Real Ultimate Engineers
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Tuesday, July 21, 2009
Friday, July 25, 2008
Poker Musings, Vol. 4 - BLUFFING
Poker players are often pegged as "lying degenerates". This post isn't intended to do anything to contradict the latter half of the stereotype. Or the former.
In my opinion, the objective of poker is to take other people's money by outthinking them. And enjoy yourself in the process. In a game 'til infinity, everybody will have the same run of cards. In hold 'em, everyone will get dealt pocket aces at the same frequency, and everyone will get dealt J4 at the same frequency.
The key is to win more and lose less than your opponents when you are in a pot.
And that requires deception.
But here's the key. Your opponent is expecting you to lie. And they're going to be lying right back to you. The key to winning is to lie more convincingly and be able to smell the BS more effectively.
There are bluffs. There are Bluffs. And there are BLUFFS.
A bluff is something you might do once every couple of rounds. It's like ducking out early for a beer with a co-worker and failing to mention it to the wife. It's a white lie. Keeps the guy happy, no one's much worse for wear. It's raising AQ preflop from early position, getting a call from the button and then firing a continuation bet on a K94 flop. Your opponent folds. It's technically a bluff, although you might have been talking business over the beer so it can be defended as a career enhancing move.
There are Bluffs. These require a little more craftiness. They're the "I'm taking one of my precious vacation days next Wednesday to go catch a ballgame with the guys and I don't want to tell the wife because she wants me to save all the vacation days for when the baby comes." You have to somewhat set the stage for this one. Make sure your buddies don't tell their significant others. Make sure to sock away the cash so you don't have to use the credit cards. Maybe you've shown a bluff or 2 in the past... "OK, gotta come clean on this one 'cause the guilt is going to eat at me. Spaced Ghost, ab and I went out for a beer after work. It won't happen again."
You raise preflop with 88. You get one caller who has half the number of chips you have. The flop comes KQJ with 2 clubs. You're first to act and move all-in.
The Bluff can blow up in your face on occasion, but you can generally survive with your marriage intact (although if caught it's going to be very tough to bluff or Bluff again for a long while.)
And then there are the BLUFFS. The scary, white knuckle, Vegas trip with your 3 buddies for a weekend of gambling and strip clubs that you not only didn't mention to the Ms. but she can never, ever find out about. I can't emphasize enough the amount of preparation that goes into setting up the BLUFF. You have to have alibis. On top of alibis. On top of misdirections. Mixed in with red herrings. Running a BLUFF requires weeks to set up and still a little luck to pull off. And if you're caught, it means the end of your life.
In poker, pulling off a BLUFF is excruciatingly difficult. It requires perfect timing and often a bad read from yourwife opponent. Here is probably one of the more memorable mainstream BLUFFS.
I am primarily a low-limit sit-n-godonkey grinder. Some of the most profitable opponents are the ones who try to BLUFF without setting the proper groundwork. Here's one I found enjoyable, along with some observations on how I knew he wasn't in Omaha at a sales convention and instead was taking jello shooters from Porsha's naval in the Rhino Club.
> PokerStars Game #19030xxxxx: Tournament #973xxxxx
9-max Seat #7 is the button
> Seat 6: MAXBOOM (7370 in chips) (overwhelming chip leader, of course)
> Seat 7: Mr. Irrelavent (3290 in chips)
> Seat 8: I'mLosingHalfofEverything (2840 in chips)
> MAXBOOM: posts the ante 25
> Mr. Irrelavent: posts the ante 25
> I'mLosingHalfofEverything: posts the ante 25
> I'mLosingHalfofEverything: posts small blind 100
> MAXBOOM: posts big blind 200
Pot is 375
> *** HOLE CARDS ***
> Dealt to MAXBOOM [3c Ac]
> Mr. Irrelavent: folds
> I'mLosingHalfofEverything: calls 100 (try to build a range here. Not a terrible player. Short stack. I think the range of hands he could have is way too broad to list.
Business trip, eh. All right then. Never been on a business trip before, though.
But the key on this one is that you can eliminate some hands that he doesn't have because he didn't raise/shove.)
> MAXBOOM: checks (I might raise, start asking some questions about what the conference is about, where he's staying, but for now I'll just let him continue to tell me his story.)
Pot is 475.
> *** FLOP *** [6s 6c 5d]
> I'mLosingHalfofEverything: bets 2615 and is all-in
(moment of truth here. I have Ac3c. He has just raised 2615 into a 475 pot.
The Omaha Holiday Inn doesn't have a reservation in his name.
I don't know what his range is, but I am confident what it isn't because he didn't raise preflop. Namely no Ace, no pocket pair. Additionally, he is shoving here. A premium hand (AA-QQ) might play the hand this way preflop, but after the flop as a short stack would almost certainly try to draw me in by checking hoping I'd make a play. Getting to Level 3 thinking, what do you think he thinks I have. Probably drawing the same conclusion because I just checked preflop, No Ace, No Pocket pair.
The office just called asking if they knew a number to reach him at.
I also don't think he'd open shove if he got any piece of this flop. It's too tasty a spot to check-raise me because he should suspect that if he checks, the random player acting behind him will make a move at this pot in this position. So there you have it, he doesn't have an Ace, he doesn't have a pocket pair and he doesn't have a piece of this flop.
"Oh that son-'bitch done went off to Vegas with Boomer and Dickie, didn't he?"
> MAXBOOM: calls 2615
> *** TURN *** [6s 6c 5d] [3s]
> *** RIVER *** [6s 6c 5d 3s] [Qc]
> *** SHOW DOWN ***
> I'mLosingHalfofEverything: shows [Kc 4d] (a pair of Sixes)
> MAXBOOM: shows [3c Ac] (two pair, Sixes and Threes)
> MAXBOOM collected 5705 from pot
(boom)
In my opinion, the objective of poker is to take other people's money by outthinking them. And enjoy yourself in the process. In a game 'til infinity, everybody will have the same run of cards. In hold 'em, everyone will get dealt pocket aces at the same frequency, and everyone will get dealt J4 at the same frequency.
The key is to win more and lose less than your opponents when you are in a pot.
And that requires deception.
But here's the key. Your opponent is expecting you to lie. And they're going to be lying right back to you. The key to winning is to lie more convincingly and be able to smell the BS more effectively.
There are bluffs. There are Bluffs. And there are BLUFFS.
A bluff is something you might do once every couple of rounds. It's like ducking out early for a beer with a co-worker and failing to mention it to the wife. It's a white lie. Keeps the guy happy, no one's much worse for wear. It's raising AQ preflop from early position, getting a call from the button and then firing a continuation bet on a K94 flop. Your opponent folds. It's technically a bluff, although you might have been talking business over the beer so it can be defended as a career enhancing move.
There are Bluffs. These require a little more craftiness. They're the "I'm taking one of my precious vacation days next Wednesday to go catch a ballgame with the guys and I don't want to tell the wife because she wants me to save all the vacation days for when the baby comes." You have to somewhat set the stage for this one. Make sure your buddies don't tell their significant others. Make sure to sock away the cash so you don't have to use the credit cards. Maybe you've shown a bluff or 2 in the past... "OK, gotta come clean on this one 'cause the guilt is going to eat at me. Spaced Ghost, ab and I went out for a beer after work. It won't happen again."
You raise preflop with 88. You get one caller who has half the number of chips you have. The flop comes KQJ with 2 clubs. You're first to act and move all-in.
The Bluff can blow up in your face on occasion, but you can generally survive with your marriage intact (although if caught it's going to be very tough to bluff or Bluff again for a long while.)
And then there are the BLUFFS. The scary, white knuckle, Vegas trip with your 3 buddies for a weekend of gambling and strip clubs that you not only didn't mention to the Ms. but she can never, ever find out about. I can't emphasize enough the amount of preparation that goes into setting up the BLUFF. You have to have alibis. On top of alibis. On top of misdirections. Mixed in with red herrings. Running a BLUFF requires weeks to set up and still a little luck to pull off. And if you're caught, it means the end of your life.
In poker, pulling off a BLUFF is excruciatingly difficult. It requires perfect timing and often a bad read from your
I am primarily a low-limit sit-n-go
> PokerStars Game #19030xxxxx: Tournament #973xxxxx
9-max Seat #7 is the button
> Seat 6: MAXBOOM (7370 in chips) (overwhelming chip leader, of course)
> Seat 7: Mr. Irrelavent (3290 in chips)
> Seat 8: I'mLosingHalfofEverything (2840 in chips)
> MAXBOOM: posts the ante 25
> Mr. Irrelavent: posts the ante 25
> I'mLosingHalfofEverything: posts the ante 25
> I'mLosingHalfofEverything: posts small blind 100
> MAXBOOM: posts big blind 200
Pot is 375
> *** HOLE CARDS ***
> Dealt to MAXBOOM [3c Ac]
> Mr. Irrelavent: folds
> I'mLosingHalfofEverything: calls 100 (try to build a range here. Not a terrible player. Short stack. I think the range of hands he could have is way too broad to list.
Business trip, eh. All right then. Never been on a business trip before, though.
But the key on this one is that you can eliminate some hands that he doesn't have because he didn't raise/shove.)
> MAXBOOM: checks (I might raise, start asking some questions about what the conference is about, where he's staying, but for now I'll just let him continue to tell me his story.)
Pot is 475.
> *** FLOP *** [6s 6c 5d]
> I'mLosingHalfofEverything: bets 2615 and is all-in
(moment of truth here. I have Ac3c. He has just raised 2615 into a 475 pot.
The Omaha Holiday Inn doesn't have a reservation in his name.
I don't know what his range is, but I am confident what it isn't because he didn't raise preflop. Namely no Ace, no pocket pair. Additionally, he is shoving here. A premium hand (AA-QQ) might play the hand this way preflop, but after the flop as a short stack would almost certainly try to draw me in by checking hoping I'd make a play. Getting to Level 3 thinking, what do you think he thinks I have. Probably drawing the same conclusion because I just checked preflop, No Ace, No Pocket pair.
The office just called asking if they knew a number to reach him at.
I also don't think he'd open shove if he got any piece of this flop. It's too tasty a spot to check-raise me because he should suspect that if he checks, the random player acting behind him will make a move at this pot in this position. So there you have it, he doesn't have an Ace, he doesn't have a pocket pair and he doesn't have a piece of this flop.
"Oh that son-'bitch done went off to Vegas with Boomer and Dickie, didn't he?"
> MAXBOOM: calls 2615
> *** TURN *** [6s 6c 5d] [3s]
> *** RIVER *** [6s 6c 5d 3s] [Qc]
> *** SHOW DOWN ***
> I'mLosingHalfofEverything: shows [Kc 4d] (a pair of Sixes)
> MAXBOOM: shows [3c Ac] (two pair, Sixes and Threes)
> MAXBOOM collected 5705 from pot
(boom)
Labels: Max Boom, Poker Musings
Friday, July 11, 2008
Poker Musings, Vol. 3 - Gracious but Vindictive in Defeat
I have no intention of turning this into a bad beat diary. But seriously...I Run Beautiful...
PokerStars Game #1875xxxxxxx: Tournament #95xxxxxx, $10+$1 Hold'em No Limit - Level II (15/30)
Seat #5 is the button
Seat 1: MAXBOOM (1580 in chips)
Seat 2:(1080 in chips)
Seat 3:(1710 in chips)
Seat 4:(540 in chips)
Seat 5:(2830 in chips)
Seat 6:(1480 in chips)
Seat 9: Lescelleur (4280 in chips)
Seat 6: posts small blind 15
Lescelleur: posts big blind 30
*** HOLE CARDS ***
Dealt to MAXBOOM [8d Ad]
MAXBOOM: calls 30 [Loose, to be sure, but the table was virginally tight except for Mr. Les, who was being the table bully and raising everything very big and was also in the big blind.]
seat 3: folds
seat 4: folds
seat 5: folds
seat 6: folds
seat 7: calls 15
Lescelleur: raises 90 to 120 [we hoped for this! Nay! We orchestrated this cheap ass move from the big blind. Sorry, Les, in this world, you get outed]
MAXBOOM: raises 1460 to 1580 and is all-in
seat 7: folds
Lescelleur: calls 1460
*** FLOP *** [7h Kc Kd]
*** TURN *** [7h Kc Kd] [7s]
*** RIVER *** [7h Kc Kd 7s] [Jc]
*** SHOW DOWN ***
Lescelleur: shows [8s 7c] (a full house, Sevens full of Kings)
MAXBOOM: shows [8d Ad] (two pair, Kings and Sevens)
MAXBOOM said, "gg" [Gracious, even in defeat.]
Lescelleur said, "wow" [You forgot to type the rest, so I'll complete... "wow, I suck."]
The case could be made that his range was broad. My observation was he didn't play his monster hands this way (a 2 monster hand sample, admittedly not a lot of intel.) He could have had AA. Or a number of hands that had me beat. I thought my hand was a favorite over his range to make that particular bet in his own big blind. I also thought that absent a monster he could fold. I was right. And wrong.
I made a parallel judgement--
Largest junk = best broad. See Ms. Fire for confirmation.
Largest cards = best hand. See Game #1875xxxxxxx for rebuttal.
Some skills aren't absolute.
Deep breath... we play this game until infinity. Eventually, proper play will be a positive investment... Proper junk is still reaping rewards.
Ugh.
PokerStars Game #1875xxxxxxx: Tournament #95xxxxxx, $10+$1 Hold'em No Limit - Level II (15/30)
Seat #5 is the button
Seat 1: MAXBOOM (1580 in chips)
Seat 2:(1080 in chips)
Seat 3:(1710 in chips)
Seat 4:(540 in chips)
Seat 5:(2830 in chips)
Seat 6:(1480 in chips)
Seat 9: Lescelleur (4280 in chips)
Seat 6: posts small blind 15
Lescelleur: posts big blind 30
*** HOLE CARDS ***
Dealt to MAXBOOM [8d Ad]
MAXBOOM: calls 30 [Loose, to be sure, but the table was virginally tight except for Mr. Les, who was being the table bully and raising everything very big and was also in the big blind.]
seat 3: folds
seat 4: folds
seat 5: folds
seat 6: folds
seat 7: calls 15
Lescelleur: raises 90 to 120 [we hoped for this! Nay! We orchestrated this cheap ass move from the big blind. Sorry, Les, in this world, you get outed]
MAXBOOM: raises 1460 to 1580 and is all-in
seat 7: folds
Lescelleur: calls 1460
*** FLOP *** [7h Kc Kd]
*** TURN *** [7h Kc Kd] [7s]
*** RIVER *** [7h Kc Kd 7s] [Jc]
*** SHOW DOWN ***
Lescelleur: shows [8s 7c] (a full house, Sevens full of Kings)
MAXBOOM: shows [8d Ad] (two pair, Kings and Sevens)
MAXBOOM said, "gg" [Gracious, even in defeat.]
Lescelleur said, "wow" [You forgot to type the rest, so I'll complete... "wow, I suck."]
The case could be made that his range was broad. My observation was he didn't play his monster hands this way (a 2 monster hand sample, admittedly not a lot of intel.) He could have had AA. Or a number of hands that had me beat. I thought my hand was a favorite over his range to make that particular bet in his own big blind. I also thought that absent a monster he could fold. I was right. And wrong.
I made a parallel judgement--
Largest junk = best broad. See Ms. Fire for confirmation.
Largest cards = best hand. See Game #1875xxxxxxx for rebuttal.
Some skills aren't absolute.
Deep breath... we play this game until infinity. Eventually, proper play will be a positive investment... Proper junk is still reaping rewards.
Ugh.
Labels: Drogging, Max Boom, Poker Musings
Monday, June 30, 2008
Poker Musings, Vol. 2 - An Illustration of Poker as a Game of Skill
Question from one of the guys I play regularly with who was playing a 80 player multi-table tournament (MTT) at the track --
I had 11.8K chips when the blinds were at 1,000/2,000. With AQ I was sixth to act. The third guy to act limped in and everyone else folded to me. I decided to take a shot and I went all in. The limper, with about 14K chips, took a very long time but decided to call w/55. A king hit on the river but I missed my cards. I am still trying to figure out if he made the right call?
A typical poker situation here, but one that requires some thought. Not all of the variables are in accounted for (his image at the table, how the game was running, etc.) Here's a purely mathmatical response from moi...
"I think your opponent made the right call. He open limps 55, putting $5000 in the pot. That's usually a bad move unless the table was really passive, but that's not at issue here. You push $11.8K. It costs him $9.8K more to win $16.8K, for about what 1.7-1 odds? Is a call correct?
Depends on the range your opponent put you on. With an M<4, so less than 4 more rounds before being blinded out, your range of hands should be fairly broad. Hypothetically say you push with any pocket pair, AK-AJ, KQ, KJ and AT. That's not unreasonable I don't think.
There are exactly 6 ways to make any pocket pair (9c9d, 9c9h, 9c9s, 9d9h, 9d9s, 9h9s, for example). Your opponent's got an 80% chance to lose to 54 pocket pairs (AA-66), and 80% to win against 18 pocket pairs (44-22). He can tie with exactly 1 pair (if you have 55, there is only one way for him to have 55), but I'll throw that out because it clouds the water.
You have exactly 16 ways to make each of the overcard hands (AcKc, AcKd, etc.) So he's roughly 50/50 with 96 possible hands.
So call that (54+18+96)= 168 possible hands that it would be reasonable to put you on, pushing late-ish in an Multi-Table Tournament with an M<4. I might widen the range if you were first to act, but with a caller already I think the range is reasonably optimal. Additionally, calling really isn't an option for you, so if you are tempted to call you have to push. Your opponent probably knows this, in case you were saying to yourself "I'd fold AT." I don't think that's a good move against a single limper, so I'm including that in the range he could reasonably put you on. You might even be lighter than that-- e.g. QJ, QTsooted, JTsooted?. I'll start by sticking to the first range above.
So these are what appear to be your opponent's percentage of winning the pot. Study carefully and ask questions if you don't understand the percentages, 'cause this is important stuff to understand why he correctly called and you should too in his position (based on long term Expected Value and ignoring tournament chip vs. cash payout equity because I don't fully understand the math on that yet).
You have overpair. Opponent's chances--
80% loss = 54/168*(-$9,800)*.8= (-$2,520 expectation)
20% win = 54/168*(+$16,800)*.2= (+$1,080 expectation)
You have 2 overcards. Opponent's chances--
50% loss = 96/168*(-$9,800)*.5= (-$2,800 expectation)
50% win = 96/168*(+$16,800)*.5= (+$4,800 expectation)
You have underpair. Opponent's chances--
20% loss = 18/168*(-$9,800)*.2= (-$210 expectation)
80% win = 18/168*(+$16,800)*.8=(+$1,440 expectation)
Total expectation for your opponent calling with 55 against your range is $(-2,520 + 1080 - 2,800 + 4,800 - 210 + 1,440) = +$1,790.
So he can expect to make an additional $1,790 every time he makes that call making that firmly a + Expected Value move by him against that range.
But taking your hypothesis even further and "he should assume 50% of the time I'm on a higher pocket pair."
To get to that, let's say you call any pocket pair, AK, AQ or AJsooted. Again ignoring pocket 5's for you because they muddy the water.
As above, 54 pairs are ahead of your opponent, 18 are behind and 36 hands are 50/50 (only 4 sooted AJ hands). 108 hands total, 50% of which are an overpair like you said.
You have overpair against your opponent.
80% loss = 54/108*(-$9,800)*.8= (-$3,920 expectation)
20% win = 54/108*(+$16,800)*.2= (+$1,680 expectation)
You have 2 overcards against your opponent.
50% loss = 36/108*(-$9,800)*.5= (-$1,633 expectation)
50% win = 36/108*(+$16,800)*.5= ($2,800 expectation)
You have underpair against your opponent.
20% loss = 18/108*(-$9,800)*.2= (-$327 expectation)
80% win = 18/108*(+$16,800)*.8=(+$2,240 expectation)
Total expectation is $(-3,920+1,680-1,633+2,800-327+2,240) = +$840.
Your opponent is still +EV to call against the range you identified, which again is pretty darn narrow and most player's ranges will be greater than that in your position if they're pushing late with an M<4.
You seem to get caught up with there being 9 pocket pairs that he's behind, 3 he's ahead of and only 3 overcard hands, so 9>6 and he should have folded. It's just much more likely to be dealt an overcard hand than a pocket pair hand (16 ways vs. 6 ways), so it distorts what seems to be an intuitive bad call."
I had 11.8K chips when the blinds were at 1,000/2,000. With AQ I was sixth to act. The third guy to act limped in and everyone else folded to me. I decided to take a shot and I went all in. The limper, with about 14K chips, took a very long time but decided to call w/55. A king hit on the river but I missed my cards. I am still trying to figure out if he made the right call?
A typical poker situation here, but one that requires some thought. Not all of the variables are in accounted for (his image at the table, how the game was running, etc.) Here's a purely mathmatical response from moi...
"I think your opponent made the right call. He open limps 55, putting $5000 in the pot. That's usually a bad move unless the table was really passive, but that's not at issue here. You push $11.8K. It costs him $9.8K more to win $16.8K, for about what 1.7-1 odds? Is a call correct?
Depends on the range your opponent put you on. With an M<4, so less than 4 more rounds before being blinded out, your range of hands should be fairly broad. Hypothetically say you push with any pocket pair, AK-AJ, KQ, KJ and AT. That's not unreasonable I don't think.
There are exactly 6 ways to make any pocket pair (9c9d, 9c9h, 9c9s, 9d9h, 9d9s, 9h9s, for example). Your opponent's got an 80% chance to lose to 54 pocket pairs (AA-66), and 80% to win against 18 pocket pairs (44-22). He can tie with exactly 1 pair (if you have 55, there is only one way for him to have 55), but I'll throw that out because it clouds the water.
You have exactly 16 ways to make each of the overcard hands (AcKc, AcKd, etc.) So he's roughly 50/50 with 96 possible hands.
So call that (54+18+96)= 168 possible hands that it would be reasonable to put you on, pushing late-ish in an Multi-Table Tournament with an M<4. I might widen the range if you were first to act, but with a caller already I think the range is reasonably optimal. Additionally, calling really isn't an option for you, so if you are tempted to call you have to push. Your opponent probably knows this, in case you were saying to yourself "I'd fold AT." I don't think that's a good move against a single limper, so I'm including that in the range he could reasonably put you on. You might even be lighter than that-- e.g. QJ, QTsooted, JTsooted?. I'll start by sticking to the first range above.
So these are what appear to be your opponent's percentage of winning the pot. Study carefully and ask questions if you don't understand the percentages, 'cause this is important stuff to understand why he correctly called and you should too in his position (based on long term Expected Value and ignoring tournament chip vs. cash payout equity because I don't fully understand the math on that yet).
You have overpair. Opponent's chances--
80% loss = 54/168*(-$9,800)*.8= (-$2,520 expectation)
20% win = 54/168*(+$16,800)*.2= (+$1,080 expectation)
You have 2 overcards. Opponent's chances--
50% loss = 96/168*(-$9,800)*.5= (-$2,800 expectation)
50% win = 96/168*(+$16,800)*.5= (+$4,800 expectation)
You have underpair. Opponent's chances--
20% loss = 18/168*(-$9,800)*.2= (-$210 expectation)
80% win = 18/168*(+$16,800)*.8=(+$1,440 expectation)
Total expectation for your opponent calling with 55 against your range is $(-2,520 + 1080 - 2,800 + 4,800 - 210 + 1,440) = +$1,790.
So he can expect to make an additional $1,790 every time he makes that call making that firmly a + Expected Value move by him against that range.
But taking your hypothesis even further and "he should assume 50% of the time I'm on a higher pocket pair."
To get to that, let's say you call any pocket pair, AK, AQ or AJsooted. Again ignoring pocket 5's for you because they muddy the water.
As above, 54 pairs are ahead of your opponent, 18 are behind and 36 hands are 50/50 (only 4 sooted AJ hands). 108 hands total, 50% of which are an overpair like you said.
You have overpair against your opponent.
80% loss = 54/108*(-$9,800)*.8= (-$3,920 expectation)
20% win = 54/108*(+$16,800)*.2= (+$1,680 expectation)
You have 2 overcards against your opponent.
50% loss = 36/108*(-$9,800)*.5= (-$1,633 expectation)
50% win = 36/108*(+$16,800)*.5= ($2,800 expectation)
You have underpair against your opponent.
20% loss = 18/108*(-$9,800)*.2= (-$327 expectation)
80% win = 18/108*(+$16,800)*.8=(+$2,240 expectation)
Total expectation is $(-3,920+1,680-1,633+2,800-327+2,240) = +$840.
Your opponent is still +EV to call against the range you identified, which again is pretty darn narrow and most player's ranges will be greater than that in your position if they're pushing late with an M<4.
You seem to get caught up with there being 9 pocket pairs that he's behind, 3 he's ahead of and only 3 overcard hands, so 9>6 and he should have folded. It's just much more likely to be dealt an overcard hand than a pocket pair hand (16 ways vs. 6 ways), so it distorts what seems to be an intuitive bad call."
Labels: Max Boom, Poker Musings

