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It is stated for both the Colosseum and the Theatre that they can only provide as much happiness as there is population. I believe they both provide +5 Happiness for a population of 5.

Do they stack on the same population meaning I would get 10 Happiness with a population of 5?

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up vote 6 down vote accepted

No, the population limit applies to the total happiness from all buildings. Theater provides 4 happiness and Colosseum provides 3 happiness; if you have a size 6 city with both buildings, you would get a total of 6 happiness. You would need a size 7 city to get the full benefit from them.

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Just a comment - this limitation does not apply to happiness gained from wonders. –  Oak Feb 27 '11 at 18:56

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