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The revised rules for preparing the Loyalty deck when using the "Exodus" expansion say that in a 6-player game, we should build a deck with an additional "You are not a Cylon" card (compared to the core rules for Loyalty deck.

So, in a six-player game, after the first round of dealing the cards, we will have 7 cards, and one of them is the Sympathizer card. So in theory, it is possible that one of the Cylon cards (or the Sympathizer card) will never be drawn. Since one card is added to the Loyalty deck before drawing a new Loyalty after execution, it is possible that even after an execution there will only be one Cylon on the board.

Did I get the rules for this right? Is this indeed a possible situation?

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You are correct it is possible to have only one Cylon.

This situation can occur if one player is dealt two You Are A Cylon or Sympathizer cards, and the remaining Loyalty card with that name is the last undrawn Loyalty card.

Using the standard Execution rules for Exodus, if you were human, you would add a You Are Not a Cylon card to the Loyalty deck when selecting a new character. This won't change the possibility of having only a single Cylon though, because the Loyalty deck will still have one extra card. If you were a Cylon, you just get moved to the Resurrection Ship, keeping both your Loyalty cards, which also doesn't change the situation.

The only exception to this, is if you were playing with both Exodus, and Pegasus expansions. Step 2 is revised to hand off the unrevealed You Are a Cylon card to another player. So you would have two Cylons in the game. This is covered on page 22 regarding Handing Off Excess Loyalty Cards

Execution - The rules for execution are slightly revised for the Exodus expansion. Use the rules as they are described on page 7 of this rulebook, even when playing with the Pegasus expansion, with the following exception. During step 2, “Prove Loyalty,” a player with one or more “You Are a Cylon” Loyalty Cards reveals one and gives all his remaining facedown Loyalty Cards to a human player of his choice, as described on page 12 of the Pegasus rulebook.

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If one player is dealt two You Are a Cylon cards, then it'll be possible of him to use the Resurrection Ship to give one of his loyalty cards to another player, thus making him a second Cylon. The situation that disturbs me is the one where the second "You are a Cylon" card remains undrawn in the Loyalty deck. –  idan315 Apr 14 '12 at 17:56
    
Is there a justification for this, balance-wise? Seems like it'll be a horrible game for the Cylons in this case. The reason why I've asked this question is to know whether it's a situation I want to prevent via house rules. :) –  idan315 Apr 14 '12 at 19:58
    
It shouldn't be necessary. The odds of it occurring are highly unlikely. Haven't worked it out exactly, but I am guessing more than 1:100. Even if it did occur, you said that the Cylon can choose to give a loyalty card away on the Resurection Ship. –  user1873 Apr 14 '12 at 21:36
    
No - again, I'm worried about a situation where the other Cylon card hasn't even been drawn. The chances for that are approx. 9%, which isn't very high, but isn't low enough in my opinion. –  idan315 Apr 14 '12 at 21:46
    
I don't see how that matters. If the other Cylon card sits undrawn, then the player with the Sympathy card reveals it immediately. When they make it to the Resurection Ship, they can hand off their You Are a Cylon loyalty card. –  user1873 Apr 14 '12 at 21:58
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The situation of having only one Cylon in a 5/6 player game is possible if using the Exodus rules for execution and loyalty deck setup. The Exodus expansion added the concept of "You are not a Cylon" deck in addition to the Loyalty deck, and also an additional step to Human Execution:

The player adds one card from the “You Are Not a Cylon” deck to the Loyalty deck, shuffles the Loyalty deck thoroughly, and draws one new Loyalty Card,which is kept hidden from the other players.

In addition, the loyalty deck rules for Exodus always leave one extra card in the loyalty deck, after all of the loyalty cards have been dealt in the Sleep Agent phase. This occurs even if playing with other expansions.

This is done in order to prevent the certainty that comes after executing a character. In the original Pegasus execution rules, executing a character meant knowing for sure whether this character is a Human or a Cylon. In the revised Exodus rules, this means that executing a Human character might turn this character into a Cylon. It does mean, however, that in a five player game, where we have 2 "You are a Cylon" and 9 "You are not a Cylon" cards in the loyalty deck, the chances of one of the "You are a Cylon" card to be at the bottom of the deck are 18% (16% in a six-player game), and thus that card won't be drawn at the sleeper agent phase.

Each execution or personal goal revealed before travel distance is 6 adds an additional card to the Loyalty deck and mixes them before dealing a new Loyalty card to the player who got executed or fulfilled a personal goal, so this probability drops down by 50% each time this happens. Even then, this means that the second Cylon can enter the game only after significant amount of time.

Various approaches exist for this. Some claim that this isn't an issue at all, as the paranoia inherent in the game makes it challenging even if there is only one Cylon in the game. Other people disagree, and have devised various mechanics and house rules in order to deal with this situation, for example, here ("Avoiding 'Missing Cylon Syndrome'") or here (an execution variant for playing with Pegasus and Exodus). It mostly comes down to the balance in your specific game group with your play style.

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I don't like adding and accepting my own answer, but I wanted to summarize the knowledge I've accumulated about this topic, plus the comments me and Ingó Vals had on the original answer. I will try to edit this answer to make it as thorough as I can in the future, perhaps adding more links to various house-rules that deal with the "Missing Cylon Syndrome". –  idan315 Dec 5 '13 at 10:30
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Answering your own question is perfectly ok and encouraged, if you have a good answer - and accepting it is perfectly fair if it is truly the best answer to your question (judge as if it were an answer by anyone else) –  Jonathan Hobbs Dec 5 '13 at 13:00
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