Quote:
Originally Posted by ArtyMcFly
Since you can't even strictly define hands as value bets and bluffs, you can't calculate a ratio for how to divide up your range.
To use an extreme example, you might bet a full house on the river and think "I have lots of boats in this spot, so I'm going to bet a lot of bluffs". And then villain snaps you off with quads.
If he has some combos of quads and boats in his range, that can mean that some of your "value combos" aren't pure value hands, because they don't always win, so you can't calculate an exact number of bluffs to match the 'value' hands.
I don't think it matters if our value is pure value or not when calculating bluffing frequencies.
Let's say we bet full pot on the river. We are betting 10 combos of pure value, which always wins when called. How many bluffs should we bet in order to make the villain indifferent to calling with their bluffcatchers? (I say 5 combos.)
Now let's change it so that we still bet 10 combos, but now the villain has some stronger hands in their range so our value hands only win 60% of the time when called. These are still valid value bets, since we beat more than 50% of the calls. But how many bluffs should we add in this new scenario, if we want to make the villain indifferent to calling with their bluffcatchers, i.e. hands that beat all our bluffs but none of our value? (I still say it's 5 combos.) Note that we can never make the villain indifferent to calling with their best hands - they will have a profitable call no matter how we divide our range. At least this is my understanding of a balanced strategy - we want the caller to be indifferent between calling and folding with the worst hands in their calling range. But maybe my thinking is overly simplified
Quote:
Originally Posted by pokerbetts
(Q2) If the above assumption is correct, we are giving villain 2/3 odds to call, meaning that he must win 40% of the time to make his call +EV. In order for us to be balanced and to make our opponent indifferent to calling we should (in a vacuum of information on an opponent or vs a good opponent) be bluffing at that same ratio of (40%)
Depends on how much equity our bluffs have, and how much equity the opponent's calls have against our value. If the worst hand in the opponent's calling range has 0% equity against our value and 100% against our bluffs, then we need to be bluffing 40% of the time as you mentioned. If the opponent has 5% equity against our value hands and 80% against our bluffs, we can calculate a bluffing frequency B which makes the opponent's EV zero:
EV = B*0.8*3*pot + (1-B)*0.05*3*pot - B*0.2*2*pot - (1-B)*0.95*2*pot = 0
2.4pot*B + 0.15pot - 0.15pot*B - 0.4pot*B - 1.9pot + 1.9pot*B = 0
3.75pot*B = 1,75pot
B = 0.467
So we'd use 46.7% bluffs and 53.3% value in this scenario.
Quote:
Originally Posted by pokerbetts
(Q3) If however, we realise that because of Villain's tendencies, or the way in which his range connects with the board, that he is likely to be folding too much how do we adjust our bluffing frequency? And how do we calculate this?
In theory, if the opponent folds too much it's profitable for us to bluff with every hand that we have. In practice people tend to notice quickly if we're
always betting in a certain spot (especially if it's a common situation). So it may be more useful in the long term to increase our bluff frequency in a less obvious way.