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Yes, there is a correlation but it is not linear.

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So what is the correlation?

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Also you have to take into account that a lot of players play an inverted style compared to you, loose early and tight late.

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So a push/fold player calls with lower ranked cards than VP$IP would suggest, in the later rounds. And the tight on the bubble players call with less hands than the VP$IP would suggest? Ignoring fold equity for a momnet.