August 25, 2020

Balance and board coverage

Let's leave poker for a bit and turn to the almost as thrilling game of rock, paper, scissors... Let's say you meet someone for the first time and you are going to play 1000 times, having written down all decisions upfront. Having no specific info on the opponent, it is pretty intuitive that the strategy that cannot be exploited is to choose each of your options 1/3 of the time.

Let's consider another game of rock, paper and scissors. This time you know that your opponent will always play rocks after being beaten by scissors when holding paper. What do you do the round after winning with scissors? You win again with paper. You just exploited your opponent's (maybe your young nephew's?) unbalanced play of rock, paper and scissors.

Similarly, in poker there are situations in which you need to make your opponent indifferent what decision to make (in principle not being able to exploit you, even if they knew your overall strategy in this position - formally you can read about Nash equilibriums where neither player can change his strategy to improve in a zero-sum two-player game), unless you want to open up for potentially being exploited.

One example of this, is to bluff just enough. If you always bet your strong hands and never when you miss, you become easy to play against and you never get paid off with your monsters. Conversely, if you bluff all the time, you will get called down by marginal hands beating you ("bluff catchers").

Another usage of the term balanced in poker, is about the hands you play from street to street - you might hear people discussing keeping ranges balanced. In the combos example, I threw in a hand in the other players range that some of you might be surprised to find there, A5s. That was not completely random, even if it is highly debatable if this specific example was "good". The same concept applies to each of the actions, ways you continue in the hand. If you never have a strong hand on certain rivers after checking the turn, you will be easy to exploit.

This leads us to the last topic of this article, namely board coverage. What I mean by board coverage is closely related to balance, but has the specific meaning of hitting flops - or other later streets - that might not be expected by your opponent (or conversely, make it hard for him to make exact estimations about which flops you hit).

Let's say you play AK, AA, KK and QQ a certain way preflop. If this can be recognized by a skilled opponent and the flop comes 589 rainbow, you opponent might easily take the pot away from you with nothing. But what if you decide to play for instance some percentage of 76s and some percentage of T9s the same way you play aces from UTG pre-flop? The exact profitability is hard to compute, but for sure you have made yourself harder to play against post-flop.

It should be noted that taking the board coverage so far as to mainly play hands for their ability to make surprising hits on the flop, is highly unlikely to be profitable. The best way to make money at poker is still to get chips in good, meaning you have a better range than your opponent. But mixing in some hands with decent equity is almost certainly better than playing 100% ABC and nitty. An important part of this is also to get paid off when value betting. You could almost just as well hold a T9s for the busted straight draw as your AA overpair, right?

Similarly, you may hear people talking about "balancing their check-back range on the flop". Same thing here: If your opponent know that if you check back flop, you never beat top pair, then you have a problem. Thus you should take some combinations, or some frequency with some hands, to check back. Top set is actually a decent check-back on some dry flops (as it blocks top pair very hard and is not so concerned with protection, the argument against is that it really wants to build a large pot - so this applies mostly when not extremely deep-stacked), as can weak top pairs be. Also, if you decide to check-raise sometimes as a bluff, you need to do the same with some value to avoid being too predictable.

Practically, if you decide to check back top set half - or some other percentage - of the time, you can do that based on suits of the cards you hold or simply by using a watch - for instance the tournament clock looking up "to check the current blinds" - and using the seconds to determine the action.

I realize this short article clearly can not teach you about balance in any complete or maybe even meaningful way by itself. I do hope it inspired further learning and research, though - a good next step can be the two Play Optimal Poker books by Andrew Brokos (as mentioned in the previous article, my name is in fact in the acknowledgements-section in POP2, after having found a couple of small "bugs" in an early edition!).

This actually completes the small 7-part series on poker math - boldly nicknamed "gems". As I mentioned in the intro, I might come back with some more advanced topics later - skill and time permitting. Shout out if there is something that you would like to see here, and I'll do my best. I do plan to write a small piece with some book recommendations as well, so stay tuned.

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