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Subject: Average Number of Turns in Friedrich rss

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Alex Carr
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A friend and I tackled this problem and with some help determined that it takes 15.2 cards on average for the four event cards that will hand Prussia the win to appear. Or in other terms, the average game length is 21 turns. Perhaps even more chilling, 22% of games will go to the last card.

The immediate consequence of this data is the revelation that Friedrich is actually a very long game if Prussia wins. Secondly, in both of my games Prussia had little chance of making it 21 turns.
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Charles F.
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Most interesting. Thanks for taking the time. Could you provide the probabilities for the various turns?
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Tom Hudson
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This seems bogus. How did you arrive at your conclusion, considering it’s possible for the game to end on turn 9--unlikely, I admit.

In my experience if the Prussia player is any good, Prussia has a decided advantage. Consider that if only one ally goes out early in the game, which is not unusual, Prussia’s chances go up dramatically.
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Luca Iennaco
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charlesf wrote:
Could you provide the probabilities for the various turns?


Turn...chance that the game is over at the end of that turn

09...00,03%
10...00,13%
11...00,33%
12...00,65%
13...01,14%
14...01,83%
15...02,75%
16...03,92%
17...05,39%
18...07,19%
19...09,35%
20...11,90%
21...14,87%
22...18,30%
23...22,22%
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Jon Dieringer
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Seems quite sound, except for the "it takes 15.2 cards" part. I see it as 12.3 cards. Otherwise 15.2 cards seems to disagree with the 20th turn average ending. 12.3 agrees more.
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Was George Orwell an Optimist?
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chemist wrote:
Seems quite sound, except for the "it takes 15.2 cards" part. I see it as 12.3 cards. Otherwise 15.2 cards seems to disagree with the 20th turn average ending. 12.3 agrees more.


To be sound the thread title would need to be changed to "Average Number of Turns in Friedrich When the Prussians Win" as well.

The average number of turns for all plays would have to take into account the games where other powers win. Those games will almost certainly have a lower average number of turns than the games which the Prussians win.

I also believe that amongst equally skillful players Friedrich will win far less than half the time, in which case the average number of turns for all games will be closer to the average number of turns in lost games than in won games.
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Luca Iennaco
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chemist wrote:
Seems quite sound, except for the "it takes 15.2 cards" part. I see it as 12.3 cards. Otherwise 15.2 cards seems to disagree with the 20th turn average ending. 12.3 agrees more.


Do the average (multiply each turn for the % that it is the last one).
The sum is 20,2 (since you do not draw in the first 5 turns, it means 15,2 cards).
Have fun!
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Luca Iennaco
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Sphere wrote:
To be sound the thread title would need to be changed to "Average Number of Turns in Friedrich When the Prussians Win" as well.


Indeed.

Sphere wrote:
The average number of turns for all plays would have to take into account the games where other powers win.


Yes, but since it depends by the the players (not by a deck of cards), you can't calculate the odds (you may keep some statistic, if you wish... but it'll need a lot of plays and probably will be significative only in your group).

Sphere wrote:
I also believe that amongst equally skillful players Friedrich will win far less than half the time


One on four would be fair (since it is a 4-player game).
Or one on three if you play it with only 3 players.
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Ralph H. Anderson
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Since there are actually 6 powers that can win (Russia, Sweden, France, Austria, Imperial Army and Prussia/Hannover), wouldn't you want them all to have a chance to win equally? So 1 in 6 would be the chances if all have an equal shot at winning no matter how many players are playing.

Of course, so far it appears that Austria wins the most - certainly more than 1 in 6 and I would love to hear if anyone has even come close to winning as the Swedes! However, I would argue that this is probably due to inferior play by all the other nations - and most probably by Prussia/Hannover. And of course, the fact that the other nations can be put our of the game lowers their chances of winning as well.

I would love to hear strategies. We are thinking that Prussia must vigoursly defend against Austria in Schleisen. Not necessarily by winning battles but by forcing many many battles that Friedrich loses by one point at a time.

Anyway - love the game!
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