Re: [risk] defending vs attacking?

[kwzh-home@gnu.org (Karl Heuer)]

>[Who has the advantage in normal Risk, attacker or defender?]

Assume both players have a really huge number of units in the battle,
it's just a matter of the relative depletion rate.

I believe the standard rules for Risk say that the attacker rolls
up to 3 dice (I'll assume exactly 3, since it would be irrational to
roll fewer), and then the defender gets to choose whether to defend
with one die or two, *after* seeing the attacker's roll.  If you take
this into consideration, and if the defender plays optimally, then
the result is an extremely slight edge to the defender: he destroys
1945 units in the same time that the attacker destroys 1943 units.

So if the goal is to approximate the behavior of standard Risk,
then you might as well treat it as a simple 1-for-1 trade.  It's
also a much simpler rule to remember, without the arbitrary
multipliers.  :-)


P.S.: The defender's optimal strategy is to roll one die if the
attacker has two "high" dice (4-6), and to roll two dice if the
attacker has two "low" dice (1-3) (i.e., if at least one "low"
die can be made to contribute to the battle).  This is not a guess;
I derived it as part of working out the 1945/1943 result.

P.P.S: As I said, this assumes that the goal is to maximize the
expected army depletion ratio given a virtually infinite supply of
units.  In real play, an attacker might be more interested in the
probability of annihiliating the defender than in the number of
surviving units, and there may be edge effects as one or both of
the forces get closer to zero.  I include this information because
I'm sure someone will want to quibble about it if I don't.  :-)