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I had a similar situation at last year's WSOP, but was in your opponent's shoes. It was a significant pot and while I knew I was behind I thought I had the proper odds based on the dealer count. However, when it turned out he had significantly more chips (I think she said 10k and it was really 18k or something like that).
I called the floor over and he decided since I verbalized "call" and pushed out 10k, those chips would have to stay in the pot. He gave me the option of saving the extra 10k by folding, but I chose to call since it was now only another 10k or so. It sucked because I would have never called 20k...
This is actually how it's handled in most places, and IMO, the most fair way to do it.
The SB should of asked for a count from the dealer, as it was the SB's responsiblity to make sure their information was accurate.
FWIW, I've had the same short circuit myself before, after playing several hours, I thought I had more than I really had, when I went all in. This mostly due to the fact they had just recently colored up the chips, and I miscounted because I wasn't used to the new colors.
The others didn't ask for a physical count, but I did have 2 callers.
They check the flop, but then one guy went all in on his bottom pair on the turn.
It forced the guy with pocket 9's out of the pot as there was a king and Queen on the board as well as a 3.
I get my 10 on the turn (I had Ace/10 suited, and even with my miscounted chips, was short stacked, which is why I went all in).
Then the river was a 9. Had not the other guy pushed all in on bottom pair, I would of been out of the tourney (of course the guy with the pocket 9's was furious, and the other guy just couldn't get why what he did was wrong ... but I made sure to thank him for protecting my hand like that
).
When the dealer counted down my chips it was then discovered I had less than I had verbally said, to which 2 others said they would of called me hand they of known that, and one said he had a King with a bad kicker, when he folded it.