Thank you Aaron for replying on this math question... I appreciate your taking the time to provide this excellent feedback.

I see what you're saying, but in both cases the probabality 'pw' is such that the Nth power can still leave you drastically in favor, even with high 'N'.

In the straight or flush example, suppose your chance of winning against one hand is .95. With 5 oppponents, (.95)^5 = 0.77... still very high, as expected.

In the other example, suppose your change of beating one hand (like k/8) is .5 (50%... in the 'middle'). with 5 opponents, .5^5 = 0.03. Much lower, as expected.

One way to resolve this objectively is to write a monte carlo simulation with multiple unknown hands, and compare to the one-unknown-hand probability (raised) approximation formula. I may explore this some more, across a broad range of test pockets, like the ones you posed.

I tend to agree that it may be unsafe with some hands, but I'd like an objective mathematical case/analysis or some sim data to really prove the point one way or the other.

Thanks again.