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Originally Posted by Acryl2
How exactly do I define the largest bet that I can make? If I know how many value-hands I'll have in that spot compared to how many possible bluffs, then figure out the ratio and somehow determine the betsize?
Suppose the effective stacks on the river are 10x pot.
If you've shown up to the river with a range of 4 winning combos for every 1 losing combo, then betting 1/3 pot allows you to bet your entire range while making him indifferent. If you bet any less, he'll always call and you won't profit as much overall. If you bet less and bluff less often to compensate, he'll be indifferent, but you won't take as many pots, so again you'll profit less overall. (Btw, when I say "taking pots" in this context, I mean "Galfond pots" or G-pots if you will. When he calls your bluff, you didn't take the pot, but you did take the G-pot because he's also sometimes paying you off with your winning hands, which comprise the majority of your range.)
In that situation I'd advise betting a little more than 1/3. If she uses pot odds and knows your range's ratio of winners to losers, she'll always fold, but it won't cost you anything and it will give her a chance to make a mistake. It won't cost you anything compared to betting exactly 1/3, because when you bet exactly 1/3, it makes her indifferent, which means your EV is Pot regardless of what she does. When you bet more than 1/3 and she always folds, your EV is still always Pot (except without variance), and you're still collecting that EV with your entire range. She's not exploiting you by always folding; she would be if you weren't already betting your entire range with this bet size.
If you have 6 value hands for every 5 losing hands, you can bet your entire range by betting 5x pot.
To bet all-in you'd need a ratio of 21:10 value to bluffs.
You always need more value than air in your betting range, so if you showed up to the river with more air than value hands, you'll have to surrender with some of your air rather than always bluff.
How to figure out these sizes, well you need to make Villain indifferent to calling, so make her EV of calling equal 0.
Her chance of winning is equal to your bluffing frequency, f.
Her payout is 1+x, where x is the size of your bet in pot units.
(1+x)f - (1-f)x = 0
...
x = f / (1-2f)
If f is a fraction a/b, I prefer: x = a / (b - 2a)
E.g. in the 6:5 example, f=5/11 so x = 5
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I wonder if theres an easy solution that allows us not to become exploitable, without having any informations about villains tendencies (GTO)?
Make the opponent indifferent. Not easy in general, but easy on the river. In your OP example, you're unexploitable if you call 2/7 of the time, so that's the GTO calling frequency. You can derive it by setting the EV of Villain's bluff to 0.
Regardless of whether you're the bettor or caller, you don't need to know Villain's range to determine your GTO frequency. However, to know whether your actual hand falls in that frequency requires that you know
own range, which most people don't well enough. For instance, if you're trying to call with 2/7 of your range, you want it to be the top 2/7. If you don't know your own range, and your hand is top 3/7, you might make the wrong call.
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Another solution might be to study common pool tendecies to see what ratio a pot or overbet turned out to be a bluff/value-hand. How do you think about that?
Yeah that can help against unknown villains if you're trying to exploit them from the start.
Edit: I made up a phrase "Galfond pots" without referencing Galfond Bucks or "G-bucks", which were coined
here (and an alternate use was written about
here). And then there is
this good article about g-bucks and beyond.
Last edited by heehaww; 01-25-2017 at 10:42 AM.