Izual_Rebirth wrote:Does anyone have any decent guides on Dice Probabilities? Looking to improve my gameplay and thinking a guide on dice probabilities might help!?!?

Also in one small article ( buggered if I can find it now) it went on to say that in a "stalemate" scenario where both players are just reinforcing every turn on a particular border equally, that the more being stacked means whoever "blinks first" and attacks has more advantage. That attacking with 100 vs 100 is more beneficial to the attacker than say 10 vs 10.

I never understood why!

[Note]

The following is based on long term law of averages and results will vary from short term attacking results.

That's because when ever 3 attacker's dice roll against 2 defender's dice, the attacker has a 54% odds of winning the roll. Now it may appear as close to 50/50 odds but what we are really looking at is close to a 10% loss for the defender over the long run (4% plus 6% equals 10%). And the more troops involved the more pronounced and definable it becomes.

The longer that the 3 attacking dice Vs. 2 defending dice is prolong the more recognizable is the advantage. 10 troops attacking 10 troops roll a maximum of 8 times with the advantage of 54% winning odds for the attacker. After that the Attacker odds are decrease by a lot. So out of 10 troops each, and after 8 rolls you can expect an average loss of (very) roughly 7.5 troops for the attacker to 8.5 troops for the defending force.

Or in other words and perhaps more correctly they both lose 8 troops each on average for every 8 rolls counted but the defender loses 1 extra troop and the attacker 1 less troop. Or The Attacker loses 7 troops to the defender's 8(+) troops lost. The end would look this. The Attacker would be left with 3 troops on the attacking region and the defender would be left with only 1+ or most likely 2 troops on the defending region (on average). At this point the odds change rather badly for the attacker.

When the 54% percent odds is then multiplied by 100 troops on the regions, then it would look something like this; 30 troops left on the Attacking region out of 100 troops for the attacker and 10+ troops left on the defending region out of 100 troops. Obviously 30 troops left over defeating 10 troops left over is better than 10 vs. 10. So the greater the troops the more pronounced and visible the 54% win ratio is. Remember that it is 54% winning odds and not 54% of the total troops. So as the number of rolls is increase so is the potential loss for the defender. (Each roll is a potential 2 troops.)

Again; 100 troops gives us a potential 99 rolls where as 10 troops gives us a potential 8 rolls at 54%. In 8 rolls the attacker loses 4 rolls or half with the rough exception of that 10% of the troops or 1 troop difference on average for every 8 rolls. With 99 rolls the potential is the same as the 8 rolls only expanded. The only thing that is carried is the analogy of 8 rolls we now use it in 80 rolls. So that both sides lose approximately 80 troops in 80 rolls but the Attacker loses 10 troops less while the defender loses 10 troops more. So that the Attacker loses only 70 troops while the Defender loses 90 troops in approximately 80 rolls (or so). So you never really get to roll 99 in 100 troops as the battle is won in some 80 rolls or so. More likely less.

I don't know how to make it any clearer as math was never really my strong suit. But perhaps there are some mathematicians out there who can either simplify this or explain it to me if I am wrong in my thinking of this exponential problem/equation.

(Revised 9/21/2012)