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Subject: En värld i flammor, part 4 rss

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Adam Thorp
Sweden
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"I find that 'pinpoint' accuracy during a bombing run increases proportionally with the amount of munitions used."
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January/February 1939

The turn begins with new units spontaneously "spawning" in both Turkey and China, due to us correcting previous mistakes with the rules. The Turkish loyalists secure their last stronghold in Smyrna with a 5-3 infantry corps, and the IJA troops battling the Chinese defenders in northern China welcome four new militias and two infantry corps with warm-yet-formal bows of greeting.

The United States go all in with their bid points to secure the first place in the turn order, and order an increase in military spending. This is quickly followed by Japan and Italy doing the same, before Italy rolls an end to the political action for this turn.

The winter weather starts out nice and the fascists seize the initiative to move troops around in Greece and in China. However, the weather quickly worsens with blizzards and snows all around, and any hope of continuing the offensives are quickly dashed. Germany forgets that it controls a loyalist cavalry unit ("Turkish Rambo") in northern Turkey, and the rebels quickly surround and crush it before it can escape. They do take a militia with them as they go down fighting however, and all the rebel forces are flipped and prevented from further movement this turn.

After the military action ends, it is time to build things! The US Navy commissions a new aircraft carrier, but Japan and Italy are also quick to make use of their increased industrial capacity with naval vessels and ground forces. The IJN forgets to place a vessel in the South China Sea, allowing the US resource convoys from the Philippines to reach Kanton, and China uses the extra production along with the US free trade bonus to build an extra unit. Japan makes a solemn vow never to repeat this mistake.


March/April 1939

Japan finally closes its first trade agreement with the Netherlands for some oil and then uses all the negative influence its past actions have garnered it to move Venezuela away from the US on the political map, denying the US the oil it needs to run its factories at 100% capacity. Germany follows up with a second alliance with Sweden. The United States then offers China an upgrade of their treaty, but roll an end to the turn before China can accept. Ten Chinese bid points are flushed down the drain.

As soon as there is a break in the spring rain, Germany declares war on Denmark! The German Heer rushes into Denmark and captures Copenhagen before the democrats can so much as blink. A Danish government-in-exile is established in Godthaab, Greenland, by the Americans. "Did you say 'Gotham'?" Italy asks to the great amusement of everybody present. No action in Greece or China due to unrelenting rain (we rolled a '1' twice in a row on the weather). The Turkish rebels slowly march down southwest towards Smyrna.

China does not build any units and instead hoards all its income to try and gear up on its own. France keeps producing more and more territorial units for some reason.


May/June 1939

The Commonwealth and France both make aggressive bids and grab first and second place for the politics. The Commonwealth makes a statement declaring that the "sovereign territory of Poland is inviolate" (guarantee), and France has an election (again with the elections!), sadly noting that fully one third of its political actions so far has been just that: elections. Italy follows and attempts to break the German alliance with Poland (the British guarantee had perfect timing, it would seem) but fails. Germany finishes up the paperwork for its invasion of Denmark and then manages to end the turn right before the US can act.

In China, Japan assaults Hang-Chow with a 4-1 odds ratio and rolls a 10! The defenders are thoroughly stomped before any pesky journalists can send pictures to the world (no US entry). The Japanese troops are fought to a standstill at Shanghai, however. An Italian assault in Greece versus Athens does not capture the capital but do eliminate one unit, so now only a single infantry corps protects the city from future attacks. The Communist rebels form up for an assault at Smyrna, but the fascists manage to roll an end to the turn after two impulses with terrible weather everywhere but around the Mediterranean before the assault can be initiated.

France weeps with joy when he finally manages to build a territorial for Indochina to stomp the pesky native rebels occupying Hanoi. The US Navy commissions the carrier Wasp and the battleship Massachusetts. The Japanese players counters with multiple vessels of his own. The production circle, which has been only sparsely populated so far, is now getting more and more cluttered.


July/August 1939

The Commonwealth goes first again and has its election in order to ensure that the fascists cannot hit her with a "Government falls" followed by a surprise invasion of Poland. Italy follows up and ends the turn on a '2' before China, who has gone all in, gets to act. China has now spent 18 bid points, three years' worth, without getting anything! Italy and the fascists are not too pleased, however, since Italy's action was to offer a pact to Germany which the latter did not get the chance to accept. They are now still only at level 1. Italy has now ended 9 of the 22 political turns in the game so far, and everybody (especially Italy!) agrees that "Il Duce" can never again be allowed to roll his own "end of turn" die.

The Communists go first and immediately assault Smyrna. Loyalist and rebel aircraft have a face-off in the skies above the city that ends with the rebel fighter unit being blown out of the sky. The rebels go in with only 1-1 in odds (risky!) but manage to achieve a 1/1 result on the assault table so each side loses a unit. This is seen as a victory for the rebels (well, at least the rebels see it as such) since their losses can be replaced whereas the loyalists' cannot. However, all the rebel troops are flipped face-down so there will be no more action in Turkey this turn.

Italy bombs Athens with two aircraft but miss both rolls before rolling a '1' on the 7-1 assault table. Athens falls, but it costs Italy a unit and all their troops are flipped, so there will be no march towards Istanbul this turn. In China, the lone 1. Infantry Division (with a mighty combat strength of 1) is given the order to "hold Nanking" as the rest of the Chinese army evacuates the city for more defensible positions in the mountains. The Chinese soldiers look at the vast horde of IJA forces around them and prepare to go meet their ancestors. However, Japan uses its impulse to assault Shanghai instead and manage to crush the Shanghai warlord unit. This time, however, the US public is made aware of the event and with great satisfaction the US player moves an entry marker from "Japanese Entry" to "Japanese Tension", the first tension marker "rewarded" to a fascist. The 1. Infantry Division takes the chance to escape the Nanking death trap and follows its cohorts up in the mountains. All over southern China, nationalist forces move towards the front lines in an attempt to shore up the defences southwest of Shanghai. In the north, the communists have formed a strong defensive line in the mountains east of Si-An. The Chinese defenders, both communists and nationalists, have finally understood how horrible the terrain in China is for the Japanese attackers (rivers and mountains all over the place) and try to make the best of it. The Chinese partisans in Tien-Tsin, however, are attacked by a combination of Manchurian, Korean and Japanese forces and succumb to a 12-1 assault. The head of the Japanese army moves his forces around to ensure that no further "peasant uprisings" can occur.

As the summer comes to an end, the chances of a "Great War" erupting in Europe look ever more slim. Germany has conquered Denmark, but is still allied to Poland which in turn is guaranteed by the British. Also, Germany and Italy only has a level 1 treaty with each other. If Germany does not break its own alliance with Poland in September, we will likely have to wait for spring 1940 for the real action to begin ...
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Simon Nicholls
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Very interesting. It looks like the consistently early finishes to the political affairs will result in a significant delay in starting the general war.
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Adam Thorp
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Yes, that might be the case. I did some statistics and arrived at an "expected value" of 3.66 political actions per turn. Playing MP0(g) to farm bid points would prolong the turn, since it does not increase the chances of ending the turn like the other actions.

Looking at our average, we are at 3.45 so we are definitely below the average. However, I think we are only "missing" four, five or maybe six actions. Statistically speaking, that is.
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Simon Nicholls
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Interesting. How did you arrive at that "expected" value?

If I remember the next time we play, I will take a note of the number we get. I doubt I will remember however, in light of the stresses and strain of actual play (and the consumption of beer).
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Adam Thorp
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nailsworthnobby wrote:

Interesting. How did you arrive at that "expected" value?

If I remember the next time we play, I will take a note of the number we get. I doubt I will remember however, in light of the stresses and strain of actual play (and the consumption of beer).

Okay, this is going to be a long and rambling post about statistics and probabilty theory. The theory behind it can be found on Wikipedia: http://en.wikipedia.org/wiki/Expected_value

The expected value for a random event (such as a dice roll or the number of actions in a DoD political turn) is also known as the mean value. It can be calculated as

[sum over all possible outcomes]:
(probability of outcome)*(value of outcome)

For example, when rolling a six-sided die the probability of getting a 1 is 1/6 (assuming the die is fair). The probability of getting a 2 is also 1/6, as it is for all possible outcomes. Hence, the expected value of a die roll is

(1*1/6) + (2*1/6) + (3*1/6) + (4*1/6) + (5*1/6) + (6*1/6) =
= (1+2+3+4+5+6)/6 =
= 21/6 =
= 3.5

The average value of a die roll is 3.5.

In Days of Decision, you roll a ten-sided die after each political action. If the number rolled is equal to or lower than the number of political actions so far during the turn, the political step ends. After the first action, you have to roll a 1 to end the politics (10% chance), after the second you have a 20% chance to end and after the tenth action the turn must end because it ends on a roll of 10 or less.

So, the formula above would be

Expected number of actions =
[sum for all turn lengths from 1 to 10]:
(number of actions)*(probability of getting exactly that number of actions)

For there to be only one political action, the first player has to roll a 1, which has a probability of 10%. So, the first term would read

1[number of actions]*0.1[probability of exactly one action]

This is 0.1.

For there to be two actions, the player taking the first action must not end the political step (i.e. roll 2 or higher, 90% chance) and then the player taking the second action must end the turn (i.e. roll 2 or lower, 20% chance). So, the term would be

2*0.9*0.2 = 0.36

For the third player to be the last player, neither the first player (90%) nor the second player (80%) can end the turn but the third player must (30%).

3*0.9*0.8*0.3 = 0.672

... and so on up to the last term (10) which is

10*0.9*0.8*0.7*0.6*0.5*0.4*0.3*0.2*0.1 = 0.0036288

Sum these all up and you get 3.66, which is the expected value of the number of political actions taken in a single turn.

Of course, my main mistake in the formula above is that I am assuming that no one is taking any MP0(g) actions to farm bid points, since these do not increase the probability of ending the turn and hence prolong it. However, the mathematics become a bit more complex if you do and could not be bothered. In simple terms you can expect the political turn to drag on significantly longer if people start taking MP0(g) actions.

Another way to look at this is the following table, which shows you the probability of getting an action depending on what initiative position you are in:

1st place: 100%
2nd: 90%
3rd: 72%
4th: 50%
5th: 30%
6th: 15%
7th: 6%
8th: 2%
9th: 0.3%
10th: 0.03%

There are only 8 players, but the table above runs to 10 because players can take multiple actions. Anyhow, the lesson to be drawn is that if you want to have a fair chance to get an action in, aim for first, second or third place. If you are fourth to act, you only have a one in two chance of actually getting to do something.

For our game, our turn average of 3.45 is significantly low, especially if you consider all the MP0(g) actions taken. However, we are still only "missing" maybe 4 or 5 actions from the average.
 
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