[2NL] 6m AA OOP rivers nut flush on baby flush board

[daviddem]

One thing that is getting at me about our bluffing range: is it not the case that we should bluff with the top of our-c/f-range-if-we-were-never-bluffing? So should we not bluff bet our pairs of kings before we bet our pairs of jacks?

Also in your math above we are supposed to be c/c the nuts some times (if Z is non zero). But in the final range breakdown you gave, we are always shoving the nuts.

[spoonitnow]

One thing that is getting at me about our bluffing range: is it not the case that we should bluff with the top of our-c/f-range-if-we-were-never-bluffing? So should we not bluff bet our pairs of kings before we bet our pairs of jacks?

No, you should bluff your jacks before you bluff your kings. The kings are much more useful in your checking range since they're more likely to win at showdown if it checks down, and they're more likely to win at showdown if you need use them as a bluff catcher. In the AKQ game, it's similar to why the IP player checks kings and bluffs with some queens.

If we were checked to in position with one bet left, our range would look like this:

<-- bluff --|-- check --|-- value bet -->

Out of position with one bet left, it looks like this:

<-- bluff --|-- check/fold --|-- check/call --|-- value bet -->

If you're interested in reading more concrete proof that these configurations are ideal, then check the half-street and full-street AKQ or [0, 1] games. These are also ideal for exploitative strategies that perform well, not just unexploitable strategies.

With multiple streets of betting left when facing a bet, especially when the ranking of hands in your range aren't as clear-cut, these configurations can change. A good example is facing a raise pre-flop. Our range could very possibly look like this:

<-- fold --|-- 3-bet bluff --|-- call --|-- 3-bet for value -->

The reason for this difference is that with streets left to come, we have the option to semi-bluff. On the river, we do not have this option, and our only value from bluffs comes from fold equity.

Also in your math above we are supposed to be c/c the nuts some times (if Z is non zero). But in the final range breakdown you gave, we are always shoving the nuts.

I was giving an example of a couple of different balanced ranges. The one in the spoiler tags is balanced, albeit not ideal. The one before the spoiler tags does check the nuts sometimes.

As an aside, Z does not have to include the nuts. Z is just the top portion of our checking range. If we are always betting the nuts, for example, then Z wouldn't include the nuts.

[spoonitnow]

Related to the difference between river spots and non-river spots:

The percentage bet/(bet+pot) will tell you how often to bluff in all-in river spots to be unexploitable when you bet. You take that percentage of your value betting range, and that's how often you should bluff. For example, if you were shoving 2/3 of the pot with 10 combinations for value, bet/(bet+pot) would be 40% and you would need to bluff with 40% of 10 combinations = 4 combinations for your betting range to be balanced.

With cards left to come in all-in situations, however, you can bluff much more often if you have good semi-bluffing hands because they can still win sometimes, and when they do win, they win a part larger than the one you're betting into. That's related to why you can (and usually should) be so aggressive like when you turn a backdoor flush draw with something like A J on Q 9 5 7 after continuation betting the flop.

This is why you choose semi-bluffing hands to bluff with before choosing hands with low equity earlier in the hand. On the river, however, showdown value is the important thing since you can't semi-bluff.

Of course, you should be more aggressive with your semi-bluffing in non-all-in situations too, but it was just an example.

[seven-deuce]

The percentage bet/(bet+pot) will tell you how often to bluff in all-in river spots to be unexploitable when you bet.

Can you use this to work out how often to call if you are against an opponent that can bluff jam the river?

So for example if the opponent bluff jams the river for 2/3 pot and you have 5 combos of the nuts and 5 combos of the 2nd nuts in your range which your obviously calling, then the bet/(bet+pot) would still come out at 0.4 (40% of 10 combos that your definitely calling) so would you add 4 combos of the 3rd nuts to avoid being exploited by folding too much?

This just truck me when i was reading through this and is probably totally wrong but worth asking nonetheless.

[spoonitnow]

Can you use this to work out how often to call if you are against an opponent that can bluff jam the river?

Yes and no. Yes because it does tell you how often you'd be calling to be unexploitable to bluffs, ie what your calling frequency would be if you're playing unexploitably. If your opponent is betting $2 into a pot of $3, he needs you to fold at least 2/(2+3) = 40 percent of the time to be profitable with a bluff. If you call with exactly 40 percent, then it's the same EV for your opponent to either bluff or check behind a bluffing hand that never wins at showdown.

No because....

If you call and win as little as 28% of the time, you will break even.

You should call with any hand that will win at least 28% of the time.

What MMM describes here is the optimal exploitative way of handling the situation. That just means making every +EV call possible and never making a call that's -EV in a vacuum. This is not always the same thing as being balanced (aka playing unexploitably).