EV of shoves

I recently played in a $4 180-man on PokerStars where I made a lot of borderline shoves.  I decided to calculate the EV of these shoves using PokerStove and Sheets' spreadsheets on PokerXFactor (which I unfortunately can't make available) and post them.

Hand 1:  1,595 chips w/ blinds at 50/100 and I have 9♥ 9♠ UTG.  Not wanting to make a normal raise b/c this is not a hand that I want flatcalled, I decided to shove all-in.  I gave my opponents a 3.8% calling range of {TT+,AQs+,AKo} against which I am 32.9% to win if called.  As it turns out the EV of this shove is -30 chips.  This is a pretty solid and optimal calling raise I think, however, if my opponents were looser or tighter, this shove would be +EV.  I would either be stealing more often, or I would be called more and winning more often against their calling range.

Result:  I shoved and everyone folded.

Hand 2:  1,420 chips w/ blinds at 75/150 and I have 8♥ 8♠ on the button.  UTG limps for 150 and the hijack raises to 599.  I have no reads on the HJ, so I figured him for a 9.4% range of {55+,AJs+,KQs,AJo+,KQo} against which I am 47.6% to win if called.  He can't really fold to my shove, since he will be getting 2.9-to-1 on a call and has to call w/ any two cards.  The remaining players need a very tight range of {TT+,AQs+,AKo} to call as well.  This shove is pretty ambiguous as the EV is +8 chips on average.

Result:  I shoved and was called by the HJ w/ K♣ K♦.  The board ran 5♠ 8♦ 9♥ 2♣ 7♣ and I luckboxed into a double up!

Hand 3:   2,390 chips w/ blinds at 100/200 and I have A♣ 6♦ on the button.  I shoved, anticipating being called by a loose 11.5% range of {55+,A8s+,KJs+,ATo+,KQo}.  I am only 32.5% against this range, but w/ only the two blinds remaining the EV of the shove is +61 chips.

Result:  I shoved and was called by the SB w/ A♥ J♣.  The board ran 10♠ 10♣ 5♥ K♦ 5♠ and I was lucky to chop.

Hand 4:  2,765 chips w/ blinds at 125/250 and 25 ante.  I have A♦ J♦ UTG+1 at a 7-handed table.  I shoved, expecting a fairly loose 10.4% calling range of {66+,ATs+,KJs+,ATo+,KQo} against which I am 46.4% to win.  The EV of this shove is +303 chips.

Result:  I shoved and everyone folded.

Hand 5:  2,740 chips w/ blinds at 150/300 and 25 ante.  I have Q♥ J♥ UTG+1 at an 8-handed table.  I shoved, expecting a 10.0% calling range of {77+,ATs+,KJs+,ATo+,KQo} against which I am 35.85% to win.  The EV of this shove is +41 chips.

Result:  I shoved and was called by the cutoff w/ 9♥ 9♠.  The board ran K♦ 6♦ J♠ 5♦ 10♥ and I won the race.

Hand 6:  5,430 chips w/ blinds at 150/300 w/ 25 ante.  I have A♥ 10♦ UTG.  I folded b/c I expected raising and shoving to both be -EV when UTG w/ an M of 8.  I would expect a tight 3.8% calling range of {TT+,AQs+,AKo} when facing a 18BB UTG shove which I would be 26.2% against.  The EV of this shove would have been -168 chips.  If my opponents are calling lighter, my EV gets even worse.  It doesn't pay to ship light UTG for a lot of chips!

Hand 7:  Blinds at 150/300 w/ 25 ante and I have 4,930 chips after posting the SB.  I am dealt Q♦ 7♦ and everyone folds to me.  I expect to be called very lightly here, perhaps as light as a 24.0% range of {44+,A2s+,K9s+,QTs+,A2o+,KJo+,QJo} against which I am 36.6% to win.  The EV of this shove is +219 chips.

Result:  I shoved and the BB called w/ A♣ 5♥.  The board ran 2♥ 5♠ J♣ 10♣ 9♦ and I was eliminated in 26th, 8 spots short of the money.

Even though I busted out short of the money, I never would have had the chance to run even that deep if I had not been making slightly +EV shoves (and one -EV shove) along the way.  I got lucky to survive a couple of times, but I was unlucky to run into a hand in those spots in the first place.  The only hand that I don't like is hand 2 where I shoved 8-8.  The EV is so neutral there that I probably should have just passed and waited for a better spot.  After all, I'm confident in my ability to beat these tournaments!

Tricky play

This is an excellent hand that a student of mine recently played in a $10 buy-in MTT Full Tilt Poker Super Stack $14K Guarantee (197451031) - 120/240 Ante 25 - No Limit Hold'em Seat 1: (10,839) Seat 2: (11,175) Seat 3: (9,975) Seat 4: Hero (19,200) Seat 5: (7,075) Seat 6: (12,567) Seat 7: Villain (16,687) Seat 8: Small blind (3,565) Seat 9: Big blind (6,230) You have been at the table for a relatively short time, but already Seat 5, the Villain in Seat 7, and the Big blind in Seat 9 have all seemed to be aggressive.  You need a strong hand to enter this pot with three aggressive players behind you, especially when one of them is the BB. All players ante 25 Small blind posts 120 Big blind posts 240 The button is in seat #7 Dealt to Hero [K♣ K♠] Seat 1 folds Seat 2 folds Seat 3 folds Obviously, you are going to raise your kings in this spot, hoping to get 3-bet so you can 4-bet to dissuade people from 3-betting you lightly in future hands. Hero raises to 600 This raise is the perfect size, 2.5BBs.  Since you may be planning to steal the blinds often, you want to minimize your chip commitment so you lose fewer chips when your steal is unsuccessful.  Therefore, you must raise the same amount with your monster hands to avoid giving your opponents a read on your play. Seat 5 folds Seat 6 folds Villain calls 600 Small blind folds Big blind calls 360 *** FLOP *** [T♦ 5♣ K♦] Big blind checks Fantastic flop, as you have flopped top set.  However, you do not want to slowplay here.  You have the nuts right now, but any ace, queen, jack, nine, or diamond could make your hand second best.  There is a 32% chance of that happening on the turn alone!  You also want to start building this pot since you and the villain in Seat 7 are both deep stacked.  If you don't start to build a pot, you won't be able to get all of his chips in the middle later in the hand.  Sure, he may fold to a bet, but that is a risk worth taking for the chance to stack him.  Notice that this also camouflages your continuation bets nicely. Hero bets 700 Villain calls 700 Big blind folds *** TURN *** [T♦ 5♣ K♦] [T♣] The turn is a fabulous card!  You no longer have the nuts, but the only way you are beat is if the villain is holding the two case tens.  Furthermore, if he is holding a hand like A-T or especially K-T, you will probably stack him here, or at least win a very big pot!  I would have bet here, but our hero has something better in mind! Hero checks Villain bets 1,525 This is a brilliant play against an aggressive opponent!  The villain could easily have been floating the flop bet, thinking that it was a continuation bet, and planning to take the pot away when you check the turn.  You don't mind giving a free card here either as the worst case scenario is the the villain takes the free card, misses his draw, folds to a river bet, and you don't win any more money.  But since our villain is aggressive, he is likely to semi-bluff with his draw now that you have shown weakness!  And if he has a ten, you give him a chance to value bet.  The key to this check is that the villain's draws will no longer beat you.  Betting is correct if the turn is a blank.  Hero raises to 4,500 Exactly right!  Check-raising is the right play here, b/c the villain will likely call with a draw, ten, or king, and he might even re-raise!  If you were to only call, what would you do on the river?  A bet looks fishy after check/calling the turn and checking would be a mistake as our villain might check behind.  He has to call 2,975 to win 6,595 so you are offering slightly less than 2-to-1 pot odds, and over 7-to-1 implied odds!  If he has a draw, he is likely to call, and hopefully he hits it and pays you off. Villain folds Hero wins the pot (6,595) Looks like you caught the villain making a play at the pot, which means you won the maximum from him.  It is also possible that he was able to fold a draw or a king after your strong check-raise.  Either way, this creative play should keep observant opponents off of your back for awhile, since you have proved that you can outplay an aggressive player!

Calling w/ Ace-Rag in the BB

Another hand played by my student in the $2 PokerStars tournament.

Seat 1: ronb19 (895 in chips) is sitting out 

Seat 2: Chula66 (5975 in chips) 

Seat 3: bigdog4all (1090 in chips) 

Seat 4: Pilo 82 (3685 in chips) 

Seat 5: Wolf_CorpS (6510 in chips) 

Seat 6: hobbesy (2840 in chips) 

Seat 7: Hero (4203 in chips) 

Seat 8: 1DeMoN1 (1672 in chips) 

Seat 9: jetsie (2205 in chips) 

hobbesy: posts small blind 50  

Hero: posts big blind 100 

*** HOLE CARDS ***  

Dealt to Hero  A♠ 8♣

1DeMoN1: folds 

jetsie: calls 100 

ronb19: folds 

Chula66: folds 

bigdog4all: folds 

Pilo 82: folds 

Wolf_CorpS: raises 200 to 300 

hobbesy: folds  

Hero: calls 200 

jetsie: calls 200 

I am not a fan of this call preflop.  An ace can be tempting to play, but if an ace does flop you are looking at either winning a small pot or losing a big one.  If you play very well postflop and the stacks are deeper (>50BBs) you can call, but calling here will almost always have a negative expectation.  A-8 is just too weak to play out of position w/out being the preflop raiser.   Folding > 3-betting > Calling.

*** FLOP ***  2♥ Q♠ 8♦

The flop is pretty favorable, as you have second pair with top kicker, but it is very possible that either of your two opponents has a Queen (A-Q or K-Q) or a larger pocket pair than your eights.

Hero: checks 

jetsie: checks 

Wolf_CorpS: bets 400  

Hero: calls 400 

jetsie: folds 

I would fold after Wolf Corps bets.  If he has a queen or any pocket pair above eights, you are in trouble.  Since you are out of position, you are likely to win less when you are best and lose more when your opponent is best.  Another concern is that jetsie could always be check-raising.  It is less likely on this dry flop, but you cannot discount the possibility.

*** TURN ***  [2♥ Q♠ 8♦] 6♦

The turn is very benign and unlikely to have helped Wolf Corps in any way.  Whomever was best on the flop, is still best.

Hero: checks 

Wolf_CorpS: checks 

Checking here is definitely the right play.  I would fold to a bet, but once Wolf Corps checks, you are usually ahead here.

*** RIVER ***  [2♥ Q♠ 8♦ 6♦] 7♠

The river is unlikely to have helped your opponent.  You probably have the best hand here, but your opponent is unlikely to call any bet unless he has a queen.  You should check here to give Wolf Corps a chance to bluff at the pot.

Hero: bets 700 

Wolf_CorpS: folds  

Hero collected 1750 from pot

Betting here is not the best play as you are unlikely to be called by a second best hand.  By betting, you have ensured that you will lose more chips when Wolf Corps has a queen, but you will not win any more chips when he has air.  If you check instead, he will still bet with a queen (though he may check behind!), but he may bluff some chips off to you when he does not have a queen.

ICM Calculations

I recently played in a $4 180-man where an interesting ICM decision came up.  ICM (Independent Chip Model) is a complicated concept that takes into account the sliding pay scale of tournament poker.  The tournament winner ends up with all of the chips in play, but not all of the money in the prizepool.  So the value of each chip in your stack diminishes as your stack grows (and vice versa).  This can lead to some complicated decisions at the money bubble, at a pay jump, and especially on the final table.

In this situation, 8 players remained on the final table. Blinds are 500/1000 ante 100.  Payouts are as follows:

1st - $216.00
2nd - $144.00
3rd - $85.68
4th - $57.60
5th - $46.80
6th - $36.00
7th - $25.20
8th - $18.72


Chipstacks (after ante and blind posting)
Hero      - 52,674
Villain    - 49,102
Player 3 - 34,447
Player 4 - 33,480
Player 5 - 31,653
Player 6 - 31,310
Player 7 - 20,798
Player 8 - 14,236

Hero is dealt A♣ K♠ and raises to 3,000.  The Villain raises all-in to 49,102.  What should the Hero do?

Chipstacks and ICM equity (if Hero folds)

Hero      - 49,674 - $98.97
Villain    - 54,402
Player 3 - 34,447
Player 4 - 33,480
Player 5 - 31,653
Player 6 - 31,310
Player 7 - 20,798
Player 8 - 14,236

Chipstacks and ICM equity (if Hero calls and wins)

Hero      - 104,076 - $145.37
Villain    - 0
Player 3 - 34,447
Player 4 - 33,480
Player 5 - 31,653
Player 6 - 31,310
Player 7 - 20,798
Player 8 - 14,236

Chipstacks and ICM equity (if Hero calls and loses)

Hero      - 3,572     - $28.95
Villain    - 100,504
Player 3 - 34,447
Player 4 - 33,480
Player 5 - 31,653
Player 6 - 31,310
Player 7 - 20,798
Player 8 - 14,236

Notice that if we call and win, we gain $46.40 in equity over folding.
However, if we call and lose, we lose $70.02 in equity.

To determine if we should call or fold, we need to multiply our winning chances against our opponent's range by our equity of winning and add that to our chance of losing multiplied by our equity of losing.  Then we compare this to our equity of folding, which is $98.97.

Some mathematical experimentation yields the breakeven point to be 60.15% here.  So if we are >60.15% against the villain's range, we should call and if we are <60.15% we should fold.
(.6015*$145.37) + (.3985*$28.95) =  $87.44 + $11.54 = $98.98

We are rarely going to be >60.15% against a hand range, holding A-K.  If the villain were to shove any pair and any broadway hand (hand where both cards are A, K, Q, J, or 10) we would be 58.84% and we should fold.  We should even fold if he somehow were to show us J-10 suited since we are only 59.49% to win!

However, keep in mind that this is a very specific scenario regarding the two chipleaders on the final table.  If we switch the Hero to the 7th place stack, things change dramatically.

Chipstacks and ICM equity (if Hero folds)

Hero      - 17,798 - $56.53
Villain    - 54,402
Player 3 - 52,674
Player 4 - 34,447
Player 5 - 33,480
Player 6 - 31,653
Player 7 - 31,310
Player 8 - 14,236

Chipstacks and ICM equity (if Hero calls and wins)

Hero      - 43,896 - $92.28
Villain    - 28,304
Player 3 - 52,674
Player 4 - 34,447
Player 5 - 33,480
Player 6 - 31,653
Player 7 - 31,310
Player 8 - 14,236

Chipstacks and ICM equity (if Hero calls and loses)

Hero      - 0            - $18.72
Villain    - 17,449
Player 3 - 52,674
Player 4 - 34,447
Player 5 - 33,480
Player 6 - 31,653
Player 7 - 31,310
Player 8 - 14,236


Now if we call and win, we gain $35.75 in equity
If we call and lose, we lose $37.31 in equity

(.514*$92.28) + (.486*$18.72) = $47.43 + $9.10 = $56.53 which is our folding equity

Now our breakeven point is 51.4%.  Even now, you must be able to include A-J offsuit in the villain's range for calling to show a longterm profit (or it will profit if you add A-Q but remove A-A, thinking that the villain will 3-bet aces w/out shoving it).

Final Table Predictions

I'm excited about the Final Table of the World Series of Poker Main Event on Saturday!  

Seat 1: Jason Senti               7,625,000
Seat 2: Joseph Cheong        23,525,000
Seat 3: John Dolan              46,250,000
Seat 4: Jonathan Duhamel   65,975,000
Seat 5: Michael Mizrachi    14,450,000
Seat 6: Matthew Jarvis       16,700,000
Seat 7: John Racener          19,050,000
Seat 8: Filippo Candio        16,400,000
Seat 9: Soi Nguyen              9,650,000

The blinds will start at 250,000 / 500,000 with a 50,000 ante.  So each revolution will cost the players 1,200,000!

Jason Senti is going to be looking for a reshove spot right off the bat.  He could be the earliest final table elimination of anybody since the November Nine format began three years ago.  His table position is fairly poor as well, since the aggressive Cheong and chipleader Duhamel are on his left.

Soi Nguyen has played very aggressively so far, but I expect the amateur to wait for Senti to double or bust before he gets aggressive on the final table.  He appears to be the player that would need the most luck to win the title.

There usually seems to be a player at every final table that freezes up and refuses to take chances.  In 2006, it was Rhett Butler.  In 2007 it was Tuan Lam (though he started with a large stack and managed to double a couple times late).  In 2008, it started as Darus Suharto until his mammoth bluff ran into Ivan Demidov's flopped set.  Instead it was Ylon Schwartz who went into a shell after his Q-Q was cracked by Dennis Phillips' A-Q.  Last year it might have been Kevin Schaffel, but his A-A was cracked, eliminating him early.  This year, I have a weird hunch that it may be Filippo Candio.  He went on tilt after calling large bets on the turn and river w/ Q-Q against Cheong's set of nines.  He then committed his stack w/ 7-5 on a flop of 6-6-5 against Cheong's A-A and luckboxed out when the turn and river came 8 4.  He went into a shell after that.  He seemed the most awed by the final table and the most likely to let it affect his game.

Matthew Jarvis lost a ton of chips on the final table bubble, but he did recover to bust Brandon Steven in 10th place.  I could see him falling into the tight trap as well, though he has gotten aggressive in all of the right spots so far.

John Racener may the best player at the table (yes, even better than Grinder, gasp!) and he has good table position.  All of the big stacks are across the table; he has only shorties to his left, which should help him avoid big pots for awhile.  However, if Candio, Nguyen, and Senti bust, he will then have Cheong on his left, which may be a problem.

Chip leader Jonathan Duhamel reminds me of Peter Eastgate.  Both are known as cash game players and both look unflappable.  Duhamel also has great position on the other big stacks, although Grinder is on his left.  If Grinder gets hold of chips, he could be a major thorn in Duhamel's side.  If he goes out early, this could be Duhamel's show.

John Dolan is a bit of a wildcard.  He seems to have the tools to take it down, but he might not enjoy the spotlight that will be on this final table.  Being sandwiched between the aggressive Cheong and Duhamel is a big disadvantage as well.  But he does come to the table with the second largest chip stack, so he cannot be ignored.

Joseph Cheong seems to be the most aggressive player at the table and perhaps the best example of an "internet whizkid".  He 4-bet John Dolan preflop w/ 7-6s on the final table bubble, showing that he has the chops take the whole thing down.  His biggest obstacle is position; he might have the worst position of anyone at the table w/ bigger stacks Dolan and Duhamel on his immediate left.

Finally, the Grinder.  Michael Mizrachi is hoping to be the first well known player to win the Main Event since 2001.  He has the best position of anyone at the table w/ big stacks Duhamel, Dolan, and Cheong immediately on his right.  He also has mid-stacks on his left, which are often bluffable.  I think we may see Grinder come out very aggressively; if he doubles up once, he could make life very tough for the chipleaders.  He also could be crippled by a couple of moves that backfire against him when Jarvis and Racener refuse to let Grinder run them over.

I know my predictions will almost definitely be way off, but here we go!


9th:  Soi Nguyen - Can't hold on any longer after Senti doubles up
8th:  Filippo Candio - Short after doubling Senti and has to make a move
7th:  Matthew Jarvis - Loses a big pot to Grinder in a bvb or button v. SB confrontation
6th:  Joseph Cheong - Awful table position forces him to play tightly until he loses patience
5th:  Jason Senti - One double-up isn't enough
4th:  John Dolan - Finds life tough between Cheong and Duhamel
3rd:  Michael Mizrachi - Pressure of the poker world is too much in the end
2nd:  Jonathan Duhamel - Spews a few too many chips in critical spots
1st:   John Racener - Takes full advantage of position on Grinder

This final table will be heads-up in ~10 hours and the heads-up battle will take <2 hours.  I also think that play will reach 6-handed in <4 hours.

Set on dangerous board OOP

I'm currently analyzing a couple of tournaments that a student of mine played a couple of weeks ago.  Here is one hand that I've analyzed so far from a $2 MTT on PokerStars that starts w/ 3000 chips and usually has plenty of fish:

Hold'em No Limit - Level I (10/20) -Seat #3 is the button 
Seat 1: HorusKomaRa (2720 in chips)
Seat 2: kane11brian (2990 in chips) 
Seat 3: bigdog4all (2720 in chips) 
Seat 4: $.PA1DNFUL.$ (3030 in chips) 
Seat 5: Wolf_CorpS (6040 in chips) 
Seat 6: hobbesy (2920 in chips) 
Seat 7: Hero (3000 in chips) 
Seat 8: 1DeMoN1 (3000 in chips) 
Seat 9: jetsie (3560 in chips) 
$.PA1DNFUL.$: posts small blind 10 
Wolf_CorpS: posts big blind 20 
*** HOLE CARDS ***  

Dealt to Hero   J♦ J♥

hobbesy: folds 
Hero: raises 40 to 60 
1DeMoN1: folds 
jetsie: calls 60 
HorusKomaRa: folds 
kane11brian: calls 60 
bigdog4all: folds 
$.PA1DNFUL.$: folds 
Wolf_CorpS: folds 

A 3X raise preflop looks fine w/ J-J from UTG+1.  


*** FLOP ***  8♣ 9♦ 7♦ 
Hero: bets 160 
jetsie: calls 160 
kane11brian: calls 160 

Your bet on the flop also looks good as you are betting 160 into a pot of 210, against two opponents.  You want to bet more than half of the size of the pot here since your opponents could easily be holding a 10, 6, or two diamonds and you want to charge them to draw. 

*** TURN ***   [8♣ 9♦ 7♦] 5♥

Hero: checks
jetsie: checks 
kane11brian: bets 140  
Hero: calls 140
jetsie: calls 140 

Things are becoming complicated.  The pot is now 690, which would be a good addition to your stack.  Most draws have missed, but any 6 makes your opponents a straight.  Betting and checking are both reasonable here as both of your opponents could easily be drawing.  I lean toward checking to see what develops.  After kane bets 140, I can't find a fold.  The pot is 830 and it is 140 to call; your pot odds are 5.9-to-1, so if you have >14.4% chance of having or making the best hand on the river, you should call.  You have the best hand often enough to continue here, even though you are out of position w/ one opponent still to act.  As an added bonus, a 10 on the river would give you a straight (you will catch a 10 around 8% of the time).

*** RIVER ***   [8♣ 9♦ 7♦ 5♥] J♣

Hero: bets 380 
jetsie: folds 
kane11brian: folds 
Hero collected 1110 from pot 

I love a bet here, but it may not be for the reasons that you would think.  Even though you have made a set, the J on the river is not a good card b/c it likely brought the straight home for one or both of your opponents.  Because of this, you really cannot call any reasonable bet from either player. Chances are that one or even both opponents have either hit their straight or missed a flush draw, either of which may bet.  But it is very possible that one of the villains flopped a small set or two pair and played it slow.  Poor players do this often, even on dangerous boards like this one.  They are caught between slowplaying a big hand and trying to keep the pot small on a dangerous board, so they make costly mistakes by not getting value when they are ahead, but paying off bets once they are beaten.  It is the responsibility of good players to punish mistakes like these!  Getting a call from a hand like J-9, 8-7 or 8-8 seems very possible.  There is also a remote possibility of getting an opponent to fold a 6 here, fearing that you have a 10.  This will not happen often, however.  I actually prefer a bet of 275-300 in this spot since the bets have been so small in this hand.  You look like you're selling a straight, while giving up fewer chips the times you are raised.


One necessary thing about betting the river here is that you must fold to a raise.  Even awful opponents are not going to be raising you here w/out a 10 in their hand, so you must have the discipline to lay your hand down if your river bet is raised.  If you know that you cannot lay this hand down, then check the river and call if one of the villain's bets.  Even then, you have to fold if jetsie bets and kane raises.  Again, nobody is raising a bet w/out a 10 here. 

In fact, at higher stakes or later in this tournament, I might just check/fold against two villains b/c a bluff would be very unlikely on this board w/ this action.  I would check/call against a single opponent who could very well bet a missed flush draw here. 

Ace-Rag essay

I figured I'd post an essay that I wrote about three years ago:

Ace-Rag (A-2 thru A-10)

            One mistake inexperienced hold ‘em players often make is to limp in early position, or call a raise from any position, any time they hold an ace.  A-x represents the opportunity to flop the best single pair possible in poker, and many new players (and some not so new) are infatuated with this potential.  This mistake is especially grievous when holding A-x off suit (as opposed to A-x suited, which can at least sometimes be played profitably, especially in a loose-passive game).  True, A-x will win its share of pots, as will any hand in poker, but there are several problems with playing it, especially for a raise.

First, in a game that is often won with only a single pair, you are restricting your ability to make top pair by playing Ace-Rag, which has only one high card.  Compare playing a hand like A-7, for example, to a hand like K-Q (another medium strength hand). With K-Q, pairing either card will usually give you top pair, whereas with A-7 you’ll likely have to hit your ace to achieve that same goal.  In a multi-way pot against two typical hands (10-9 suited and 8-8) K-Q now becomes the favorite at 30% to win while A-7 ties the pocket eights as the worst hand at 22% to win.  Change your hand to only A-J and it is now even with K-Q at 29% to win.  The only real difference is that your J kicker now can make a higher pair than the 10 or 9, thus beating the pocket 8s, while pairing a 7 kicker cannot beat the eights even if they don’t improve.

With that said, A-7 is, in fact, a small favorite over K-Q when heads-up (57% to 42%), due to the small possibility that neither hand will pair, or that both hands will make two pair.  If both hands were guaranteed to make just one pair, however, A-7 would win whenever the A paired, but it would lose whenever the 7 paired, winning only 2 out of every 4 times.  Contrast this with holding A-Q against K-J.  Now the only combination you would lose is if the K and Q pair.  A-Q would win 3 out of every 4 times.  Of course, guaranteeing both hands to make a single pair is a gross oversimplification, but it helps to exemplify the point: a lone ace heads-up against two high cards is much weaker than an ace with a strong kicker.

As such, not only are your odds of winning a hand with A-7 (or something similar) fairly poor, but, even more importantly, the pots you do win will tend to be rather small – especially in relation to the pots lost when you think you are best; i.e., when an ace flops.  The reasoning is simple: when an ace rolls out on the flop, everybody notices.  Players without an ace tend to fold to any bet.  Even players holding big pocket pairs will tend to play passively after an ace flops.  However, if your opponent is also holding an ace – and if you’re playing Ace-rag it’s safe to say he or she probably has you out kickered – they are not going anywhere and will typically raise you.  Since folding a pair of aces is very difficult for the beginning player (and, for that matter, most players), players whom get involved in a hand with A-rag stand to lose a big pot.  The object of poker is not to win pots.  The object of poker is to win money.[1]  These two statements are not contradictory; though you must win pots in poker to win money, it is the size of the pots won, rather than the number of pots won, that is important.  If you were to win 20 pots averaging $5 and lose 10 pots averaging $15, you are obviously way behind – even though you have won most of the pots!  Avoiding the loss of a lot of money in big pots where you would be drawing very slim (three outs to your kicker) is worth sacrificing a couple of small wins.

My next point is more advanced and will require some thinking from beginning players.  If you are raised after betting a pair of aces on the flop, your opponent may in fact be semi-bluffing.  For example, you hold A-4, the flop comes A-8-7, you bet and an opponent raises.  If your opponent is a strong player, he may hold A-Q or 7-7, or he may be semi-bluffing with 10-9 (only a straight draw)!  You just don’t know, and even if you think a semi-bluff is likely, you should still fold!  The problem with calling here is that your opponent is getting implied odds from you, which means he will make more money if he makes his straight than he will lose if he misses.  Continuing this example, unless you are lucky enough to catch a 4 on the turn, you will likely check.  Your opponent can then check and see the river for free if he has not yet made the straight.  Now he can fold and get away with not paying any more money if he misses his draw!  Of course, if a J or 6 comes on the turn or the river, you are probably going to have to call any reasonable bets and lose more money!

While Ace-Rag is largely a losing hand, there are two situations where it can be played profitably: in an attempt to steal the blinds from late position, and, when suited, at a loose-passive table.  Thus, when holding A-x on the button at a table where everyone else has folded, you should raise in an attempt to try and steal the blinds.  This play is especially profitable if your opponents play either too tightly or too loosely from the blinds.  If they are too tight then you should be raising with all but your worst hands, while if they are too loose you will be in position after the flop and, usually, ahead.  In order for this play to show a long term profit, if one or both of the blinds call and then check on the flop, you must bet regardless of whether or not you hit the flop.  Your opponent(s) will fold the majority of the time.  If you are called, however, and you still only have ace high, you should give up the hand and hope for a free showdown.

The other profitable play for A-x requires that your hand be suited, and that your table be both loose and passive – meaning that many players see the flop on most hands, and pre- and post-flop raises are kept to a minimum. If those preconditions exist, then you can correctly call.  Although the hand should generally be folded in early position, it can be a decent play to call if most pots are contested by at least four players with very little preflop raising. Nevertheless, limping from middle to late position is far superior because of the improved chance that the pot will not be raised after your bet.  Your goal in playing this type of hand is to accomplish one of several things: flop a flush, which will happen only 1.6% of the time; flop a flush draw, which is more likely at 14% (one time out of seven); or get really lucky and flop two pair or trips.  If you do flop the flush draw, you will now be getting implied odds from your opponents.  What this means is that you stand to win more money from your opponents than they stand to win from you, because you will fold if you miss your draw, while your opponents will likely call if you make your flush.  (For full details on Implied Odds, see Chapter 7 of The Theory of Poker).

Clearly, although it can be played profitably in the right situation, A-x is generally a chip burner; it stands a low chance of making top pair, and a high chance of being dominated by a stronger ace.  As such, the few small pots that the hand stands to win do not even come close to compensating for the large losses that it tends to incur. Play it at your own risk.

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[1] The Theory of Poker by David Sklansky p. 6

1st Post

First post of my new poker blog!  Stay tuned for some actual content!