Optimum bluffing frequency question

[jr4284]

Alright, it's been a while since I've really read through Theory of Poker, but maybe someone could clear this up for me. I'm interested in tweaking my game so as to bluff optimally. This results in a situation where we don't care if he calls or folds - we win long run either way.

Let's just take a scenario.

I raise KJss on the button and get 3b by a TAG BB. I call. (pot: 6.5 sb)
flop is 235r and he continues, I call. (pot 8.5 sb)

I'm assuming he's going to lead any turn, making the pot 5.25 BB. If I raise, he is getting 7.25:1 on the call, so my bluffing frequency should be 1:7.25, or 12.1%, which equates to about 5 cards in the deck (47*.121).

I am going to choose any 8 and the 9 [img]/images/graemlins/club.gif[/img]. I chose these over cards like As, Qs, and Ts, because those make up more of his 3b'ing range.

So the optimum way to play this turn is to raise any K, J, and any of my 5 randomly chosen cards. amirite?

Another thought: If you're going to commit to bluffing the turn AND the river, how should this affect our numbers? Should we change our turn bluff frequency to be 9.25:1 (9.8%)?

[johnnyrocket]

well you are seeming to think of them independently, u need to apply okay he calls turn x amount of the time so if i bluff the river this amount of the time also its break even. Its almost impossible to put an exact number on these, if you understand the concepts he explains for them u are in good shape

[yourface]

you have to consider that you are semibluffing with your pair outs. sometimes he will call and you still win on the river

also 235r is a bad flop to bluff because an ace is never folding before the river, and by then they'll just call for the hell of it

[Saikkonen]

This talk about bluffingtheory in TOP is not supposed to be some kind of DIRECT tool, but more an INdirect tool to helps one mind how often to bluff in marginal situations. This is game theory and it also assumes that your opponent knows gametheory. One of the points that can be drawn from TOP is actually if u have an average bluffingfrequency about 10% then when the pot is bigger than 9 bets you should bluff and if it is less you should not. But of course there is a lot of other factors to consider as f.ex. how often does your opponent thinks you bluff. A fish doesn't consider folding at all and he assumes u bluff 100% of the time - against this type of player forget about bluffingfrequency.

[maxter]

It's more complex than that. The classical example of optimal bluffing frequency (a river bet) assumes that you have nothing or the nuts, so we bluff 1/(pot+2) of the time to avoid being exploited and make the villian indifferent.

There are some differences in the example you provided (let's ignore if this is a good board to bluff or our opponentt tendencies). When there are cards to come, you are in fact semibluffing, so you'll win sometimes when you are called against some of his bluff-catchers (as yourface said). That inclines us to semibluff slightly more than betsize/pot+2 of the time.

On the other hand, when we .raise for value, we don't have the nuts 100% of the time. We are raising with certain equity against his range. We may raise for value and still lose to a better hand or a worse hand that improves on the river, so that should incline us to bluff less

An approximation of the optimal actions here must take into account 1) What range we have and 2)What we do with each hand in our range. The key is balancing semibluff raises and value raises in a manner our opponent can't exploit us easily (optimal strategy is impossible to calculate). A good idea is thinking that our opp knows our strategy but we don't care because he won't improve his EV adding more or less hands/call-downs/re-bluffs/value re-raises.

I recommend you The Mathematics of Poker for deep explanations on this topics.

[Romulet]

I know the game theorists and mathematicians have devised thie game theoretical optimal bluffing strategy however on the internet I really think that you have do consider a number of factors with game theory being low on the list.

Ie probablity of getting called, number of outs should your opponent call, number of opponents, is there a chance your hand is good?, opponents hand range, skill level of opponent(s), texture of the board etc etc

If you can fathom these and more factors out your level of error calculating this will have the optimal bluffing strategy more than covered during the short space of time allowed on the net.

If anybody is good enough to make this calculation faultlessly in the time allowed and then add the necessary bluff outs to the calculation they are playing at a very high standard.

[Wolfram]

Seems to me that a zero bluffing frequency is optimal since nobody folds anything anymore (small-stakes at least).

[jr4284]

All have made valid points, but I'm mainly thinking about how Sklansky works it to be profitable whether they call or fold. So even if, yes, "nobody folds anything anymore" we're still happy with that result. I dunno. Part of my brain agrees with you guys ("dont' bluff the unbluffable") and part of me agrees with Sklansky ("numbers don't lie").

[maxter]

Numbers don't lie, of course, the optimal bluffing frecuency makes our opponent indifferent (zero EV for him), it doesn't matter if he always calls or always folds (in the nuts-or-nothing situation).

But if our opponent is unbluffable we should never bluff because we know that is -EV. Our strategy of value betting the nuts or bluffing at the right frequencies is not -EV though, because is optimal, but the strategy of value betting 100% and never bluff has a higher expectation. We found and exploitive strategy against him, but we must be aware that exploitive strategies are also exploitable. If our opponents notices that (in the example), he'll start folding 100%, so we gain nothing.

In real life, we try to find exploitive plays all the time, because that's where the money comes from. Playing pseudo-optimally against a calling station is nonsense, of course. However, optimal strategies can help us to find balance in our lines, and that's extremely important when we face good players, who are looking for leaks in our strategy.

For me is extremely difficult to find out balanced strategies, but trying to think on them had helped me in various postflop spots where I was uncomfortable, specially those where my hand was revealed. Tons of work to do yet, though.

[RudeboyOi]

first off that section in TOP

is more applicable to noncommunity card games
where your cards are hidden

if you want to bluff in the LHE
its all about board textures
kindof like writing a story

the action must make sense up to that point

and only bluff vs those who arent sd bound
they have a low WTSD% and b/f far too often

example hand

you raise from CO or button with your KsJs
the sb folds and the TAG bb 3bets

flop is Ts 6 5

so you currently have 6 pair outs and 1.5outs for a bdf
but your K outs may be dirty so we discount those by half

all together you have about 6outs

getting 7.5:1 from the pot makes this an easy call

turn is a 9 youre better off just calling here
with your monstrous amount of outs

hes unlikely to fold any hand in his range
and you may have as many as ten outs

if the turn is lets say an A

this is a good spot to bluff
if your opponent will b/f many of his pps

we no longer have the odds to call because
at this point all we can hope for

is for villian to barrel again with pps lower than Ts
if vililan is a true tag this pretty much means 99

but if we now turn our hand into a bluff by raising
we may get him to laydown the best hand
if his hand does not include an ace in it

and if he 3bs given that we may get
1 or 2bets in on the river

we now have the odds to call
drawing to our gutshot

just make sure if you had an A in this spot
youd routinely play it the same way

or anytime you raise this spot it looks like a bluff

we can easily have an ace here ourselves
given our preflop raise and our flop peel

so our TAGgish opponent will be hardpressed to call
with anything less than an ace

just be sure to not attempt bluffs
against those who wont fold

hope this helps

gl