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Subject: An Endgame Quandary - How To Play It? rss

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Alex Harkey
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I'm interested in understanding the optimal decision in a recent game I played. It was agonizingly close for me and I'm interested in learning what others would do.



Would you play the White 8 or the Blue 8?

Some context:

If I play the Blue 8 & 9 for 51 points and the White 8 & 9 for 34 points my current potential max score is 9. I have the ability to draw from the deck twice [followed by picking up discards] to allow the chance to play a fifth useful card.

The White 6, 7 & 10 each score at least 12 points and attain the 8 card bonus of +20 which pushes us ahead of our opponent. The Blue 6 & 7 score us 18 and 21 points respectively. The 18 points only brings us to a score of 27 which is not enough to secure the win with certainty but it may be enough.

My opponent has 6 useful cards, of which they may play from four to six dependent on their pace.

My opponent's optimal outcome is to play the White 6, 7 & 10, Green 8 & 10, Red 10. The cumulative scoring impact as a result would be 92 additional points. Adding to their current score of -64 this brings their theoretical max to 28 points.

This game is currently in turn 19. Each player has taken at least 18 turns (So in baseball terms we are in the bottom of the 19th inning).
On turns 1 & 2 they played the Green Investment & Green 3. They may hold the Green 8 & 10.

On turn 3 they played the White Investment Having played this person several times before, its unlikely they would do this without holding an additional white card to provide some assurance (I played the White 5 on turn 15). They likely would have played the White 6 if they held it by now.

On turn 8 they completed their blue expedition by playing the Blue 10. They have had 11 turns to potentially accumulate more Blue cards.

How would you play it?
Poll
Which card should be played for optimal results?
Blue 8
White 8
The decision is insignificant
      46 answers
Poll created by Solid
 
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True Blue Jon
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Why did you two play to so many expeditions?
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Josh Chen
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I've voted Blue 8
Now I want to know how you played and the outcome whistle
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Simon Woodward
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White 8. Blue 6 and 7 and white 6 and 7 are still out there. Blue 6 and 7 are worth more to you.
 
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Fraser
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Back in the days when there were less maps we played every map back to back
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manukajoe wrote:
White 8. Blue 6 and 7 and white 6 and 7 are still out there. Blue 6 and 7 are worth more to you.

However playing the White 8 concretely tells your opponent that you do not have the White 6 or 7 and that they are available to be picked up.

Playing the Blue 8, means that your opponent only knows about the white cards in their hand.
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Nacho Facello
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manukajoe wrote:
White 8. Blue 6 and 7 and white 6 and 7 are still out there. Blue 6 and 7 are worth more to you.


But what about the +20 bonus? I'd say that white 6/7 is worth more given that bonus. Of course, the complication comes because white 10 is also out still...
 
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Simon Woodward
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nachof wrote:
manukajoe wrote:
White 8. Blue 6 and 7 and white 6 and 7 are still out there. Blue 6 and 7 are worth more to you.


But what about the +20 bonus? I'd say that white 6/7 is worth more given that bonus. Of course, the complication comes because white 10 is also out still...


True, you only need 1 more white card (out of the 3 unaccounted for) to get that bonus, which is a good bet.
 
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Sebastian
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I voted for blue 8. Not becuse I'd calculate the exact points as you did, but because I'd hold my hopes on getting an 8th white card for the 20 bonus.
Also I'd assume if opponent has white 6 in hand, he would have played it by now.
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M K
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In my opinion, playing White 8 is clearly correct here.

1)While going for the bonus is tempting I think there is a much higher chance of Blue 6 or Blue 7 being in the remaining deck than the White 6 or 7. Your opponent played the White Investment on 3rd turn and I expect him to have either White 6 or 7 (or even both) fairly high percentage of time. The reason he hasn't played a White 6 so far is probably because he was waiting for the small White numbers to begin with, which you happened to have.

2)Getting blue 6 should be enough to win. It will get you to 27 points, and your opponent's maximum is 28 points. It is highly unlikely that he has ALL of his 6 top cards to reach his maximum, and even if he does, it also means he has a White 6 and 7, in which case it makes no sense for you to wait for them, thus making the White 8 once again clearly correct play.

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Moose Detective
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Late to the party but since the original poster never responded I'm going to go with option D. none of the above - discard a card.

Your opponent has NO reason to draw from the discard piles and drag the game out so you have only ONE draw left. might as well take it now, see what it is and then play your hand in any order while drawing the rest of the way from the discards.
 
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Alex Harkey
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Thanks for everyone's responses. Life got in the way of writing a response but I wrote a blog post conclusion to this problem.

Link

In the game I played the White 8. I can't know for certain what the opponent had at this moment in time but they didn't have the White 6 as I drew it and the Blue 7 to finish the game.

Thank you!
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