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Subject: Diplomacy Card Frequency
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There are twelve special cards, viz, 2 x Birds of a Feather, 2 x Isolationism, Brothers in Arms, Ethnic Ties, Fear & Loathing, Ties that Bind, Versailles, Foreign Aid, Guarantee, Intimidation.
The last three don't name any specific countries. The other nine do.
These six cards allow the named Faction either to add 1 Influence point or to remove one Rival Influence point from the named Neutral.
BF, BF  Birds of a Feather.
BIA  Brothers in Arms.
ET Ethnic Ties.
TTB  Ties That Bind
V  Versailles.
F&L  the Fear & Loathing card allows the named Faction to remove a Rival's Influence point from the named Neutral.
I, I  The two Isolation cards allow any Faction to remove one Rival's Influence from either USA, Spain, Sweden, Poland, Turkey, Low Countries. I put "I" cards and F&L in parentheses because they tend to make a country more stableless inclined to be Influenced.
Each time a Neutral country below is named on one of the above cards, the card's abbreviation will appear next to the name of the Neutral country, along with the beneficiary: West, Axis, or USSR.
There are fortythree Action Cards each with two neutral countries' names, for a total of 86 country names. From least frequently to most frequently appearing, along with their Resources and Populations, they are:
0 RES 0 POP Baltic States 2 Action Cards + AxisBF (USSRF&L)
4 RES 1 POP Persia 2 Action Cards  (WestF&L)
2 RES 1 POP Sweden 3 A.C. + AxisET, WestBF,(I, I, USSRF&L)
1 RES 2 POP Turkey 3 A.C. + AxisV  (I,I, WestF&L, USSRF&L).
1 RES 0 POP Portugal 3 A.C. + AxisBF.
1 RES 2 POP Poland 3 A.C. + WestV; AxisBF, USSRET,  (Axis F&L, USSR F&L.)
0 RES 0 POP Afghanistan 3 A.C.
1 RES 0 POP Denmark 3 A.C. + WestBF,BF.
1 RES 0 POP Norway 3 A.C. + WestET,BF; AxisET  (Axis F&L).
0 RES 1 POP Low Countries 4 A.C. + West TTB, ET, BIA, BF;  (I,I, AxisF&L).
0 RES 2 POP Spain4 A.C. + USSRTTB,BIA,BF,BF; AxisBF, AxisBF,  (I,I).
1 RES 0 POP Bulgaria 4 A.C. + AxisTTB,BIA,BF; USSRET.  (West F&L).
1 RES 0 POP Finland 4 A.C.  (USSRF&L).
2 RES 1 POP Romania 5 A.C. + WestET,BIA  (AxisF&L,USSRF&L).
4 RES 3 POP United States of America5 A.C. + West TTB,ET,BIA,BF,BF;  (I,I, AxisF&L; USSRF&L).
2 RES 1 POP Latin America5 A.C. +Axis BF  (WestF&L)
1 RES 0 POP Greece 6 A.C.
1 RES 1 POP Hungary 6 A.C. + AxisTTB,V,BIA  (West F&L).
0 RES 1 POP Austria 6 A.C. + AxisTTB,V,ET,BIA  (West F&L).
0 RES 1 POP Czechoslovakia 6 A.C. + WestV,BF,TTB; USSRBIA,  (AxisF&L).
1 RES 0 POP Yugoslavia 6 A.C. + WestV; AxisBF; USSRTTB,ET,V  (Axis F&L).

 Last edited Mon Sep 7, 2015 2:53 pm (Total Number of Edits: 6)
 Posted Sat Sep 5, 2015 4:51 pm
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 Great analysis!
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High practical value; high value as grist for milll for historical debates.
I wonder if its possible that refine this and say that:
If I draw one card next turn, what are the odds of picking up a chance to influence Nation A
Assuming
* 55 card deck and assuming
* that one knows the whether the nation you care about is on any of the, say, 4 action cards already in one's hand, and assuming
* not knowing the state of cards held by rivals or enemies,
can I say:
The odds of drawing a card that affects Austria are 7 out of 55 if I am the West, 10/55 if I am the Axis, and 6/55 if Iam the USSR ?
or, similarly,
The odds of drawing a card that affects Afghanistan are 3/55, regardless of what faction I am ?
etc.

 Last edited Sun Sep 6, 2015 3:34 pm (Total Number of Edits: 1)
 Posted Sat Sep 5, 2015 9:47 pm
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You are asking about the following situation?
You are Axis. You hold an Austria Action card. You are drawing 10 more cards  all Action Cards? What are the odds then of drawing a second, third etc. Austria card?
The odds are very good. There are nine possible successesthe five remaining Austria cards plus the four Axis multination cards which name Austria. Assume also that 45 cards are unaccounted for, the fortyfive not in the Axis's hand.
According to the hypergeometric (without replacement) binomial distribution, drawing 10 of 45 cards, 9 cards of which are successes, there's a 26% chance of one success and a 66% chance of two or more successes.
The West or USSR might try to thwart you in Austria by playing Austria cards of their own or by the West's play of "Fear and Loathing" on Austria. So if you're determined to win Austria, you want two or more successes.
As it's a three player game I imagine there's usually little to gain by thwarting another player's interests as opposed to advancing one's own interest. While X is thwarting Y, Z will be running wild. The obvious exception to that advice is the need to keep USA neutral as long as possible if West is your enemy.
Also as Resourcepoor Axis I would worry most over grabbing unstable Neutrals with Resources, such as Greece, Hungary, Rumania, and Yugoslavia. I wouldn't worry overmuch about securing Austria, which has 1 POP but no Resources.

 Last edited Sun Sep 6, 2015 4:04 am (Total Number of Edits: 1)
 Posted Sun Sep 6, 2015 3:56 am
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I agree with most of this...and strongly believe this is one of the more interesting topics to address. BUT, Im unclear, in your example, about how the probability of two successes can be higher (66%)than a 'chance of ONE success (26%). Was that typo, or am I missing something?
Perhaps I am....and the key seems to be how many cards I am drawing. If I draw ten, the chances of drawing ONLY one Austria card are the same as saying that 9 of the draw must be nonAustrian. That can, intuitively, and statistically, be less than the odds that 8 of the draw are non austrian.
If so, then chances of 2 Austrian affects can be higher than chances of only one Austrian effect.
As to the value of Austria itself, that seems very dependent upon likelihood of war, since in times of war, a neutral or enemy Austria greatly complicates the passage of resources from Southeast Europe to Berlin.
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 Austria is very important for the Axis. The ability to move troops from Germany to Italy is useful. We discovered this the first time we played. The Axis can just go for it with a war, but the West taking it on turn one vexed the Axis player.
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blakestiger wrote:Austria is very important for the Axis. The ability to move troops from Germany to Italy is useful. We discovered this the first time we played. The Axis can just go for it with a war, but the West taking it on turn one vexed the Axis player.Good observations guys.
You are getting down into it for sure.
Great!
Craig
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As you observed, the math doesn't work. However, allow me to math nerd out.
Let's say you have 52 regular cards from a normal deck. The chances of drawing an ace is 4/52 or 1/13 (<7%). Drawing a second ace after you draw the first is now 3/51 or <6%. The chances of drawing 2 aces in a row is 12/2652 or 1/221 (<0.4%).
The odds do go up each time you fail, but that is "not a good prize."
initial draw 4/52,
fail creates new odds of 4/51 or 7.8% on the second card
fail creates new odds of 4/50 or 8.0% on the second card
fail creates new odds of 4/49 or 8.2% on the second card
fail creates new odds of 4/48 or 8.3% on the second card
fail creates new odds of 4/47 or 8.5% on the second card
...if you fail 48 times in a row your get a 100% chance on the 49th draw.
The odds are likely worse in TnT if only because other people will have some of the cards you need.
The math aside, you'll find that you have a use for most of the command cards early in the game. As countries become puppets, this will force combat. If you want to prevent combatAxis trying to be peacefulyou can keep the diplomatic rounds going longer by playing for influence but no puppets.
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