Nah, it's completely random. I play on 2 mobile. At one point, one account is like 4 times while another is just 1 (Both open all the time). I really hate this kind of randomness, not equal between player¬ base on playing.
Note that both of my account have level 60, and every play also 8700-9000 points so I'm sure the level and score is not affect appearance rate at all. It just determine Bakura level as official notification.
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