[cartman]

I apologize in advance if there are errors, because I did these calculations very quickly. I also used a couple of extremely simplistic assumptions:

1) The only hands SB would have played this way are overcard(s) plus gutshot, K high, and A high (which rivered a pair)

2) He would always have played all of these hands this way preflop, on the flop, and on the turn

3) He will always fold to your river raise if he doesn't have a pair

4) He will always donk the river when he has an Ace


Given that you have one T and one 4, by my quick estimate there are 201 overcard(s) plus gutshot combinations, 168 K high combinations, and 152 Ace high (now one pair) combinations. So for your bluff to be profitable he has to be bluffing 3.5 times as often as he actually has an Ace (because you are getting 7 to 2 = 3.5 to 1 odds.)

Since our assumptions tell us he will bet with all 152 of his hands which actually contain and Ace, he needs to bluff with 152/3.5 = 43.4 additional hands. Since there are 353 combinations which do not contain an Ace, he needs to be willing to bluff the river 43.4/353 = .123, or a little over 12% of the times that he is unpaired for our river raise to be profitable.

If he will fold the K high hands on the turn and therefore can have only Ace high or an overcard(s) plus gutshot hand, he needs to be willing to bluff 43.4/201 = .216, or almost 22% of the time for our river raise to be profitable.

Cartman