@ muebarek:
many misconceptions in your thought process imo. villains on such a limit don't have any idea what terms like "made hand" "relative hand strength" or "turning made hand into a bluff" mean. not at all.
ofc they dont "turn a made hand into a bluff" when they play A9 that way. but they just do what feels natural to them. c/c down cuz they have a pair and on the river they dont know exactly what to do and just bet cuz if feels to be their best option/feels naturally right to them. they have no sort of strategy behind their game. thats why u need to absolutely understand math and thats why this is the easiest snapcall on the river, not cuz of board texture or ranges ... cuz u only need to be good one in three and still turn a profit!!! almost impossible that that is not the case.
i didnt wanna write it before and i think u should forget about it after u read it. but to make things clear. i value raise the river 2.5x before i fold this hand. i think the decision whether to call or raise is waaaaaaay closer than folding vs calling.
and if u start telling me "my range looks soo strong, what weaker hand in his range can call .... " => i tell u its nl20 and if he has KQ, AJ he is just not folding to a 2.5x raise on the river.
my suggestion to everyone who thinks about folding here: play 10k hands of live poker. nl100 or 200. and your gameplan should be to only focus on river actions by all plrs at the table. also plan on make light calls even if u think they could be -ev longterm. just to see many showdowns. that will help u realise that recreational plrs have absolutely no clue about the basics of the game and just do what feels naturally to them.
@ prof: pls coach toby some elementary maths!