Dealing with blinds in an ante dealer's choice

[Lottery Larry]

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What will happen is, the deck moves ahead and the button will lag behind, keeping track of who posted a blind the last time where blinds were used.

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So, the button and the deck could be several players apart for several hands of games with blinds, until the button catches up?

Interesting solution. Maybe a PITA to keep everything moving around, maybe not. However, if I'm going to be in a blind, I'm not calling a blind game... and so the button might lag for a while or even get lapped by the deck?