River bets

[Aisthesis]

I almost posted this in the TxRedman thread, but thought it might be better in a separate one. I noticed there that Tex bets full pot on the river.

I do that sometimes, but more often I go with somewhere around 1/2 pot. If they're kind of timid but might call when beat, I'll sometimes even go 1/3 pot. Or, if they're really cally or have a hand I know I have beat but has to call I'll go full pot (examples: I have quads and know they have overfull, or I have straight flush and know they have nut flush). And the 1/3 or 1/2 pot bet can also be a bluff, but is usually a value bet.

Anyhow, I've also noticed a lot of good players betting full pot a lot more often than I do, and I just wondered what others think.

Maybe it's really a question of how often you're bluffing and how often you're value betting. I figure my value bets get more calls by being less, but also my bluffs do, too (although they don't HAVE to work as often either, since the cost is less).

I'm fairly happy with the half-pottish type bets in these situations, but I'd be very interested from hearing a case for full pot, too, as it does seem to work well for some players.

[Troll_Inc]

I think the "mistake" with 1/2 pot value bets in a lot of PLO games is that they will get called by the same people that will call a larger PSB. And if you make value bets cost even less, they do get called more , but of course if they are 1/5 pot, then you need them to get called 5 times for every 1 time someone will call your PSB to be the same.

I'm no expert on bluffs, but they really should be used to increase the chances of your full PSBs (when you have the nuts) getting paid. So they'll need to look like your nut PSBs and follow at the appropriate frequency.

[Aisthesis]

Agreed pretty much.

I will say that, really as a matter of principle more than anything else, I just can't bring myself to bet less than 1/3 pot essentially ever. I guess maybe if I had flopped quads in LP in a raised pot and it checked around all the way to the river with no one looking like they had the vagues piece, maybe. But that's even more of an exceptional bet for me than a FP river bet after some previous action.

I also think you're quite right in terms of varying bet size in terms of reads on your opponents--assuming we're not dealing with "protect your hand" or semi-bluff issues on earlier streets.

Your last comment also raises an interesting mathematical question, which I may try to address in a separate post.

[Aisthesis]

Ok, first, I'm going to assume you're bluffing and bet pot of $100 on the river. The probability of a call is p, and your opponent will always win if he calls. When is this bluff profitable?

Well, you win $100 when you win and lose $100 when you lose, so a call-rate of 50% is the break-even point for the bluff.

I'm just not completely sure what conclusions to draw in terms of bluffing frequency. One MIGHT say that that means you should be bluffing slightly less than 50% of the time (if we count as bluff any hand that doesn't win, which also isn't quite right, since we're sometimes dealing just with two strong hands, one of which is a little stronger).

Anyhow, I'm not sure just how to look at this from a mathematical standpoint, but, in any case, if you're typically half-potting on the river, then you now risk $50 to win $100. So, the bluff is break-even if you win only 1/3 of the time.

Yes, I think one problem with those equations (which are correct, just don't include a lot of other relevant information) is that there's typically a history behind the river bets. You're repping something specific or at least some range, as is your opponent, so there's always a plausibility issue on the river, if it changed anything--and if it's a blank, then we're asking who was actually already ahead.

Also, the propensity of your opponent to call is going to be lower as a rule on full pot rather than half-pot. So, one effectively needs some kind of function f that maps a bet into a call probability.

For example, if you could say that for opponents of type A, the call (and fold) probabilities are exactly equal whether you bet half-pot or full pot, whereas for opponents of type B, the call probability is much lower for the pot-sized bet, and the table is a pretty much equal mix of groups A and B, then you'd probably want to make your bluffs half-pot against A and your value-bets full pot, but do exactly the opposite against group B. Or something like that.

I just think it would be very hard to determine that particular function in specific instances, since for sure the betting sequence on the particular hand as well as exactly how other hands have played out at the table is going to have an influence on how your call probabilities look.

[Troll_Inc]

Effective stacks 100

Villain: K[img]/images/graemlins/heart.gif[/img] K[img]/images/graemlins/spade.gif[/img] J[img]/images/graemlins/spade.gif[/img] 9[img]/images/graemlins/diamond.gif[/img]

Hero: 6[img]/images/graemlins/spade.gif[/img] 5[img]/images/graemlins/spade.gif[/img] Q[img]/images/graemlins/club.gif[/img] J[img]/images/graemlins/diamond.gif[/img]

Preflop: You are on the button have been minimum raising from the button and then continuation betting full pot >80% of the time on the flop when it is checked to you. You raise to $4 and the villain calls from the SB hopping to trap. Some dude named Aisthesis picks up AKT8s in the BB and folds. Pot is $10.

Flop
K[img]/images/graemlins/diamond.gif[/img] 7[img]/images/graemlins/diamond.gif[/img] 4[img]/images/graemlins/club.gif[/img]

Villain checks his set of kings hoping for a nice check raise. The hero decides to take the free card and checks behind.

Turn is a blank 2[img]/images/graemlins/club.gif[/img]

The gig is up and the villains bets pot ($10). The hero thinks a second and calls hoping to either get some implied odds if the straight hits or bluff out the villain if the flush hits.

River 1 - 3[img]/images/graemlins/spade.gif[/img]

River 2 - T[img]/images/graemlins/diamond.gif[/img]

Pot is at $30

The villain checks and knows that you are capable of bluffing x% of the time.

How often should you bluff with a PSB and how often should the villain call?
With a 2/1 PSB?

Extra credit: Is it more profitable for the hero to ever lead out at either of these boards? If so at what frequency?

[grizy]

Soooooo, how often does teh hero call the turn with that board?

[Troll_Inc]

[ QUOTE ]
Soooooo, how often does teh hero call the turn with that board?

[/ QUOTE ]

In this example he calls it 100% of the time.

Wait, let me go check.

Yup I just checked my post, he called it again.

[Aisthesis]

Well, wait a minute, while this seems to me to be moving toward a solution, you ASSUME that hero bluffs x% of the time, right? So, isn't that just what hero actually does on river 2?

If so, then the solution should be easy.

Let's call x1 the frequency with which hero bluffs with a PSB. Then if x1 > 50, villain should always call, and if x1 < 50, villain should always fold, and if x1 = 50, it doesn't matter.

Similarly, for x2, if x2 is the bluff frequency with 1/2 PSB. Now you only have to win 1/3 of the time to make this break-even. So, you should call if x2 > 33, etc.

Anyhow, I really think hero's bet (or check) on river 2 is more of a question of assessing villain's propensity to call. The question seems to me to be whether villain, or set-man, as I'll call him since I'm getting myself confused with hero and villain here, THINKS x1 is higher than 50%. If that's the case, then flush-bluffer should never bet full pot. And if set-man thinks x2 is higher than 33%, flush-bluffer should restrain himself completely.

Or, to make this a little more practically oriented, if flush-bluffer has in this game shown a lot of value-bets of 1/2 pot but a bluff at full pot, then flush-bluffer might be well-advised to mix it up and maybe make a bluff of 1/2 pot here.

I dunno, I think the willingness to bluff river 2 is more of a statement about set-man's propensity to call than anything else; hence, if set-man is rational, it's a statement about the values he attaches to x1 and x2.

[JacKnight21]

here are the wrong answers
#1 question regarding river 2 I assume
bluff>x%

ExCred- more profitable than what? one board vs other board?
assuming bet vs check
2 100%

[Troll_Inc]

[ QUOTE ]
Well, wait a minute, while this seems to me to be moving toward a solution, you ASSUME that hero bluffs x% of the time, right? So, isn't that just what hero actually does on river 2?

[/ QUOTE ]

I don't think so. Here's why:

The villain (set man) won't know which draw the hero hit so he'll have to pay off river 1 while winning river 2. The more the hero is called on river 1, the more money he makes.

If villain (set man) calls less than 50% of the time, then the villain can't lose money on river 2.

I then get that if the villain's calling rate is 50% and hero's bluffing rate is 20%, then the hero's expectation is $36.

If no one every does anything out of line, then the hero's EV is just $30.

Also, you have to look at it from the villain's (setman's) perspective to see what is his best action.