"Hero" Calling

I am sure you have all heard of the term hero calling. It means calling in a spot where we have a very poor hand that can only beat a bluff. In today's aggressive games there is probably more spots to hero call than a decade ago. So how do we know when we should be hero calling and when we should we fold?

Well right off the bat I am going to tell you that I hate the term hero calling, I only use it in this blog as it is term every poker player understands. However, it suggests that by making the call you are being a hero, making some brave move against all the odds. Well if you are hero calling correctly then you aren't a hero at all. You will be nothing more than a cool calculator, because you will have made the decision to call based on the odds given to you and weighed that up against the chance that you are actually ahead (i.e. that your opponent is bluffing). If you are calling to be a hero without thought to the odds etc. then you are doing it for all the wrong reasons and even if you happen to call and have the best hand then you have still made a mistake.

Calculate correctly and you won't need to be a hero again!

Hero calling is often done against aggressive opponents and when a lot of draws have missed on the river. This is because an aggressive opponent is more likely to bluff than a passive one, also if there are draws that have missed the river usually the only way for a busted draw to win the pot is to have a stab and bet the river.

So does this mean we should just blindly call every aggressive player on the river when a flush draw missed? Well not always, it depends on any reads and history you might have, bet sizing and most importantly what range you can put the player on given the action in the hand and how accurately you can narrow this range down. Usually to consider hero calling we would expect our opponent to have a polarised range (that is they either have a massive hand or a very weak one), but against good opponents this is not always true as they can beat medium hands for value in spots where lesser players want to go to showdown. So against really good aggressive players hero calling is a bit tougher.

You shouldn't be put off hero calling because you are afraid to look like a fool when you turn over your cards, it can be slightly embarrassing and frustrating to call with a King high hand when your opponent actually flopped a monster, but if you have correctly assessed their range and the odds then you should be happy you have likely made the correct play.

I recently played the PartyPoker Dusk Till Dawn Grand Prix, I had made day 2 by playing day 1 online and so when day 2 started I had no reads on anyone. About 20 minutes into the tournament it is my big blind and it folds around to the small blind who limps in, I look down at 73o and decide to check.

OK so a little info first, I have about 500,000 with the blinds at 5,000/10,000/a1000. The small blind has about 2.5million at this point having already doubled up with 88 v AJ all in on a JT8 flop. He seems to be a competent aggressive player. Note when I am new to a table I always pay most attention to the players sitting near me first as those are the players I am more likely to be playing marginal pots with. I had noticed that in a couple of hands he had bet more than half the pot with good hands and this was to prove crucial in this particular hand.

So after I check the dealer spreads the 832 flop with the 8 and 2 both being spades (I had the 3 of spades but an offsuit 7). The small blinds bets the minimum 10,000, this sizing feels like a bit of an info bet here so I suspect he likely has a 2 or a 3, I think he bets bigger with a bluff or an 8. I could raise at this point and look to take the pot down but he might still call and the pot would start to get bigger than I really want in the first level with a 50bb stack so I decide to call.

The turn is the Qs so I now have the nut low flush draw to go with my poor pair poor kicker. He continues for 22,500 and I think for about 30 seconds considering all 3 options at this point, I dismiss folding fairly quickly as I don't think he hit the flush as I believe he would bet more on the flop with the flush draw. This leaves raising or calling, I was tempted to raise as I think I can get him to fold some random spade cards that beat my 3s but in the end I decided to call.

The river is an offsuit ten and he leads for about 35,000 (I forget the exact amount) and I immediately feel like I am ahead, but one mistake I have made quite a lot in the past in these kind of spots is to call too quickly so I take a minute to work through the hand.

The pot at this point is 20,000 (blinds) + 9,000 (antes) + 20,000 (flop) + 45,000 (turn) and his 35,000 bet on river, so 129,000, so it costs me 35,000 to win 129,000, therefore I don't have to be right that often to show a profit.

I am pretty sure he doesn't have an 8 due to the small flop bet. It is possible he hit the ten or queen but again I think he would have bet larger on the turn or river if he had. I also don't believe he has two pair or better for similar reasons. This leaves bluffs, 2x or 3x (both of which I think he might turn into a bluff). I beat all 2x hands which leaves only the 3x hands that have me beat. Remember this was a limped blind versus blind pot so the ranges are pretty much any two cards! Given my indecision on the turn I believe he probably thinks I was thinking more about folding or calling rather than calling or raising (which was actually the case) so I in turn believe this is more likely to make him take a stab here, coupled with the great odds I decide I have to call. As such I put my chips in the pot and he declares one pair, he then turns over 24o and I table my hand to win the pot.

He later said he couldn't believe I called down with just the 3 and that he had bluffed the river because of my apparent reluctance to call the turn. Although this isn't necessarily the greatest example of a hero call (I had 4th pair after all!), it is more an illustration of the basic thought process I went through before making the call, after all I can't beat any hands he is betting for value! When I made the call I didn't feel proud or do a fist pump or sigh with relief or anything, I simply raked the chips up and moved onto the next hand. Remember, making good calls means not being a hero, but being a cool calculator instead!

I ended up making day 3, but sadly bust in 35th place out of over 7,000 entries, not bad but also tantalising close to a big score. There is always next time....

Counting Cards

When people who do not understand poker ask me about it, they usually say things such as “You must be good at counting cards”, they associate gambling at cards with card counting. This is usually because they have heard of card counting at Blackjack. Basically to card count at Blackjack you assign a point value to cards depending on their ranks and this tells you how many high cards are left in the deck. The more high cards there are then the more chance that the dealer will bust and the odds can actually be in your favour if the deck is heavy with high cards. This means you can make a short term +EV play by betting more when the time is right, because of this casinos frown on card counting.

The film "21" tells the story of a group of MIT students attempting to count cards at Blackjack.

I don’t want to talk about card counting in Blackjack (Watch the film 21 if you want to see card counting in action), but when I am asked about card counting, it is easy to be dismissive and say there isn’t a need to count cards in hold-em, after all it is a game of non-perfect information (we don’t know what our opponents cards are) there are only 5 known community cards and the 2 we have in our hand that we know for certain. However despite not having perfect information, we can still utilise what information we do have to card count in selective ways when playing Hold’em. Whenever we have to make a decision in poker, we should try to put our opponent on a range of hands, the more accurately we can do that then the better our decision making will be and in the long run the more money we can expect to make.

Blockers

The easiest and most useful way of “counting” is to look at your cards and those on the flop and see how this might affect your opponents range and their chances of hitting their hand. Let’s say we hold AhJs and the flop is Ac 9h 3h and we are heads up against one opponent. What is the chance they have the nut flush draw? This isn’t a difficult question to answer and it doesn’t involve calculating any ranges, the answer should be really simple. If you have not worked the answer out yet go back and read the question, paying particular attention to the cards and their suits. Don’t read on until you have the answer, once you have the answer you will know it’s the right one.

Clue: Don't think about your opponent's hand at all, look at the cards we have and work out how this changes the odds for our opponent holding the nut flush draw.....

The answer is 0%! Since we have the Ah they cannot have the nut flush draw…in order for them to have the nut flush draw they must have Axhh, but they cannot have this as we already have the Ah! This can be really useful in some situations, say for example we raised pre and they called from the SB, and they check raise our continuation bet. If we have notes of them that say they would only check-raise with 2 pairs or better or the nut flush draw (i.e. they would just check call with one pair hands or flush draws that aren’t the nut flush draw) then in this scenario when we get check raised we can easily work out that we are beat and assuming we don’t have the correct odds we can fold. If instead of the Ah we have the Ad then this becomes a trickier spot as they villain might have Ah6h for example as that would be in their check raising range according to our notes.

It is also less likely they have two pair here as well when we hold any ace as it is less likely they have A9 or A3 and they probably don’t have 93. All of a sudden their range looks a lot like a set when we hold the Ah, whereas it is a bit wider if we hold another ace and wider still if we don’t have an ace at all.

The above example is a bit contrived as it assumes the villain plays a certain way and we know this, however even if we don’t know that for certain, clearly their semi bluffing range is smaller when we have the Ah than when we don’t, most opponents are more likely to play Axhh this way than a lot of the other xyhh combos (how many would call pre with J2hh for example then check raise the flop? It’s certainly less than would play A2hh that way). This means their range is usually skewed more towards value than semi bluffs.

Another scenario might be where we have AdKd and the flop is Ah9h3s. Although the Ah is om the board, it still means your opponent doesn’t have it. Although they may have the nut flush draw with Kxhh, the range of Kxhh they would play preflop is likely less than Axhh (e.g. more players would call pre with A2hh than K2hh) so we can still skew their range in a similar fashion to that above, although we should note hands like KQhh and KJhh are more likely in their c/r range than in the first example.

The lesson here is to pay attention to any cards you have that may affect the range your opponent has, which leads me nicely onto the next point.

Combinatorics (EV)

Now let’s suppose we have AKs and a player has opened, we have 3 bet them and now they 4 bet shove for around 35bb (which is the same stack we have). Our notes tell us they always have AK or QQ+ here, let’s assume the villain always 4 bet shoves these hands and nothing else. Given this we can work out our EV in the hand, to do this we can work out our EV against each hand and take the average.

                Our EV against AK = 50%

                Our EV against QQ = 46%

                Our EV against KK = 34%

                Our even against AA = 12%

So our average EV = (50 + 46 + 34 + 12)/4 = 35.5%.

However, there is a flaw in this calculation; can you see what it is?

The flaw is that when we took the average EV we assumed each of those 4 hands is equally likely, when in fact they aren’t! We forgot to take account of the effect of our blockers on the combinations of these hands available, let me explain further.

There are 4 aces in the deck, spades, diamonds, hearts and clubs. We can get dealt any of those 4 aces and in any order. Note that getting dealt Ah Ad is the same as Ad Ah. So how many combinations of these 4 aces are there? Well let’s work it out:

1. As Ad
2. As Ac
3. As Ah
4. Ad Ac
5. Ad Ah
6. Ac Ah

There are 6 combinations of Aces when none of the aces are known to be elsewhere. 

For the record there are 1,326 combinations of starting hands in holdem, each of which are equally likely. The chances of being dealt aces preflop is the number of combinations of AA (6) divided by the total possible combinations of any two cards (1326) so 6/1326 = 0.45%

Now let’s go back to our example where we have the As, how many combinations of Aces are there? Well Combo 1, 2 and 3 can no longer be valid as they have the As in so there are now only 3 combinations left. This holds true for any pair so there are also only 3 combinations of KK since we hold the Ks. However we know nothing about any Queens, so there are still 6 combinations of QQ. This means our opponent is just as likely to have QQ as they are to have KK or AA combined!

Now let’s consider the combos of AK (given that we have AKss):

1. Ah Kh
2. Ah Kd
3. Ah Kc
4. Ad Kh
5. Ad Kd
6. Ad Kc
7. Ac Kh
8. Ac Kd
9. Ac Kc

There are an additional 7 combos if we ignore the fact we have AKss:

1. As Kh
2. As Kd
3. As Kc
4. As Ks
5. Ad Ks
6. Ah Ks
7. Ac Ks

Ok, so how does that affect our EV calculation? Well now we can calculate a weighted average, which is we assign a weighting to each hand to reflect its chances of being the actual hand compared to the others. There are 3 combos of AA and KK, 6 for QQ and 9 for AK. That makes a total of 3 + 3 + 6 + 9 = 21 combinations. So the chance of the hand actually being AA is 3/21 for example.

If you recall:

    Our EV against AK = 50%

                Our EV against QQ = 46%

                Our EV against KK = 34%

                Our EV against AA = 12%

So our weighted average calculation is:

50% * (9/21) +

46% * (6/21) +

34% * (3/21) +

12% * (3/21) = 41.1%

All of a sudden we have over 5% extra EV then we originally calculated, just because we “counted” our two cards.

If you are calculating EV versus a range, it is important to use combinatorics to ensure you adjust each hand based on the chances of it being the actual hand. Even if we didn’t know we had AK then it is still more likely someone has AK than AA (this should be obvious since once we get the first Ace there are only 3 other Aces left but 4 Kings). However if we have AK ourselves, it is even more unlikely our opponent has AA compared to AK (assuming we have AK then once they get their first Ace there are only 2 in the deck compared to 3 Kings).

As with a lot of my blogs, I wouldn’t worry too much about the exact maths behind this, but just try to understand the principle that our cards can make a huge amount of difference to the ranges of our opponents and also the combinations of each hand they might have. If you can get your head around this then it can often help your make the right decision in marginal spots.