The essence of a winning move and a bit of math.
  • 7 posts
  • Page 1 of 1
Matty wrote:
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:
  • 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. Strenght lies in nights of peaceful slumbers." ~Maria
Matty wrote:
This post is reserved for a later addition to this tutorial, if I'll ever get to it.

P.S. Sorry for the use of the old Great Britain and Ireland map, the screenshots are from a while ago before the map was remade by Aeronautic.
"Strength doesn't lie in numbers, strength doesn't lie in wealth. Strenght lies in nights of peaceful slumbers." ~Maria
maxrebo wrote:
so you mean that at some point you have to start moving troops into an attacking position... but when?
what about six player games where you have enemy territories with many troops...and this happening on most regions..?

i know that being able to recognize these moments is what defines a good player...
i guess practice is key

:)
Matty wrote:
maxrebo
so you mean that at some point you have to start moving troops into an attacking position... but when?
I just opened a few random live games, and one of them had a card bonus of 15, and some players had 20-30 troops.
At that point, if you have 5 cards and you can kill someone else with 5 cards, you get a double turn in, which is worth way more than those 20 troops - so at that moment in the game you want to be ready for the kill.

Which means you have to start moving your troops in an attacking position before that. How many turns before that depends on how many territories aren't in an attacking position :)
Note that if a person has a +2 bonus, 11 territories, 3 cards and 20 troops, then in 2 turns from now (assuming he won't turn in) he'll have 5 cards and approximately 29 troops (+2 from regions, +3 from the territories and say he'll lose one troop in trying to get a card from an attack).

If you setup really well, your troops are both attacking and defending, so you don't really need to move around. Of course, that's not always possible.


Does that help a bit?
"Strength doesn't lie in numbers, strength doesn't lie in wealth. Strenght lies in nights of peaceful slumbers." ~Maria
farspaceplace wrote:
just a quick question - i know its written somewhere else, but...what is the chance of double turn in with 6 cards, (and 2 wild cards in deck fx)?
Matty wrote:
farspaceplace
just a quick question - i know its written somewhere else, but...what is the chance of double turn in with 6 cards, (and 2 wild cards in deck fx)?
In this topic that question is asked, also here and here.

To summarize:
- A turn in with 3 cards: 42.28%
- A turn in with 4 cards: 81.70%
- A turn in with 5 cards: 100%
- Two turn ins with 6 cards: 33%
- Two turn ins with 7 cards: 93%
"Strength doesn't lie in numbers, strength doesn't lie in wealth. Strenght lies in nights of peaceful slumbers." ~Maria
bluebonnet wrote:
you guys should think about expanding out all this information into a searchable wiki.
kind of a pain to search forums for links, information, and downloads.

a wiki could be 1 stop shopping, easy to update, reduce questions, etc etc etc
bluebonnet is online.