by **Kaskavel** on Sat Oct 04, 2014 6:51 pm

I am not certain I exactly understood what you ask, but I can probably imagine. Indeed, the 4 vs 3 does not have any advantage or disadvantage compared to the 5 vs 4, except for the fact that the second one has more "attacking advantage". In other words, the only advantage a 5 vs 4 has over a 4 vs 3 is of the same nature of the advantage a 400 vs 399 has, over a 4 vs 3. More troops in the battle, more advantage to the attacker. If there is any extra advantage or disadvantage between a 4 vs 3 and a 8 vs 7, it is probably random between random pairs and probably insignificant to the practical CC player.

That is not though what I casually mentioned in my point b, which is the point I guess created some confusion. What I wrote, is that it is favourable to attack with the difference of attackers and defenders being odd. Equal troops, +2 troops,+4 troops,+6 troops etc. This is indeed something that I am not aware any other player has ever suggested, it is my own invention and I cannot prove it, although I can try to explain it and see if it finds acceptance.

FACT The 2 is the best number in defence. A line of 2s is superior to any other distribution of defenders

FACT The 3 is the worst number in defence (after the horrible 1s of course)

ASSUMPTION It is not good to have 3s around the board. This is very close to a fact (for me, it is a fact) and I think we will agree. You do not want a bunch of 3s over the board, you want a bunch of 2s and some remaining stack. A 2,2,2,10 is better than a 3,3,3,7, both for defensive and for offensive reasons. You have bigger stack to attack and the 2s are very good in defence. If I have a 3,3,3,7 line, I will add one troop in all the 3s and the remaiming in the stack. Some of the 4s will win and split 2-2, some will lose and become 2s. All those 2s are now "fine". Those 4s that made a draw and became 3s again are problems that I will probably try to solve again next round, the same way, by making them 4s and attacking. A 3 is very bad, not only it is vunlerable as nothing else in defence, but it also contains an extra useless troop, that cannot be used for attacking purposes.

If we agree to the points above (and I think we should), here comes the idea

SUGGESTION It is better to assault with an attacking advantage (or disadvantage!) of 2n troops, rather than 2n+1 troops.

SUPPORT OF THE SUGGESTION The suggestion cannot be proved mathematically, or it is very difficult to do so. There are 2 reasons I support the idea.

ARGUMENT 1 An "odd" assault has more chances to end up in a finishing 3 vs 1 attack, which may make the difference. A 8 vs 6 attack can end up in a 3 vs 1 attack more easily than a 7 vs 6 attack. All is needed is a draw in last dice (or an odd number of loses in n vs 1), while the other one needs an even number of losses in n vs 1. I have not checked the math, someone could do for me if he likes, what chances do a 8 vs 6, a 7 vs 6 and a 9 vs 6 end in a 3 vs 1 (with attacker stopping attacking if he is left with 3 troops of course, not attacking 3 vs 3)? If the board supports making 3 vs 1 attacks and/or the battle involved is important to be won, then this 3 vs 1 attack, an "extra cheating" in fact, may make a difference.

ARGUMENT 2 Argument 1 may in fact be wrong, it may be an illusion of the mind. It may be wrong, I have never done the math. But this is the more important one. An "odd" assault cannot end up 3 vs 2. Ending the battle at 3 vs 2 is a bad bad senario. Defender is left with a wonderful 2 and you are left with a problematic 3 (as mentioned in ASSUMPTION above). Of course, one might reverse the argument and suggest that an "odd" assault cannot also end up in a 2 vs 3, which is the reversed situation. True, but a 2 vs 3 is not a significant success for the attacker for the reason that it is now defender's turn to play and he can "fix" the mistake by immediately taking his turn and either adding up many troops to the 3 to attack or adding a single troop and attack (possibly 66% solving the problem) or, if his position is defending in nature (a bonus boarder or something), add a single troop and stay with a 4 in defence (which is the next best thing to a 2 that exists). The 3 vs 2 senario is bad and the 2 vs 3 is not so good as it may seem. In "odd" battles the outcome may be 3 vs 1, which is good, 2 vs 2, which is also good leaving decisions of continuing the assault or ignoring the now "stalemated boarder" for next round and the 3 vs 3 which is bad, but not as bad as the 3 vs 2 one, because in the 3 vs 2 senario, the defender may as well ignore your problematic 3, while now, in the 3 vs 3 senario, he is forced to take some action to prevent his 3 from getting attacked.

EXAMPLE you have to make a 10 vs 7 and a 8 vs 6 attacks and you have one extra troop to place. You do not care winning the battles, just to make optimal troop exploitation in numbers. I believe you have to increase the 10 vs 7 into a 11 vs 7 "odding" both assaults. The alternative is to "even" both attacks. People tend to choose the option that equalizes the difference of the assaults, in the above example most people would bring both attacks at +3, rather than a +2 and +4...it just somehow seems more natural to do so, but I think it is wrong if it evens both differences. Be careful here, the argument is NOT that 11 vs 7 and 8 vs 6 are a mathematically superior pair to 10 vs 7 and 9 vs 6. It may be or it may be not, there should be some minor difference if someone does the math, randomly favoring the "odding" or the "evening" depending the example. The math will suggest the option that maximizes the chance to finally battle against 1s in both assaults (in cases like the above where we have superiority in numbers, you see, the example I brought is not in my favor I think) or the option that maximizes the chance to face one 1 (in cases we are below in troops overall) The argument is not that. The argument is that the odd assaults will leave the attacker in a much better situation "after the round" with no chances of getting stuck with a 3 vs 2 inferior outcome

CONCLUSION Since the argument takes into account the events of the following round, it is very difficult to prove it correct or wrong. I think many CC players have such a behavior from experience already, mainly by feeling that a 5 vs 2 attack is a "bad attack". I have heard and seen some good players avoiding those attacks, while having no problem making 5 vs 3 attacks, although they do not seem ready to explain the reasons of their behavior.

If that is true, then, although at the start of the game it is good to make many 4 vs 3 attacks to get rid of our 3s, it is not necessarily a good things to build up 4 vs 3s attacks later on from a 2 vs 3 situation. If we bother increasing a 2 vs 3 into a 4 vs 3, then we probably need to further increase it into a 5 vs 3 as well.