6 V 2 or 4 V 1 tactical choices

by **universalchiro** on Thu Oct 20, 2011 11:55 am

The situation: You are the attacker, with the larger number ( 6 & 4), attacking the smaller number (2 & 1).
The question is: If you had 1 troop to deploy, which one would you deploy it on, The 6 or 4..
Which one needs the extra troop in order to win both battles?
Thanks,
Troy Lawrence,
AKA Universalchiro

by **manchild1** on Thu Oct 20, 2011 2:08 pm

add the extra troop to the 6.
Using the battle odds calculator here (http://gamesbyemail.com/Games/Gambit/BattleOdds), I calculated that the odds of winning 6v2 are 93.4% and the odds of winning 4v1 are 97.2%.
As a rule of thumb, to maximise your total chances of winning you want to try to even up the chances of winning each individual battle. For example, you would prefer two 50% chances over one 40% chance and one 60% chance. So, we add the extra troop to the 6v2 battle.

by **trinicardinal** on Thu Oct 20, 2011 2:28 pm

didn't even bother to calculate... I'd go with the 6 also...lol

by **Rodion** on Thu Oct 20, 2011 5:54 pm

They are both wrong.

If you MUST win both battles, drop the extra army on the 4.

A 4v1 + 7v2 gives you roughly 85,6% odds.
A 5v1 + 6v2 gives you roughly 86,4% odds.

While two 50%s are better than a 60% and a 40%, you have to consider that dropping the extra army in one place will give you higher odds than dropping it in the other.

by **manchild1** on Thu Oct 20, 2011 6:46 pm

No, even accounting for the difference in odds from dropping the troop, the 7v2 is still better
The odds of winning 5v1 and 6v2 are .99013*.9339797 = 0.92476
The odds of winning 4v1 and 7v2 are .9715441*.9666495 = 0.93914

The only time that is possible that the change in odds from where you place the extra troop could make the rule of thumb invalid are if the odds of you winning one of the battles is less than 50% (I haven`t checked this claim thoroughly, but I am pretty sure its right).

by **Rodion** on Thu Oct 20, 2011 7:00 pm

4v1 is below 92%, so your numbers are wrong.

by **manchild1** on Thu Oct 20, 2011 7:07 pm

I am assuming that you have 4 attacking armies (so 5 in the territory). I guess you are assuming there are 4 in the territory, so only 3 attacking armies.
Can OP clarify

by **safariguy5** on Thu Oct 20, 2011 7:09 pm

Another way of thinking about it is maximizing the % of success gained by the additional troop.

4v1 is about a 91.6% win, 5v1 ups it to about 97.1%= a gain of about 5.5%
6v2 is about a 88.9% win, 7v2 ups it to about 93.3%= a gain of 4.4%

So I'd drop it on the 4v1 because you're getting a larger percentage increase in attack success.

by **usernamer** on Fri Oct 21, 2011 1:49 am

I agree with Safariguy. You do get slightly better odds if you drop on the 4v1 than the 6v2 because it increases the chances of making that assault successful by more than it would dropping on the 6v2.

What Manchild said about evening out %ages is generally true, and two 50's is definitely better than a 40 and a 60, but as putting an extra troop down doesn't necessarily give the same % increase to each assault, so 40 and 65 is better than two 50's, for example.

by **zimmah** on Fri Oct 21, 2011 4:35 am

usernamer wrote:I agree with Safariguy. You do get slightly better odds if you drop on the 4v1 than the 6v2 because it increases the chances of making that assault successful by more than it would dropping on the 6v2.

What Manchild said about evening out %ages is generally true, and two 50's is definitely better than a 40 and a 60, but as putting an extra troop down doesn't necessarily give the same % increase to each assault, so 40 and 65 is better than two 50's, for example.

right.

i was at first a bit surprised by rodion's reply, but after calculating it, he's right.