- Mark as unread from here
- Posted: 9 years ago
- Modified: 3 years ago
-
Post #1
The essence of a winning move and a bit of math.
This is an attempt to show a bit of how I think when I play an increasing card game.
To do so I will look at two alternatives setups of the same game.
But first...
Some important facts:
The statistics:
Below is a picture of the statistics of some game. We are the blue player and receive 6 troops this turn. The card turn-in value is 15.
Now here's the plan:
If we kill the orange player we will lose about 17 troops (37 + 6 - 17 = 26 troops left) and get 4 cards. We already have 3, so that makes 7 cards.
With these 7 cards, we can almost be sure to have a double turn in: which gives us 15 + 20 = 35 troops.
Notice that we now have 1 card left and something like 26 + 35 = 61 troops.
With our remaining troops kill red: we will lose approximately 27 troops, and get 4 cards. Together with our remaining 1 card, we now have 5 cards, so we can turn in a set and receive 25 new troops.
The balance now is 61 - 27 + 25 = 59 troops.
With these 59 troops, we can kill the 41 troops from the cyan player and we won the game - yay!
But...
The board:
If we look at the board however, we cannot use all our troops - only the troops in Clwyd can move.
And 10 + 6 = 16 is not going to be enough to kill orange, because you leave one troops behind on each territory
(you have about 16.5% chance to kill orange - you should never do that).
So we can't win - aaaw.
A different setup:
What would happen if we didn't spend so much troops defending our region?
Now we suddenly have 21 + 6 = 27 troops available, which is more than enough to kill orange - yay!
This shows you that, even though regions are useful in the early game, in the end of the game they don't matter - killing your opponents and getting their cards is the important thing.
Some odds:
For those who are interested in the actual battle odds:
16 vs 1,3,1,6,2,5 = 16.5% chance of winning
27 vs 1,3,1,6,2,5 = 84.8% chance of winning
These odds are calculated using an odds calculator (Note the (One less than in territory) for the attacker).
A somewhat more simple to use calculator is this one: http://riskodds.com/
This is an attempt to show a bit of how I think when I play an increasing card game.
To do so I will look at two alternatives setups of the same game.
But first...
Some important facts:
- With increasing cards every time you or anyone else turns in a set of cards, the value of the next set increases.
These are the values: 4, 6, 8, 10, 12, 15, 20, 25, 30, 35, ... (+5 each set). - With 7 cards you almost always turn in two card sets (the probability is about 94%). This is called a double turn in.
- If you kill a player you lose troops, but you get his cards. If these cards are worth more troops than it costs to kill him, than you make a profit.
- If this profit is big enough to kill the next player and get his cards, you can get a chain reaction and kill everyone. This is generally how you win an increasing card game.
The statistics:
Below is a picture of the statistics of some game. We are the blue player and receive 6 troops this turn. The card turn-in value is 15.
The statistics (click to show)
Now here's the plan:
If we kill the orange player we will lose about 17 troops (37 + 6 - 17 = 26 troops left) and get 4 cards. We already have 3, so that makes 7 cards.
With these 7 cards, we can almost be sure to have a double turn in: which gives us 15 + 20 = 35 troops.
Notice that we now have 1 card left and something like 26 + 35 = 61 troops.
With our remaining troops kill red: we will lose approximately 27 troops, and get 4 cards. Together with our remaining 1 card, we now have 5 cards, so we can turn in a set and receive 25 new troops.
The balance now is 61 - 27 + 25 = 59 troops.
With these 59 troops, we can kill the 41 troops from the cyan player and we won the game - yay!
But...
The board:
The original board (click to show)
If we look at the board however, we cannot use all our troops - only the troops in Clwyd can move.
And 10 + 6 = 16 is not going to be enough to kill orange, because you leave one troops behind on each territory
(you have about 16.5% chance to kill orange - you should never do that).
So we can't win - aaaw.
A different setup:
What would happen if we didn't spend so much troops defending our region?
An alternative board (click to show)
Now we suddenly have 21 + 6 = 27 troops available, which is more than enough to kill orange - yay!
This shows you that, even though regions are useful in the early game, in the end of the game they don't matter - killing your opponents and getting their cards is the important thing.
Some odds:
For those who are interested in the actual battle odds:
16 vs 1,3,1,6,2,5 = 16.5% chance of winning
27 vs 1,3,1,6,2,5 = 84.8% chance of winning
These odds are calculated using an odds calculator (Note the (One less than in territory) for the attacker).
A somewhat more simple to use calculator is this one: http://riskodds.com/
"Strength doesn't lie in numbers, strength doesn't lie in wealth. Strength lies in nights of peaceful slumbers." ~Maria