In a 3v2 dice situation, who got the advantage? The attacker or the defender?

6 sided dice? Attacker edge: Defender loses roughly 6 units per 5 units that the attacker loses.

The attacker has a light advantage, a 1.07 hope of win I believe.  

It depends.  Rolling a stack of 4 against a stack of 4 does not give the attacker the advantage.

I would recommend googling "risk dice probability", or "risk dice statistics".

Sorry Hugh, I did not see your reply as I was writing mine. your figure seems too high I believe.

Toto wrote:

Sorry Hugh, I did not see your reply as I was writing mine. your figure seems too high I believe.

Hugh is correct (in an extended 3v2 battle), attacker will lose 0.92 dice per each roll and defender will lose 1.07 dice per roll

It's an overestimate, but it isn't by much, and is usable. For more precision, we can use the often cited single roll probabilities: 37.17% defender loses 2, 33.58% is a split, 29.26% attacker loses 2. The expected attacker loss is 0.9210 per roll, and the expected defender loss is 1.079 per roll. The defender expects to lose ~1.17 units per attacker unit lost. Rounding to 1.2 gives the nice and usable 6 to 5 I just gave, though 1.17 to 1 is certainly more precise. 13 to 11 is also close :) 

If you roll 20 times, the precise estimate and the 6 to 5 both give defender losing 22, attacker losing 18 after rounding to the nearest integers. So, I think it's dirty, but decent. For larger numbers of rolls, you might want to use the more precise estimates.

M57 wrote:

Toto wrote:

Sorry Hugh, I did not see your reply as I was writing mine. your figure seems too high I believe.

Hugh is correct (in an extended 3v2 battle), attacker will lose 0.92 dice per each roll and defender will lose 1.07 dice per roll

This is also what I was trying to say when speaking of a 1.07 hope of win for the winner :)

Hugh wrote:

It's an overestimate, but it isn't by much, and is usable. For more precision, we can use the often cited single roll probabilities: 37.17% defender loses 2, 33.58% is a split, 29.26% attacker loses 2. The expected attacker loss is 0.9210 per roll, and the expected defender loss is 1.079 per roll. The defender expects to lose ~1.17 units per attacker unit lost. Rounding to 1.2 gives the nice and usable 6 to 5 I just gave, though 1.17 to 1 is certainly more precise. 13 to 11 is also close :) 

If you roll 20 times, the precise estimate and the 6 to 5 both give defender losing 22, attacker losing 18 after rounding to the nearest integers. So, I think it's dirty, but decent. For larger numbers of rolls, you might want to use the more precise estimates.

Great, this is much more accurate. Your estimate was indeed not that bad.

I wrote some online tools that are available to anyone that wants them:

http://prestopnik.com/wargear

They both allow you to set attack/defense bonuses.

The one on the left is a simulator and after you enter the initial starting situation, it runs 1000 simulations (by default), and tells you how often the attacker wins, and the distribution of units left.

The one on the right is a calculator.  It tells you on average what your odds are.

Good thing Hugh never took a statistics class...can you imagine if he had?

Ozyman wrote:

I wrote some online tools that are available to anyone that wants them:

http://prestopnik.com/wargear

They both allow you to set attack/defense bonuses.

The one on the left is a simulator and after you enter the initial starting situation, it runs 1000 simulations (by default), and tells you how often the attacker wins, and the distribution of units left.

The one on the right is a calculator.  It tells you on average what your odds are.

Very cool.  Any way we can have this as a sticky or in the Help tab so new players (and non-statisticians like myself) can reference easily?

AttilaTheHun wrote:

Ozyman wrote:

I wrote some online tools that are available to anyone that wants them:

http://prestopnik.com/wargear

They both allow you to set attack/defense bonuses.

The one on the left is a simulator and after you enter the initial starting situation, it runs 1000 simulations (by default), and tells you how often the attacker wins, and the distribution of units left.

The one on the right is a calculator.  It tells you on average what your odds are.

Very cool.  Any way we can have this as a sticky or in the Help tab so new players (and non-statisticians like myself) can reference easily?

http://www.wargear.net/help/display/FAQ#Calc