Re: Equity and value betting
Ummm.. I'll take a stab.... I think the basic thought here would be to answer this question: Given by read on the vil and his range, how likely am I to get called by a hand that I can beat? Taken to the extreme, if I am only going to get called by a hand that beats me, then you have no additional equity in the hand by betting and hence you check it down (UNLESS, OF COURSE, YOU DON'T WANT YOUR HOLE CARDS SEEN - IF, FOR EXAMPLE, YOU WERE RAISING WITH SOME ODD COMBO FROM EARLY POSITION OR SOMETHING WHICH WAS IN CONTRAST TO YOUR TABLE IMAGE, IN WHICH CASE, IT WOULD PAY TO MAKE THE BET AND HOPE TO WIN THE HAND WITHOUT EXPOSING YOUR CARDS). On the other extreme - if you KNOW you are going to get called on the river by a substandard hand that you surely have beaten, then, by all means, you would try to extract every $$ possible by betting.
As far as the math - you really don't need much fold equity at all to make it a positive EV play on the river - I mean, if you have a hand thats gonna be a loser 2 out of 3 times on showdown, and your opponent is going to call 70% of the time, you still have a 53% EV position and, if you arent risking much of your stack percentage wise, it's clear that you should make the bet, unless there is a possiblity that your opponent could be check-raising 5th street. But if your read on him is right and you don't think he will, then by all means make the value bet. The question becomes, "how much to bet so that I maintain what little fold equity (30%, lets say) that I have. If there is 1000 in the pot, and you bet 200, your opponent is getting 6/1 pot odds (200 to call to win 1200) and might make the call just figuring he can lose this 80% of the time and still make money. So your river bet must be large enough to maintain the "fold equity" that you require depending on your assessment of your hands chances on showdown.
If you feel that your hand has a higher chance to prevail on showdown adjust accordingly and feel free to offer what seem to be better pot odds for the call.
not sure if this helps
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