Blind defense thought experiment

[Nate tha' Great]

Suppose that you're playing in a very aggressive limit hold 'em game against fairly tough opponents. You feel that you have an edge in this game, but not a large edge.

Suppose now that you are in the big blind. It's folded to the button who open-raises. He will do with about 40-50% of his hands, including a typical mix of pairs, aces, broadway hands, as well as some random suited and connecting hands. The button respects your play, but he knows that you're capable of aggression too and will play back at you when warranted, and sometimes when unwarranted.

We'll assume that the small blind has folded.

Suppose that the dealer is a friend of yours and he offers you the following proposition: he will deal any three-card flop that you like. However, you will not be able to look at your hole cards until the turn betting round. The Button will not be aware that you have not looked at your cards until the turn, nor will he know when you do look at your cards.

Two-part question:

1) Is this a winning proposition for you?

2) What three-card flop would you most like to see?

[partygirluk]

ii) Something like 87 suited should be scary enough that, combined with aggresion, you can push him off most hands (or get lucky and flop something yourself).

[Chris Daddy Cool]

i'm going to take a stab and assume you want a flop that isn't likely to hit his range of hands here.

i'd think the less cordinated the better because you'll get called down/played back at too often with a coodrinated board if he thinks you're semibluffing with draws and he has a somewhat showdonwable pair or A (even K) high type hand.

i assume this could be profitable if you can get a good range of his raising hands and put out a flop that is least likely to hit him in terms of pairing up or giving him a draw.

so i'll say 2 /images/graemlins/club.gif7 /images/graemlins/heart.gifT /images/graemlins/diamond.gif

or perhaps 3 /images/graemlins/club.gif3 /images/graemlins/heart.gif8 /images/graemlins/spade.gif

these aren't based off of anything mathematical or factual or even logical, just a "hunch".

[Michael Davis]

I definitely think two is wrong. It's just too easy to call down with high cards here. I think T72 is close but something like T75 is just a bit better.

-Michael

[fnord_too]

1. I don't think this is a winning proposition for you. You have less information than and are out of position against a strong player.

2. I think I go with something like 567 suited or two tone and get to the turn for one additional small bet. A flop like that will be less likely to hit my opponent (except maybe for the suit), so if it happens to hit me I should be in decent shape on the turn where I can hopefully offset the 1.5 BB I paid in the blind.


I suppose another way to go is to ask for something like TJQ or 9JK and reraise preflop and play the flop and turn very aggressively. Or ask for Axx and do the same thing. You will probably win a smallish pot when villain has a small pair, a weak ace (in the first) or high cards that don't connect (in the second), but it is going to cost you when he hits the flop or plays back on the turn when you finally see your cards and they are rags.

[memphis57]

I can't make it profitable but I think I can get it back close to 50-50. Before the flop, the button will have the edge, because he will (should) only play a hand that beats two random hands. So I'd ask for a flop of trips below tens (222-999). Button is more likely than me to have at least one card T or higher, so I have a slight edge on scoring a quad, and then we have equal chances of pairing one of our cards on the turn/river to score a full house. However, if nobody pairs, he's more likely to take it on a high card so it's probably still under 50-50 for me. With SB's money in the pot and check-calling all the way (but withthe option of pot-building if I hit), I'd need like 45-48% odds of winning to make it profitable, and my odds would probably be slightly below that.

[mmcd]

I 3-bet preflop and tell the dealer to put up AAJ.

[Michael Davis]

The button doesn't know you aren't going to fold and he doesn't know you're not looking at your cards.

-Michael

[LinusKS]

[ QUOTE ]
I 3-bet preflop and tell the dealer to put up AAJ.

[/ QUOTE ]

I agree with the 3-bet, although my initial thought is an uncoordinated A - something like A72 rainbow.

If you three-bet preflop and bet into him when an A hits the board, it will be hard for him not to credit you.

On the other hand, he'll have an A quite a bit less than 50% of the time himself.

Putting two aces up makes a flop bet look more bluffish, especially since he might think you'd check/call a genuine A, since top trips hu is pretty strong.

[mmcd]

I don't know about you, but when I 3-bet a TAG steal raiser from one of the blinds, I am betting out every single flop 100% of the time, regardless of whether I have AA and the flop comes AA7 rainbow, or black 8s and the flop comes AKQ of hearts.

When a single A flops: 1) Bayes theorem says it's more likely he has one than when 2 of them flop, not that this is really the case here since we are controlling the flop, BUT he doesn't know this, and; 2) He's more likely to try and take a stab at the pot somewhere along the line postflop, because many of the hands you will be 3-betting preflop will be pocket pairs < AA.

[johnc]

I don't see this as a winning propostion because:
1) This is a purely bluffing situation (due to the hole card senario) that would require perhaps a 50% sucess rate to make money, 1/2 a bet from the small blind. You invest x bets to win 2x(+0.5) bets 50% or 1/2 of the time which works out to 1/4 bet positive expectation.
2) No matter what you do or the cards you choose to flop, you'll never be able to control your hole cards (or his for that matter). This situation relies far too much on an unrealistically optimistic bluff % vs an aggressive, decent player who's capable of bluffing himself.

I don't see way out of these variables.

[MaxPower]

I think you would want a flop where your opponent fears that he is drawing dead. I think these are the best flops for bluffing an aggressive player.

[Derek in NYC]

[ QUOTE ]
Two-part question:

1) Is this a winning proposition for you?

2) What three-card flop would you most like to see?

[/ QUOTE ]



1. No. Under your definitions, you are increasing the amount at risk based on a random hand (blind + value of calling PFR + value of calling flop bet, assuming you check and villain autobets as the PFR). By definition, the button raiser is playing a better than average hand. (You have indicated that he plays, a "mix of pairs, aces, broadway hands, as well as some random suited and connecting hands.")

2. The flop you should want is a flop that will not improve his better-than-random hand, but will improve you. Again, you have indicated that he is playing a "mix of pairs, aces, broadway hands, as well as some random suited and connecting hands." Given this, a few things seem apparent.

First, choose a flop with no aces. By doing so, you do not improve the villain when he holds an ace, thus leaving your unpaired undercards live. By contrast, in situations where you hold an ace, you will be ahead where the opponent does not hold an ace (and holds no pair). Where you both hold an ace, it doesn't matter, since the side card will be determining.

Second, choose a rainbow and gapped flop. Villain prefers suited and connected cards, so coordinated flops will tend to help him. By contrast, coordinated flops tend not to help your (random) hand. Your odds of being dealt two suited cards are 3.3:1 against, and the odds of being dealt a suited connector are about 27:1.

Third, excluding aces, which you think about separately because of their uniquely strong ability to win unimproved, there are 4 Broadway ranked cards and 8 unBroadway ranked cards. Thus, by playing any two Broadway cards, the villian is playing the top 33% of the deck, twice. He is a significant dog to be dealt two broadway cards as a starting hand, I'd guess roughly 8:1 against.

Using this reasoning, I'd guess that the best flops would be something like 5 8 2 rainbow. True, given that villain plays any pair, he will sometimes flop a monster set with this hand. However, in order for this outcome to occur, villain must both be dealt a pair (16:1 against), and flop a set (8:1 against), i.e., very unlikely.

But this answer seems too obvious. What am I missing?

Edited to add:

I see from the responses I've read that some people assume you're going to play back at the opponent in the dark until 4th street (e.g., three betting preflop, betting the flop). Fair enough. I think that three-betting is a mistake unless you're going to ask for the AAQ type flop, and even in that situation, I think it is very high variance to do this.

In terms of betting the flop, given the likely hand distribution discussed above, because a ragged flop is least likely to help the villain, you should definitely prefer ragged flops to try to bet/checkraise the flop.

Final point: game theory issues are relevant such as whether you expect this to be a repeat play or a one-time experiment. If this is a repeat play, the 3-bet/AAQ flop line is definitely wrong. Under any repeat player scenario, the ragged flop gives you the greatest latitude to take down this pot either on the flop or later streets.

[brick]

3-bet preflop
AK3r
Bet flop.

We have put in 4 to win 3.
This might be profitable if he would steal with range of hands that has more hands (say 60%) without an A or K or 3, than with a K or A or 3. (say 40%)

I'm not sure how to caclulate this, but my gut says all the combination of cards he would raise that include an A , K, 3 is greater than 40% of the total range of hands he would raise. (probably not profitable. Anyone care to figure the probablity of A, K, 3 based on the range of hands above?)

[Vee Quiva]

I think the flop has to be middle to low cards all of the same suit. Lets say 3 /images/graemlins/heart.gif6 /images/graemlins/heart.gif9 /images/graemlins/heart.gif. One suited boards usually slow down aggressors. Even if he has AA with no hearts he's not going to feel too good about his hand if you lead out on the flop and turn. You need to get him to fold his hand a lot to make your scenario profitable. This would seem to be the easiest way to put some fear into him.

[brick]

Based on my math if the opponent steals 45% then they will have about one of about 529 combinations of hands (out of a total of 1176). 49 * 48

So to make a profit by bluffing with a board of AK3r he would have to have a hand that does not contain an A or K about 40% of the time. (Probably more if he is very tough and will call down with other pairs or raise to test us out.)


We know that one A and K will come on the flop.
AA, KK: 6 combinations
AQ-A4, KQ-K4: 204 combinations
AK: 9 combinations

Total of 219 Steal Attemps combinations contain an A or K.
219 / 530 = 41%

It's seems closer than I guessed.

[SeattleJake]

How about JJ7?

It avoids AX, KX, QX, yet still gives you a wide range of possibilities to be betting on the flop.

It also scares any XX holding, and makes a JX holding very unlikely for your opponent.

A bet on the flop is essential no matter what, since you can't look to see what you have until the turn, and you can't afford to show weakness before then.

This is a great question from a information theory standpoint!

[Nate tha' Great]

[ QUOTE ]
How about JJ7?

It avoids AX, KX, QX, yet still gives you a wide range of possibilities to be betting on the flop.

It also scares any XX holding, and makes a JX holding very unlikely for your opponent.

A bet on the flop is essential no matter what, since you can't look to see what you have until the turn, and you can't afford to show weakness before then.

This is a great question from a information theory standpoint!

[/ QUOTE ]

See I think it's hard to bluff toughish slightly overaggro opponents off of a flop like JJ7. I'm going to try and get to a showdown quite often there if I'm Button.