Interesting situation, check my math
 

I flop an OESD in live play and check it. It's checked around and the turn card is dealt, which completes my straight, but last to act says "I never checked." So according to the rules, the turn card is pulled to the side, flop action is completed, the river card is dealt as the turn, then the original turn card is shuffled back into the deck and another card is dealt. Obviously I was pissed off that my card was returned to the deck because some retard kept hiding his cards and wasn't paying attention, but I started to wonder how this would affect my odds. My odds on the turn are easy enough to figure out, they decrease slightly from 8/47 to 7/46, but the river is a bit more complicated. There are 25 cards left in the deck and I know at least one of them makes my hand, so I put my odds at (1/25)+(7/45)=44/225. So it seems that by the river my chances increase from the standard OESD of 31.45% to 33.25%, so the situation is actually better than if the last to act had been paying attention and protected his action. As the hand turned out, the original turn card came right back out on the river (good job dealer) and I won the pot, but the players and the dealer made comments suggesting that I was retarded for chasing knowing that one of my outs was missing on the turn.

Re: Interesting situation, check my math
 

I think you math is right. The comment of the other players and dealer is stupid. I presume you had sufficient pot odds even with one less out on the turn.

Paul

Re: Interesting situation, check my math
 

Your math is close. I assume there are ten players for 20 pocket cards, plus 4 on the board. Then there was a burn card before the flop and turn, plus another one before the second turn (the original river card). That gets us to 25 left in the deck. Is that right?

Given the 25 cards in the deck, there are two possibilities. 1/25 chance of getting the old turn card to complete your straight and 24/25 chance of not getting it, in which case you have 7 chances in 45, as you say, of completing your straight. So the correct computation is:

1/25 + (24/25)*(7/45) = 71/375 = 18.9%

not 44/225 or 19.6%. Your overall odds go down slightly from 31.45% to 31.27% (your numbers should give 31.80%, not 33.25%).