How long do I withhold tips? Dealer mistake costs me $1800. (long)

[RR]

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As an example, if I was deciding whether to make a call on the flop to fill a gut shot and while I was making that decision the dealer prematurely turned over one of my 4 outs for that gutshot, it changes the pot odds I would need to make that call. I now have 3 outs on the turn and 4 on the river. Before the fiasco I would have thought I had 4 outs on the turn (4/47) and then 4 outs on the river (4/46) to hit or: 1 - (43/47 * 42/46) = 16.5%. But after the fiasco my turn chances have been reduced to 3 outs (3/46) so by the river my chances are 1 - (43/46 * 42/46) = 14.7%.

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You chances of hitting on the river are better than you suggested because you have a 1 in 24 chance of hitting exactly the exposed card.