MTT Luck Part 2 - Positive Hands

In Part 1 I described what an Orthodox hand was and how these were essentially flips regardless of the actual cards dealt, if you can get around to this way of thinking for Orthodox hands it may well help you deal with tilt issues when you get that set of 6s cracked by AA as in my previous example. It also highlights how in MTT endgames nearly every hand can become a flip as the play becomes standardised due to shallow stack sizes. So what about hands that we wouldn't play the same as our opponents?

Let us consider another simple hand, it is folded around to Player A, who is in the SB with 10bb, player B in the BB also has 10bb. Player A looks down to see QJs and decides to shove, player B looks at their cards and sees pocket Aces so snap calls the shove, the board runs out A27 T K giving player A the pot with a runner-runner gutshot, how sick was that hand? Note that player B would not have shoved the QJs if they had been in the SB, so this is not an Orthodox hand as discussed previously so we can not consider it a 'flip'. As such, on the face of it, it looks like player A got terribly lucky and player B terribly unlucky but luck in this hand is not a zero sum equation; that is that Player A is not as lucky as player B is unlucky. Why is this the case? Well let us analyse the hand again but this time we will do some basic calculations of the expected value of each players move. If you don’t want to get bogged down with the maths, skip this bit and go to the final figures I give in the table.

For simplicity let us assume at the start of the hand each player has exactly 10,000 chips, the SB is 500, the BB is 1,000 and there are 10 antes of 100 each in the pot, so the pot before any action is (100 x 10) + 500 + 1000 = 2,500 chips.

It is folded around to player A, who after posting the SB and ante has 9,400 chips left, they expect the BB to only call a shove with the top 20% of hands, so if player A shoves, player B folds 80% of the time. Of the 20% of the time player B calls, then player A has 44% equity against the top 20% of hands (check PokerStove to work this out if you wish).

We now have 3 possible outcomes: 

1.             80% of the time player A wins the pot of 2,500 chips so their stack becomes 9,400 + 2,500 = 11,900, the EV here is 0.8 x 11,900 = 9,520     
2.       When player A calls, player B still wins 44% of the time, this happens 44% x 20% = 8.8% of the time, the EV for player A here is 1,830. Calculated as 20,800 (the total size of the pot when both players call) x 0.088
3.       The rest of the time 11.2% player A loses and has zero stack

We now add these 3 figures together 9,520 + 1,830 + 0 = 11,350, this is the prior expected stack of player A after he shoves and this is a gain of 1,950, this is an increase of over 20%! (Prior Expected Stack is the stack that player A can expect to have on average when they shove prior to player B acting).

What happens to Player’s A’s expected stack size when B calls with AA, well AA v QJs is 80% v 20% so the posterior expected stack (This is the Expected stack of player A after B calls and shows AA) of A is 20,800 * 0.20 = 4,160. 

When player B sees AA, they don't really care what player A has, but let's assume that they expect play A to shove the top 50% of hands, player B has 85% equity against this range , we can calculate player B’s Prior Expected Stack (this is prior to Player A shoving  but given that Player B knows his own cards) and this is 14,540.

Similarly once player A shoves, we can work out that Player B’s Posterior Expected Stack is 16,640. I have summarised the scenarios and outcomes in the table below:

As we can see, both players have a positive expectation at the time they make their action (their Prior Expected Stacks are above their current stacks). I will label these types of hands as Positive Hands, in which both players make plays that have a positive expectation at the time given the info they have. Of course this is subjective depending on factors such as playing styles and there may be multiple streets of action some of which maybe slightly negative or have implied odds calculations etc but it highlights a good principal.

How can both players have positive expectations in the same hand? Well there are dead chips in the pot, but also player A makes a move against an unknown random hand, which means his shove is profitable long term. The fact here is that each player does not know his opponent’s hole cards so they both have different expectation levels to those that exist once the action plays out and the cards are shown. Note that the sum of the 2 Prior Expected Stacks do not equal the sum of the 2 stacks, but the sum of the Posterior Expected Stacks do, this is because the Prior stats take account of folding and ranges of random hands, the Posterior Stats have complete information. Once the hands are known one player can only gain at another’s expense as is seen in the table above.

So that’s a lot of number crunching, how does this fit in with luck in MTT’s?  Well we can see that when player A shoves he makes a good move that is profitable long term, but all of a sudden he expects to lose lost 7,190 (11,350 – 4,160) because player B has AA, this is out of A’s control so A can rightly say he has been very unlucky.

Also, Player B obviously makes a +EV move since he has the nuts at the time, but he has been lucky to get dealt AA at the start of the hand in a spot where player A can make a +EV move, he has a big +EV situation at the start of the hand but this increases further when player A shoves, even though A does not make a mistake by shoving. Since A has not made a mistake, we cannot state that he has been outplayed, as such player B is very lucky to have found himself on the right side of a positive hand. This is an often overlooked side of luck, it is very easy to get AA in the BB and the SB finds 84o and folds, the maths shows that AA wants the shove long term, but this is not under his control so he is lucky when he gets the shove.

Naturally when player B wins with the AA here he will want to congratulate himself on doubling up, but his double up is entirely down to luck, therefore when he loses with AA in this spot he should take it in good grace, this hand is in the hands of luck much like the orthodox hands but only these spots generally favour one player over the other since both players wouldn’t play it the same way. Player B is losing out in the long run when they have QJs in the SB but fold here, but this does not mean that they should begrudge player A winning occasionally when they shove QJs, remember QJs should beat AA about 20% of the time. In the long run here if Player A shoves QJs from the SB but Player B would fold, player A will crush player B assuming a random hand in the BB. Note this means there is a skill element in the prior element of the hand for Player A, but not for Player B, as such Player A has more right to be aggrieved at being unlucky that Player B, even though player B actually has the best hand when the stacks go in!

In summary, Positive Hands are hands where both players make a move that has a positive expectation prior to them knowing their opponent’s hole cards, however if the roles were reversed each player would act quite differently so these cannot be considered Orthodox hands, if both players were to act the same way then the Orthodox hand logic from part 1 should be applied. In Positive hand situations it is not necessarily the player with the best hand when the stacks go in who should feel the most upset when they lose the hand, but often it is the player who has the worst hand but runs into a better hand. They gain the most against a random hand but also lose the most when they are unlucky to run into the top range of hands. The player with the best hand also gains when the other player makes their own positive move which in itself is down to luck, so this player is lucky in two ways, firstly that they have such a good hand and secondly that their opponent has a hand good enough that they can make a positive move, therefore when you lose with the best hand in these spots you have already used some good luck up at the start of the hand. I have intentionally given an overly simplified example to illustrate my general point but there are lot of permutations and other factors involved of course. Try to bear this example in mind next time someone shoves a positive hand into your AA which gets cracked.

MTT Luck Part 1

I've had a terrible few days of luck following a short spell of running above EV, on the train back from London this morning I was dozing and thinking about Luck in MTTs, and what it really means and whether I could reduce the luck effect in my games, I will share some of my early morning half-asleep thoughts over a few blogs:

A lot of poker players will talk about how they get more than their fair share of beats or how they never win crucial flips, or how so and so is always in god mode. Luck is much more than your pocket kings holding to ace rag, or your queens winning a race v AK. Luck can take many subtle forms some of which we don’t appreciate.

Table Draws

The first element of luck in an MTT is undoubtedly the table draw, imagine sitting down to a table where you have known sharks all with position on you, while your friend has a table full of fish, clearly you have been unlucky and will find it harder to gain chips than your friend. This can be particularly true in deep stack MTTs for two reasons, firstly the game is deeper stacked so players skill edges are more apparent, on a table full of sharks it is harder to get paid with a set when your opponent holds top pair, but on a fishier table it may well be much easier. Also deep stack games generally mean that your table will stay together for longer, so you will be playing with you current players for a lot longer, if the table if full of sharks it can be hard for anyone to gain chips, while the players at the neighbouring tables collect the chips of the weaker players.

Further to this I believe that if you are at a tight table, this means you will as a rule be playing lots of small pots, this means there is usually low variance at the beginning of the MTT but this gets higher towards the middle/end of the game game as you are frequently shorter stacked as a result of not winning many big pots.

Conversely a looser table means fewer but bigger pots, so variance levels can be quite high at the beginning but comparatively less in middle as your stack size is usually better when you survive the loose play.

So which table is preferable at the start of an MTT? I would say a loose table that allows me to play a tight aggressive game where I can look to get paid handsomely when I hit, since this is my preference I must accept a high level of variance at the start of a MTT, it will mean making more marginal decisions, such as stacking off with JJ preflop to a known loose shove but the same hand would be an instant fold on a tight table. It also means accepting that the loose player will chase his draws and inevitably will hit some of the time. However, winning bigger pots enables the player to take more control in the middle stages and provides a cushion against variance as they can usually take one or two hits from shorter stacks, it also allows the player to use their stack to apply pressure in the mid stages. A player coming from a tight table may have won numerous pots but may not have even doubled their starting stack, whereas a player from a loose table may have tripled or quadrupled their stack playing 2 or 3 pots only. I know I have been frustrated many times playing at a tight table, where I can chip away and win lots of small pots but still fall behind the average stack and find myself in shove fold mode too quickly, I definitely want a loose starting table, particular if the structure is deep. Of course I have no influence over who starts at my table or how they play so this is 100% luck.

Orthodox Hands

For the purposes of this blog I am going to define what I call an orthodox hand:

An orthodox hand is a hand where you and your opponent would play the hand virtually the same way if the roles were reversed, let suppose player A has 20bb and picks up AK in mid position and raises it up to 2.5x, player B in the BB has QQ and 20bb so shoves and A calls. Now let us suppose player B is in mid position with AK and raises it to 3x, now player A is in the BB and also shoves QQ, clearly the action is virtually the same and this is what I call an Orthodox Hand. AK v QQ is the classic example and is probably the most frequent race seen in MTTs and the outcome can be the difference between winning a title or busting out early on a final table.

Let us take another example where player A has AA and player B has 66, A raises and B just calls, everyone else folds and the flop comes 36T rainbow and A bets half the pot and B calls. The turn is a Jack and player A bets again and B now shoves over the top, now if player A is tight and B is loose, then A will usually have a hard time folding here but if the roles were reversed then player B might be able to fold their overpair if they know that A is a tight player with a narrow range here which comprises mostly sets. Therefore if A goes broke with AA but player B would not go broke with the same hand then it’s not an orthodox hand as there is some skill in deciding whether to call, but if both players were to go call with the AA (if the stacks are too shallow to fold AA here for example) then this becomes an orthodox hand. Clearly this is a matter of judgement and it is not easy to identify whether a hand was orthodox or not, but bear with me because it is the conclusion drawn from this rather than the exact definition that is important.

Here is a recent hand from the PKR Open:

Blinds are now 30 / 60

Button is at seat 9

Seat 1: Mutufs - 2,280

Seat 2: englANDfans - 2,870

Seat 3: ForFoxSake - 5,140

Seat 4: checkerr87 - 2,360

Seat 5: buscseb - 4,182

Seat 6: GoldHands - 5,500

Seat 7: Toffeyman - 2,480

Seat 8: bpitman - 5,725

Seat 10: brentos - 2,440

Moving Button to seat 10

Mutufs posts small blind (30)

englANDfans posts big blind (60)

Dealing [A s][A h] to ForFoxSake

ForFoxSake raises to 180

checkerr87 folds

buscseb folds

GoldHands folds

Toffeyman raises to 540

bpitman folds

brentos folds

Mutufs calls 540

englANDfans folds

ForFoxSake raises to 1,260

Toffeyman raises to 2,480 (all-in)

Mutufs folds

ForFoxSake calls 2,480

ForFoxSake shows [A s][A h]

Toffeyman shows [K s][K h]

Dealing Flop [8 d][2 c][Q c]

Dealing Turn [K d]

Dealing River [3 c]

Toffeyman has Three of a Kind: Kings

Toffeyman wins 5,560 with: Three of a Kind: Kings

I get AA cracked by KK, but if I had been Toffeyman here with KK I would have played it the exact same way. We are equally likely to be on the good (AA) or the bad (KK) side of this hand, furthermore my EV when I have AA v KK here is the same as Toffeyman’s EV when he has AA and I have KK. This means over the longrun our EV in this orthodox hand is the same. Note in effect here I may as well have had KK and lost to AA as it wouldn’t have affected either of our play in the hand. Since I am equally like to have got the KK side of this hand rather than the AA, the hand above is not a bad beat, it is actually a flip!

In an orthodox hand note that since both players would play the hand virtually the same, there is no skill difference involved in the hand whatsoever, and since no skill is involved the hand is 100% luck, this includes your hole cards and any and all community cards dealt. Whenever the luck element is 100% in a hand it is essentially a flip as the cards are meaningless, it is just in effect a lottery. Taking the AA v the set of 6s example above, if the villains calls your shove but you would also call the shove if the roles were reversed then you have not outplayed your opponent or been outplayed, so the skill element is 0% which means it is all down to luck!  So if you hold the set of 6s but would have called the all in if you had the AA, then if your opponent calls and hits the 2 outer Ace on the river and you lose the hand then it is not a bad beat but merely a flip (you were just as likely to be the one holding the AA here and rivering the 2 outer).

Let’s just clarify that again, you could get your money in as a 90%+ favourite and lose the hand but it is not a bad beat if you would play the hand the same way in the villain’s shoes, the hand is in essence a flip as the roles are just as likely to have been reversed and over the long term neither of you will gain any EV from the other as you both will have been on each side of the orthodox hand the same number of times.

Note the more orthodox hands you are involved in the larger variance will be (as you are essentially flipping each time), this is why variance in the late stages of MTTs is huge because the stacks are so shallow that most hands play themselves and everyone plays them in a similar way, so most hands become orthodox hands. 

The only way to try and combat this is to use your skill edge to win as many non orthodox hands as possible, the more chips you have the more orthodox hands you can afford to lose before being eliminated. Good MTT players will win non showdown pots which weaker players do not take advantage of and the weaker players fall victim of orthodox hands a lot more as they are invariably shorter stacked and they play hands in a standard way. The best MTT players are often deeper stacked and so can avoid orthodox hands more because their deeper stack allows them to play hands in a different way (if you have 20bb it is very hard to fold AK preflop for example, but with 70bb you might find you are behind and can fold).

Another way to reduce the effect of luck is to control tilt, the next time you get a big hand cracked think about how you would have played the villain's hand, if it was practically the same as they played it, then try to think of that hand as an orthodox hand in which you lost a flip rather than losing to a 2 outer or however the hand played out.

That's all I will say on the subject for now, hopefully I have explained the concept of orthodox hands well enough for you to understand, but if it is not clear then feel free to leave me a comment and I will try and provide a more detailed example. I will give more thoughts on MTT Luck in the near future, until then good luck!

2012 First Quarter Review

January started with a trip to the Fox Club for their main event, having made day 2 and busting to a cooler a few places from the money in December I was hoping to do better this time around. There were 143 entries with 15 paid and a top prize of just over £13k. The first few levels were fairly standard and I was winning a lot of pots without showdowns by mixing up my play, I won a big pot when I opened with Aces over a limper who called, the flop came down 2cJc8s and I ended up getting it in v T9c, I had the guy covered and it was only about 50% of my stack but it was still a sweat, but the board bricked and I was amongst the chiplead after winning another decent pot turning the nut straight with KT, although I chopped with another player who had KT also, we got a 3^rd player’s stack who had the small end of the straight. Soon after I got A8o on the button and opened to 1,400 from an 85k stack, the blinds are 300/600 and at this point I get distracted by the Fox Club blogger who wanted a chip count etc from me, meanwhile the BB shoved for 9k and slightly distracted I made a quick call, it felt like the guy was making a stand to the button open, I had been fairly aggressive and so I called and he flipped AQh and I lost the pot and kicked myself somewhat for making the call, however soon after the same player 3 bet shoved rags and busted which made me feel a little better since he was clearly capable of raising wide but I just happened to run into him having a hand. At the end of the first day I bagged 102k; with an average stack of 84k and 38 players left I was happy with my play and looking forward to day 2.

Soon into day 2 I get AA and raise over a limp and get called, the flop comes 884 and I c-bet and get called, I know the limper is loose and I have heard him say previously that 8 is his favourite number so I am very wary and check the brick turn, he fires on the brick river and I call and he shows 83o and I drop to 75k ish. After this I struggle for momentum for a while before doubling with JJ v Ace rag and we go down to 2 tables, with 15 being paid I try to pick up the aggression and win a few small pots but by the time the bubble burst I am just below the average stack, soon after a strange player shoved 5bb or so from EP it folded to me in the BB and I had JQo, this guy had previously shoved hands like 92o while folding Ax hands, I decided I was in good shape against him and called, he flipped 84 but he made a full house and that left me short, soon after I open shoved J2h and ran into kings and busted in 15^th, which while it was a cash was also a disappointment since I had had a good stack for most of the tournament.

The very next day I won Welllbet’s Home Game on PKR but despite this January was a miserable month a few minor cashes and winning Welllbet’s again at the end of the month didn’t stop me recording a loss for the month, I also played the £540 APT event at the Fox but didn’t really get anywhere in it and lost a flip with JJ to AK, all in all January was pretty bad and I had had higher hopes for February. 2 wins in a month without many other serious cashes is not enough for someone who plays lots of mid and high stake MTTs throughout the month.

February would prove even worse, a 2^nd and 3^rd in the Monte Carlo were my only notable results and my bankroll was taking a severe hit. I was feeling really low  about my game and was seriously considering taking a break, I decided to give it another week or two and I managed to win the Monte Carlo, this helped me to regain some of my confidence and a few days later I won a Primetime and the day after that the Dirty Dozen, these 3 wins combined were worth nearly $5k and suddenly things were looking up again, a more steady stream of minor cashes also helped maintain my bankroll and I won the Dirty Dozen again towards the end of the month. March had proven to be a really good for me and had more than made up for my losses in the previous two months.

It just shows how quickly things can change in MTTs, I was down and out a few weeks ago but suddenly my confidence was back. I am a firm believer that confidence is a huge factor in MTTs, when I am feeling confident my instincts are generally better and I make better decisions in marginal spots. Let’s take an example of where I have been card dead in an MTT for a while and I get dealt QQ, UTG raises and I 3 bet from UTG+1 and all of a sudden a mid position player cold 4 bet shoves, instinct tells me they have AA or KK most of the time but if I am feeling low on confidence then I am more likely to call because I have no belief that I can get chips elsewhere, either because I am not playing my A game or the cards are not going my way or a combination of both, whereas when I am confident I can hit the fold button easier trusting my abilities (and also variance) will allow me to regain chips in a better spot. Confidence also naturally means I play more aggressive and providing this doesn’t lead to over-confidence and over-aggression this can only be a good thing as controlled aggression will win more chips without showdowns than a tight game will, this in turn usually leads to better results since less showdowns means less luck is involved and this generates a confidence cycle. As I type this I am feeling confident about my game and have had a few decent results recently, which have been a combination of me playing my best game and also getting a good run of cards (I don’t think I have been in god mode in terms of variance but I have been running above EV which is always a welcome change).

April has so far continued as March left off and I am going to play the London Calling Main Event at the Fox club over the Easter weekend so I am hoping I can transfer my online results into a deep live finish, hopefully my next blog will be about me winning my first live MTT J