http://tvtropes.org/pmwiki/pmwiki.php/Main/GayOption

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Oftentimes in video games, the option exists for the main character to pursue a romantic relationship with some other character. Aside from dedicated Romance Games, this is most common in more open-ended games, such as RPGs and Wide Open Sandbox games, rather than games that follow a tight, "every note must be hit" plot, where any romance happens at the behest of the story. As video games are traditionally a medium aimed at a male demographic, and the general thought is that most males are heterosexual, most of the romance happens between a male character and a female character of the player's choice.

In some cases, however, game designers began to realize an increasing interest in same-gender love interests, as gay, lesbian, and bisexual people become more visible. And as an interactive medium, it's possible to include such content while giving those uninterested in same-sex romance the option of skipping it. This means that games that include romance have increasingly allowed the protagonist the option to romance a few characters of the same gender.

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For Japanese games where being gay is not just an option but the game itself is themed on it, see the video game sections of Yuri Genre (for lesbians) and Yaoi Genre (for gay males). This may or may not overlap with Optional Sexual Encounter, since a game won't always go that far.

Examples:

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Games and series offering male/male options

Games and series offering female/female options

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Games and series offering both

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