganger, Poison , Shadow, V Swing, X Swing
Player: ElihuRoot *Dead Dude* *Fanatic*
Your Button Man: Jellybean (p20 s20 V X) Score: -5 (-38 sides) Rounds Won/Lost/Tied: 1 / 0 / 0 (Out of 3 wins)
Your Captured Dice: Doppleganger 12-sided die

Poison 20-sided die	V Swing (with 6 sides)		X Swing (with 20 sides)
12	5		12 Captured last turn
Doppleganger 4-sided die	Doppleganger 6-sided die	Doppleganger 10-sided die	Doppleganger X Swing (with 4 sides)
1	4	9	2

Opponent: devious
Button Man: Envy (D4 D6 D10 D12 DX) Score: 52 (38 sides) Rounds Won/Lost/Tied: 0 / 1 / 0
Captured Dice: Shadow 20-sided die, X Swing 20-sided die

second friday quickie.

I'm in bad shape here; and I'm completely dead unless I reroll my turbo and capture one of his shadow dice... but to what size should I set the turbo?

Player: ElihuRoot *Dead Dude* *Fanatic*
Your Button Man: Zeppo (4 12 20 X!) Score: 28 (-13.3 sides) Rounds Won/Lost/Tied: 1 / 2 / 0 (Out of 3 wins)
Your Captured Dice: X Swing 20-sided die, 4-sided die

4-sided die	X Turbo Swing (with 4 sides)		20-sided die
2	1		18 Captured last turn
2-sided die	Shadow 10-sided die	Shadow 20-sided die
1	9	15

Opponent: theAlmighty *heavenly*
Button Man: Merlin (2 4 s10 s20 X) Score: 48 (13.3 sides) Rounds Won/Lost/Tied: 2 / 1 / 0
Captured Dice: 12-sided die, 20-sided die

2 friday quick ones... #1

What do you think? should I take the speed-12, or the speed-X4. Is it worth it to increase the chance he
can take my 10-sided die (by only 10%) to eliminate the chance that his speed-12 will roll higher than 10?


Player: ElihuRoot *Dead Dude* *Fanatic*
Your Button Man: Reaver (4 10 10 12 pX) Score: 12 (-11.3 sides) Rounds Won/Lost/Tied: 2 / 1 / 0 (Out of 3 wins)
Your Captured Dice: Speed 12-sided die

10-sided die	10-sided die	Poison X Swing (with 10 sides)		4-sided die
10	10	1		1 Captured last turn
Speed 10-sided die	Speed 12-sided die	Speed X Swing (with 4 sides)
2	2	3

Opponent: Desdinova
Button Man: Morgan (z10 z12 z12 zX) Score: 29 (11.3 sides) Rounds Won/Lost/Tied: 1 / 2 / 0
Captured Dice: 12-sided die, 4-sided die

OK, last post on that BMAI game

Though I did save one more position, it would wreck the continuity to put it here.
Again, maybe this one is too easy, it certainly yields to direct computation very quickly.

I have several possible moves, but one is much better than all the others.


Button Men Game #601416
Play the AI! You will be assimilated and stuff.

Skills in this game: Poison, Shadow, V Swing, X Swing

Player: ElihuRoot *Dead Dude* *Fanatic*
Your Button Man: Lucky (6 10 p12 20 X) Score: 25 (18.3 sides) Rounds Won/Lost/Tied: 2 / 0 / 0 (Out of 3 wins)
Your Captured Dice: Shadow 20-sided die, X Swing 4-sided die

6-sided die	Poison 12-sided die	20-sided die		X Swing (with 4 sides)
2	1	20		2 Captured last turn
Poison 20-sided die	V Swing (with 7 sides)
4	1

Opponent: bmai *AI* *111111101001000001100 as of 9-22-03*
Button Man: Jellybean (p20 s20 V X) Score: -2.5 (-18.3 sides) Rounds Won/Lost/Tied: 0 / 2 / 0
Captured Dice: 10-sided die, X Swing 4-sided die

OK, a little later in the same round with bmai

Maybe this one's too easy --there's only one move with any chance of winning [a good chance of winning, in fact], and it's not too hard to see just by checking the score. But I didn't say they'd all be hard!


Skills in this game: Poison, Shadow, V Swing, X Swing
Player: ElihuRoot *Dead Dude* *Fanatic*
Your Button Man: Lucky (6 10 p12 20 X) Score: 6 (-15.3 sides) Rounds Won/Lost/Tied: 0 / 0 / 0 (Out of 3 wins)
Your Captured Dice: Shadow 20-sided die, Poison 20-sided die

6-sided die	10-sided die	Poison 12-sided die		20-sided die
1	8	2		6 Captured last turn
V Swing (with 6 sides)	X Swing (with 4 sides)
2	1

Opponent: bmai *AI* *111111101001000001100 as of 9-22-03*
Button Man: Jellybean (p20 s20 V X) Score: 29 (15.3 sides) Rounds Won/Lost/Tied: 0 / 0 / 0
Captured Dice: X Swing 4-sided die, 20-sided die

BMAI is not in a good position at the moment...

the odds are he (it?) won't be able to win this round, but it does still have some chance of winning this round, right? what should it do?

* Next Turn * Player: bmai *AI* *111111101001000001100 as of 9-22-03* * Next Turn *
Button Man: Jellybean Score: -15 (-28.6 sides) Rounds Won/Lost/Tied: 0 / 0 / 0 (out of 3 round(s))
Captured Dice: None

Dice	Poison 20-sided die	V Swing (with 6 sides)	X Swing (with 4 sides)
Value	3	2	4
Dice	6-sided die	10-sided die	Poison 12-sided die	20-sided die	X Swing (with 4 sides)
Value	1	8	2	13	3

Player: ElihuRoot *Dead Dude* *Fanatic*
Button Man: Lucky Score: 28 (28.6 sides) Rounds Won/Lost/Tied: 0 / 0 / 0
Captured Dice: Shadow 20-sided die

I think 2-3 posts per week is all I can consistently manage -- what should D. have done?

I'll do my best to post a puzzle when I can; I also want to go back and offer some comments and replies on older puzzles (though it's probably best that I don't give my own opinions too soon). Finally, I need to write a few more detailed strategy essays (like telling you what that essay left out about Crab)

In the meantime, here's something from a recent game. (say, challenge me to a match to help me generate more of these situations! Pick whatever buttons you think lead to interesting problems. I don't care about the odds, I'll take either side, though if you give me a ridiculously outmatched button, I'd mildly prefer the match to be "just for fun" -- or we can play both the game and the reverse match.)

In the game below, Desdinova just made a power attack that, unfortunately for him, rolled high enough for me to recapture it with my own 20-sided die -- on the other hand, it forces me to reroll that die and puts it at risk. He could still eke out a tie. (actually, if I reroll a 2, I suppose there's a chance he might win!) Was there a better move D. could have made?



Button Men Game #600869
Tournament Legal challenge, copying communication from game 600484

Skills in this game: Poison, Shadow, X Swing

Player: ElihuRoot *Dead Dude* *Fanatic*
Your Button Man: Caine (ps4 ps4 s20 s20 sX) Score: 26 (8 sides) Rounds Won/Lost/Tied: 0 / 1 / 0 (Out of 3 wins)
Your Captured Dice: 16-sided die, X Swing 4-sided die

Poison Shadow 4-sided die	Shadow 20-sided die		Shadow X Swing (with 4 sides)
3	17		4 Captured last turn
Poison Shadow 6-sided die	Poison Shadow 12-sided die	20-sided die
1	1	18

Opponent: Desdinova
Button Man: Bluff (ps6 ps12 16 20 X) Score: 14 (-8 sides) Rounds Won/Lost/Tied: 1 / 0 / 0
Captured Dice: Shadow 20-sided die, Poison Shadow 4-sided die, Shadow X Swing 4-sided die

Results from last turn

Desdinova is performing a power attack with a 20-sided die showing 10, targeting ElihuRoot's Shadow X Swing 4-sided die showing 4. The 20-sided die is rerolled and the new value is 18. Desdinova takes ElihuRoot's die.

From a game today -- what would you do?

Maybe this is obvious, but I do think there's a point worth making here, too.


Should I take his die with value 17 using mine with value 18? Should I take his
die with value 9 using mine with value 10? Any other bright ideas?

Button Men Game #600484
Reverse Battle From Game 599998

Skills in this game: Option, X Swing
Player: ElihuRoot *Dead Dude* *Fanatic*
Your Button Man: Aylee (8 10/20 12 12/20 20) Score: 50 (5.3 sides) Rounds Won/Lost/Tied: 2 / 0 / 0 (Out of 3 wins)
Your Captured Dice: 20-sided die

8-sided die	12-sided die	Option 12/20 (with 20 sides)	20-sided die		Option 10/20 (with 20 sides)
4	4	10	18		6 Captured last turn
20-sided die	20-sided die	X Swing (with 4 sides)
17	9	4

Opponent: Desdinova
Button Man: Dirgo (20 20 20 X) Score: 42 (-5.3 sides) Rounds Won/Lost/Tied: 0 / 2 / 0
Captured Dice: Option 10/20 20-sided die

a little later in the same round as one of Friday's posts

D's turn is coming up, and he has to take my 20-sided die with a value of 1. Which die should he take it with? This is pretty straightforward, isn't it? You can go through the computation
to get the exact chance of winning with each decision, but is there a general principle you can extract that would allow you to more easily figure out the best move in similar situations?

Button Men Game #599998
Tournament Legal challenge, copying communication from game 599661

Performing a power attack
ElihuRoot is performing a power attack with a 20-sided die showing 9,
targeting Desdinova's 12-sided die showing 7.

The 20-sided die is rerolled and the new value is 14.

ElihuRoot takes Desdinova's die.

Your Dice:	Opponent's Dice:
20-sided die showing 14 20-sided die showing 1	8-sided die showing 6 Option 10/20 10-sided die showing 7

Rounds Won/Lost/Tied: 1 / 0 / 0 (Out of 3 wins)
Your Score: 72 (15.3 sides)
Opponent's Score: 49

What's Zegota's best move?

OK, this is an easy one, isn't it?

What should he do? What are his chances of winning?

Player: Zegota, score: 41 (-0.6 sides)
capture dice: 20-sided die, focus X-swing (with 15 sides)

Dice	4-sided die	8-sided die
Value	4	3
Dice	4-sided die	4-sided die	8-sided die
Value	4	1	2

Player: ElihuRoot, score 42 (0.6 sides)
captured dice: 4-sided die, 20-sided die, focus X-swing (with 10 sides)

here's the filler:

Button Men Game #309173
Tournament #5695: #32
Current Round: Round 3. (organized by bowler190)

Tonase vs. Tonase

Rounds Won/Lost/Tied: 2 / 2 / 0 (Out of 3 wins) (for both of us, obviously)
Most recent move:
ElihuRoot is performing a skill attack with a 4-sided die showing 2 and a 8-sided die showing 2, targeting Zegota's 4-sided die showing 4.

The 4-sided die is rerolled and the new value is 1.
The 8-sided die is rerolled and the new value is 2.

ElihuRoot takes Zegota's die.

Speed dice #1: Does this article on "countering speed dice" make any sense at all?

I almost thought we were playing a different game!

http://www.cheapass.com/bpu/strategy6.html

I think this article may have been written before the growth of the buttonmen.com web game -- back when people thought Tirade was really strong, etc. But still, the notion that what you want are lots of dice of different sizes! There MIGHT be something to the idea that you want
to get initiative: any speed attack your opponent can make is also a skill attack you can make on her, if you go first --Bunnies is actually a pretty good button against recipes with speed dice, both since it will get initiative and because the dice don't change when you reroll them.

Still, your main hope in defanging Bennett is that you won't be a target -- and if all your dice are large, it's much less likely that they'll be vulnerable to a massive speed attack.

Forgetting poison, etc, for the moment, look at Bennett's record against Soldiers buttons:
Bennet wins against all of them, but there's a big difference between winning 56% of his
games, or even 59%, and winning 76% or more. Admittedly, I suspect
Changeling, in particular, is not well-played against Bennett -- maybe all of these numbers would be a little lower with better play (I think Bennett is much easier to play in all these matchups than his opponent) -- I'll also confess to being a little puzzled by Kublai's relatively good showing on this list - maybe it's that "disparate dice" thing!

Hammer (Soldiers)	78/61 = 139	56.11%
Kublai (Soldiers)	13/9 = 22	59.09%
Shore (Soldiers)	58/40 = 98	59.18%
Karl (Soldiers)	16/8 = 24	66.66%
Changeling (Soldiers)	13/4 = 17	76.47%
Iago (Soldiers)	24/7 = 31	77.41%
Avis (Soldiers)	51/12 = 63	80.95%
Stark (Soldiers)	56/14 = 70	80%
Bauer (Soldiers)	19/4 = 23	82.6%
Clare (Soldiers)	32/7 = 39	82.05%
Hannah (Soldiers)	20/4 = 24	83.33%
Niles (Soldiers)	21/3 = 24	87.5%
Kith (Soldiers)	14/1 = 15	93.33%

And note that Giant, whose overall record against ALL buttonmen is about 56%, does nearly that well against Bennett:

Giant (Brom)

51/42 = 93

54.83%

And Yeti does BETTER against Bennett than its overall record of about 60%:

Yeti (Majesty)

52/146 = 198

26.26%

(though the question there might be what percentage of these Yeti-Bennett games were played by Anders as this is pretty close to HIS average value with Yeti...)


aside from what button to play, there's also the question of how to play the button against speed dice -- of course, all things being equal, you want to try to take speed dice early, though small speed dice may not be that big a threat. And you want to be very alert when rolling your dice how much risk you are exposing yourself to -- you want to minimize the chance that you roll into a speed attack. That usually means you'd prefer to roll as few dice as possible and you are alert to the values on your unrolled dice -- ideally they add up to as few threatening values as possible. Some illustrations might make this more clear, but I'll either have to construct
them or play a bunch of games against speed dice to generate examples.

Am I in good shape here? What should I do?

Maybe the next move is obvious here... but do you think I'm in a good position in this game?

Button Men Game #599998
Tournament Legal challenge, copying communication from game 599661

Skills in this game: Option, X Swing
Player: ElihuRoot *Dead Dude* *Fanatic*
Your Button Man: Dirgo (20 20 20 X) Score: 50 (3.3 sides) Rounds Won/Lost/Tied: 1 / 0 / 0 (Out of 3 wins)
Your Captured Dice: Option 12/20 20-sided die

20-sided die	20-sided die	20-sided die		X Swing (with 20 sides)
9	10	1		18 Captured last turn
8-sided die	Option 10/20 (with 10 sides)	12-sided die	20-sided die
3	2	5	8

Opponent: Desdinova
Button Man: Aylee (8 10/20 12 12/20 20) Score: 45 (-3.3 sides) Rounds Won/Lost/Tied: 0 / 1 / 0
Captured Dice: X Swing 20-sided die

Did you ever see this article on buttonmen strategy?

It's very pretty! And I do understand that there's a world of Legend of the Five Rings outside of buttonmen (though I have no idea what it's all about -- how could it possibly be as interesting as buttonmen, anyway?). And I'm not *necessarily* objecting to how wordy it is, or how much time is spent saying the obvious (I'm known for doing that, myself).

But.. but... but... some of it isn't true -- and see what he says about my beloved Crab! He doesn't understand her at all!

http://www.geocities.com/stormson_2000/buttonmen.html#strategy

Maybe I'll have to do some Crab examples -- but I don't have any saved (I've sort of been cleaning out my garbage pile this week -- well, it's more of an archaeological excavation, I suppose. These are snippets and situations, not necessarily deep, that I happened to have saved temporarily at the time of the game, but forgot to delete them. )

This one may be harder to agree on:

The previous examples I posted were all at or near the end of the game -- which gives us the ability to actually compute the exact probability of winning -- or at least make a pretty decent approximation. It's harder (for me, at least), to be so precise at the beginning of a turn.


Game #166629 from June 2003, and something called "IBMF (provisional)" -- I had to search the message boards to remember what that was!

Anyway, it's the start of the last round of the game, I have the initiative -- but what do you think I should do? I know what I *did*, and I have my reasons, but I'm not going to promise you it was the right thing to do.

Player: randomlife *Fanatic* *Pesky* *Teen Girl Squad*
Button Man: Sailor Mercury Score: 23 (10.6 sides)
Rounds Won/Lost/Tied: 2 / 2 / 0 (out of 3 round(s))
Captured Dice: None

Dice	4-sided die	8-sided die	8-sided die	12-sided die	10-sided die	4-sided die
Value	3	7	8	2	8	4
Dice	10-sided die	Poison 20-sided die	20-sided die	20-sided die	X Swing (with 4 sides)
Value	10	9	20	9	1

* Next Turn * Player: ElihuRoot *Fanatic* *Dead Dude* * Next Turn *
Button Man: Crusher Score: 7 (-10.6 sides)
Rounds Won/Lost/Tied: 2 / 2 / 0
Captured Dice: None

Is this an interesting position?

(Again, I don't think I'll be maintaining this pace of posting in the future).

I can't tell if this one is obvious or not -- insert favorite math joke here. It's still a somewhat similar idea.


OK, in this game, it's DanaMorrigan's turn to move. Her move is forced, she's going to have to take my Stinger 8-sided die with her X Swing 7-sided die. What's the best thing I can do in response? (Of course, it might depend on what she rolls -- she might even roll a 7, too high for me to catch it with my own X swing...). What are my chances of winning in the worst case? What is the worst case?

Player: ElihuRoot *Dead Dude* *Fanatic*
Button Man: Buck Score: 53.5 (8.6 sides) Rounds Won/Lost/Tied: 2 / 2 / 0
Captured Dice: 20-sided die, 12-sided die, Stinger 8-sided die

Dice	Stinger 8-sided die	Stinger 10-sided die	X Swing (with 9 sides)
Value	3	8	6
Dice	Stinger 10-sided die	X Swing (with 7 sides)
Value	1	4

* Next Turn * Player: DanaMorrigan *Dagda* *Ms. Funny Pants* * Next Turn *
Button Man: Buck Score: 40.5 (-8.6 sides)
Rounds Won/Lost/Tied: 2 / 2 / 0 (out of 3 round(s))
Captured Dice: 20-sided die, 12-sided die

What's gryphon's best move?

Granted these very-near-the-end positions are perhaps too straightforward, if you stop and compute what to do. But how many people do that consistently?

And is this situation any muddier? Would you take my 10-sided die or my 20-sided die? Does it make much difference?

* Next Turn * Player: Gryphon * Next Turn *
Button Man: CynCyn Score: 34 (3.3 sides)
Rounds Won/Lost/Tied: 0 / 1 / 0 (out of 3 round(s))
Captured Dice: 12-sided die, 6-sided die

Dice	6-sided die	20-sided die	6-sided die
Value	3	20	1
Dice	10-sided die	20-sided die
Value	9	6

Player: ElihuRoot *Fanatic* *Dead Dude*
Button Man: Sailor Jupiter Score: 29 (-3.3 sides) Rounds Won/Lost/Tied: 1 / 0 / 0
Captured Dice: Doppleganger 10-sided die, X Swing 4-sided die

Results from last turn:
ElihuRoot is performing a power attack with a 20-sided die showing 10,
targeting Gryphon's X Swing 4-sided die showing 4.

The 20-sided die is rerolled and the new value is 6.

What's my opponent's best move?

Don't expect so many of these, in general! Maybe I can post two or three a week, normally.

Here's another one, maybe it's a similar theme to the last one -- maybe not! This is from a long time ago, I don't really know why I saved this position to my online notes -- and I didn't have the graphics, so pardon my quick and sloppy attempt to make it look a little like the game screen.

It was game 167611 from tournament 4706. I had BANG (p(4,4), 6, 12, 12, X), my opponent, SG_1, was playing AGATHA (4, 6, (8,8), 20, X). It's the first round, first my X swing was set to 4, his was set to 20. I had just performed a skill attack with a 6-sided die showing 3 and a X Swing 4-sided die showing 1, targeting SG_1's 6-sided die showing 4. after the reroll, things looked [something] like this:

Me: ElihuRoot
My Button Man: Bang (p(4,4), 6, 12, 12, X) Score: 39 (2 sides)
Rounds Won/Lost/Tied: 0 / 0 / 0 (Out of 3 wins)
My Captured Dice: (8,8) twin die, 6-sided die, X Swing die (20 sides)

ice	Poison Twin Die (Both with 4 sides)	6-sided die	X Swing (with 4 sides)
Value	2	5	1
Dice	4-sided die	20-sided die		6-sided die
Value	4	16		(4) captured last turn

Him: SG_1
His Button Man: Agatha (4, 6, (8,8), 20, X) Score: 36 (-2 sides)
Rounds Won/Lost/Tied: 0 / 0 / 0 (Out of 3 wins)
His captured dice 12-sided die, 12-sided die

So: what should he do? He has five possible power attacks, two with the 4-sided die and three with the 20-sided die.

OK, here's a sample "what's the best move?"

Maybe this isn't the best example, but it just came up online in a game I was playing. I'm pretty sure I made the "best" move under these circumstances, what do you think it was?

So: In the below situation, you are me ("ElihuRoot"). [And, for those unfammiliar with buttonmen.com notation, the 20-sided die on the top right has just been captured by Anders]. You have eight different possible power attacks, and one possible skill attack. What is the move that maximizes your probability of winning this round?


Button Men Game #599271

Skills in this game: Reserve
Player: ElihuRoot *Dead Dude* *Fanatic*
Your Button Man: Diamond (4 6 12 20 r8 10 r10 20) Score: 52 (1.3 sides) Rounds Won/Lost/Tied: 1 / 2 / 0 (Out of 3 wins)
Your Captured Dice: 20-sided die, 12-sided die

4-sided die	6-sided die	20-sided die	10-sided die		20-sided die
3	3	17	10		1 Captured last turn
6-sided die	10-sided die	20-sided die
6	1	19

Opponent: Anders *ONE MILLION POINTS* *Fanatic*
Button Man: King Endymoin (6 10 20 20 r6 r10 12 r20) Score: 50 (-1.3 sides) Rounds Won/Lost/Tied: 2 / 1 / 0
Captured Dice: 12-sided die, 20-sided die