About containing a weaker player within your empire. If, with the use of mission cards one being eliminate a certain player.
yellow has completly ecompased green to Madagascar. This is greens last stronghold with only 1 Infantry on. You could easily take him out on your next turn, but if you do another player may win with the "Elim Green" card.
Is it worth the risk that your yellow player takes out green?
You are yellow in the game above, but are playing the 1993 US edition secret mission rules where you must complete a secret mission in order to win the game. (Us edition as eliminating a player can cause a win for another player. Unlike the UK edition where this would cause the opponent with that mission card to have to capture 24 territories instead)
You have the option of killing off green, which would normally be fine. But what if someone else wants them gone? Do you take out green and pray to the RNG gods that someone doesn't have the card that says "Eliminate green"? Or is it better to take the risk of letting green reinforce at least 3 players per turn? (say you let green keep Madagascar as his safe haven.)
MISSION CARD %
With 12 mission cards and 6 players there's a 38%-48% chance that the destroy green card is drawn by one of the 4 enemy players that isn't yourself(yellow) or green. (The percentage range comes from the order in which players pick cards.)
In the best case senario, where you pick your card last and green picks his card second last. There is ~38% that "elim green" is held by another player.
So if you take out green there is a 1/3 chance that you lose the game on the spot as another player claims victory at the start of their turn with the "Elim green card"
However if you do not take this risk and allow green to sit in Madagascar(Mad) then he will slowly build up a force. Which you either have to deal with, with your own reinforcements to keep him in check. Or let build up.
Any decent player will deal with him building forces.
So say he has no cards and gets only +3 per turn. He will have 4 men sitting in Mad.
You will gain between 5-6 rein. per turn (going by an average mid game board map) (you control all of africa minus Mad. and let's say for arguments sake. South america.)
REINFORCEMENTS TO KEEP HIM IN CHECK
To keep him in check with minimum losses you need to kill those 3 rein. every turn. allowing him 1 guy in Mad. To do this you need to be sending in 7 guys for a +80% win rate. (We don't need to kill all 4. Just 3 to leave him with 1. so our win rate for our objective raises slightly higher than normal win rates.)
Also, to make sure he dosen't gain a card we need to leave at least 4 men in 2 territories to give him a small 20% win rate.
So within 1 turn (let's say he didn't attack) we need to commit 7 men out of the 2 adj.territories to Mad. (8 total -> 7 = -1 as we need to leave 1 guy in each territory) So already we lose 1 rein. to do this on turn x. The fight to keep his forces to 1 loses us another 2 men, which is a respectable loss. So to stay even during turn x we need to commit 3 rein. to keeping green down and confined to mad while still leaving us with 4 men in 2 territories to stop his rein from gaining a card.
So our cost to keep green down is 3 rein per turn. With +2 surplus to attend our other agendas.
CARDS INTO THE EQUATION
Let's say we have 3 cards on turn x+2. Assuming there is an equal chance of drawing each type. (33%) Excluding the 2 wild cards. There is ~4% chance you have 3 of a kind on x+2 and a ~4% chance you hit the straight (inf. calv. gun.) So 1 in 10 times you wont hit on this turn.
On turn X+3 You have a 37% chance of a 3 of a kind and a 37% of a straight. So a 74% chance you hit.
On turn x + 4 you have a 100% chance to hit.
In a worst case scenario, you dont hit cards until turn x+4. By turn 5 you will have committed +12 rein min. To keep the green insurgence in check in Mad. Your surplus forces in this time will have been around +8-10
and net of -4 -> -2
SO ON TURN X+5 ARE WE UP?
If we hit 3 inf cards (+4). our net gain on surplus to Green rein. is '0 - +2'
3 Calv. cards.(+6) = +6-+8
3 gun. cards (+8) = +8-+10
straight (+10) = +10-+14
Thus by protecting green as well as keeping it's forces low. We will come out slowly ahead on reinforcements by, at the latest turn x+5.
Realistically you are going to hit card rein. by x + 4.
During this quell you will stagnate on the board and more than likely lose some presence on your boarders. (as you try and gain a card per turn.)
Not until turn 5 from putting green in Mad. (x + 4) will you be in a better position again on average. But by doing this are you put yourself at a greater disadvantage to win the game than if you had just taken the RNG by killing of green.
and thus. Would you lose more games this way than if you had just killed off the green player? Making that 38% chance that you lose on the spot better than the possible tactical disadvantage of bleeding yourself trying to control green?
Of course there is the player element to this argument. If someone was trying to kill green and they had to go through you, you could tell via verbal pressure on you to kill green. Or board pressure to get to him. Is holding off those 5 turns until you know this information damaging to your chance of winning beyond repair? Assuming your objective was not achievable within these 5 turns.
(Please note out and correct any maths errors I may have made.)