Re: [risk] defending vs attacking?

[Bob Harris <nitlion@mindspring.com>]

> There is currently no difference in attack vs. defense, but
> *should* their be?

In my opinion, yes.  That's one of the features that makes Risk work.  You
get more out of your armies by attacking than defending.  That, the bonus
(in cards) for wiping out another player, and the increasing cards bonus are
what make the game progress.

I really think that if you give a bonus to the defender, we're all just
going to sit at the board and never move.

As we have it now, if I instigate an attack, I lose some armies, he loses
some armies, and four other players sit there laughing at us.  Outside of
continent bonuses, there's no advantage I can see to acquire territory.  IN
game 101, we're all a long way from the 12 territories we'd need to gain one
extra army every third turn.  I'd have to invest an awful lot of armies to
win enough territories to get that-- just doesn't seem worth it.

> You'll note that the odds are skewed dramatically towards the defender

That's only for small battles.  For large battles, say 30 against 30, the
attacker has a significant edge, gained from being able to roll 3 vs. 2.

And of course, for a campaign through a series of territories, the attacker
also loses a little strength to leaving troops behind in each country.

But on the whole, when there's a big clash, the attacker has a big
advantage.

I think Schmittberger's rules captured that pretty well, and I thought
Richard's earlier proposal, which tried to extend those to multiplayer,
would be pretty good.  I don't recall the exact details, but the main
feature of Schmittberger's rules was, the bigger your troop count, the even
bigger the amount you'll be left with.  You have one more attacker than
defender, you're left with 2; you have two more, you keep 4, and so on.  I
think I'd try to maintain a relationship like that, though perhaps with a
multiplier smaller than 2.

So my suggestion, thinking out loud, is ...
- when A attackers attack D defenders,
- compare 2A to D+2
- if 2A is bigger, attack succeeds with 2A-(D+2) armies left
- if D+2 is bigger, or same, defense succeeds with (D+2)-2A armies left

This means that D=1 can defend against A=1, but D=5 gets beaten by A=4.

That's probably very close to Schmittberger's rules.  Of course, this could
be tweaked by changing 2A to something like 1.4A, rounded up.

For multiplayer attacks on a defended territory, it'd be exactly the same as
above, almost (that's *supposed to be funny), but with these changes
- compare defender to the largest attacker using 2A-to-D+2
- if D+2 is bigger, or same, defense succeeds as above, and all attackers
are eliminated.
- if 2A is bigger, and there's one attacker who's largest, his attack
succeeds, as above, and all the other attackers are eliminated.
- otherwise, two or more attackers are tied, and everybody loses (i.e. the
territory is now empty)

For a mutual attack across a border (A attacks B at same time B attacks A),
battle goes to the larger force, with ((2*larger) minus smaller) armies
remaining.

Now, it is rather unrealistic that, say, 24 attackers can lose to 10
defenders, *if* the attackers attack six each from four different
territories.  But that's what we have no, anyway.

By the way, if the same player attacks from a couple different territories,
his forces should count as a single attacking force.

Another possibility for breaking ties is to allow cohabitation.  But that
might get pretty messy.

> Odd Table (as calculated by richard) ...

Good work!  Your table matches the one from the risk FAQ (below).  I can't
count how many of these tables I've seen, most of them different.  By the
way, the risk FAQ used to be at, and for all I know is still at,
   www.bath.ac.uk/~mapodl/html/riskfaq.html
and
   www.uwm.edu/~baker/riskfaq.html

Attacker    Defender rolls:  2 dice                     1 die
rolls:  +-----------------------------------------------------------------+
        | Att lose 2:  29.26% (2275/7776) | Att lose 1: 34.03% (441/1296) |
   3    | Def lose 2:  37.17% (2890/7776) | Def lose 1: 65.97% (855/1296) |
  dice  | Each lose 1: 33.58% (2611/7776) |                               |
        +-----------------------------------------------------------------+
        | Att lose 2:  44.83% (581/1296)  | Att lose 1: 42.13%  (91/216)  |
   2    | Def lose 2:  22.76% (295/1296)  | Def lose 1: 57.87% (125/216)  |
  dice  | Each lose 1: 32.41% (420/1296)  |                               |
        +-----------------------------------------------------------------+
   1    | Att lose 1:  74.54% (161/216)   | Att lose 1: 58.33% (21/36)    |
  die   | Def lose 1:  25.46%  (55/216)   | Def lose 1: 41.67% (15/36)    |
        +-----------------------------------------------------------------+