How to extract max value from a poker hand was a question that was presented to me by a stranger who was aware of my unusual poker vocation. Considering me an insightful, and furthermore a winning poker player, he came to me with a broad inquiry – How do I get the most value from my poker hands? Fortunately enough for me, which such an expansive question, I had a bit of time to think resourcefully seeing as though this conversation began on Skype. But even after pausing, I still couldn’t present an encompassing response that I felt would satisfy his question. I ended up telling him “it’s too opponent and hand-dependent,” and although it may be, I still felt disappointed by my vague poker advice.
Hopefully being able to write about this topic in more totality will cure my conscious of the mediocre answer I gave. But even if it doesn’t, I still think that it’s worth getting into, because even experienced poker players should revisit the criteria behind making the highest EV play – or, in other words – extracting maximum value.
My buddy gave me a situation from a local live casino poker game in which he had lead out on the first two streets with a set, only to be confronted with both straight and flush completions by the river. This was against a tight-ish regular poker player. While he didn’t have too much information on the villain, I explained that after seeing the river, unless you’re certain your opponent will call with a worse hand than yours (which was nearly implausible), you can’t expect to bet this river and make a profit consistently. To look at very general math – you’d need to be sure after calculating your bet size, pot size, and how many hand combos you beat, that betting the river would make more money than checking in this spot. While I’ll attempt to get into more mathematical detail when making the highest +EV play during a poker hand, I initially just want to relay the message that these are the things your should be thinking about when trying to get the most value.
Example of How to Extract Max Value From a Poker Hand
$2/$4 No-Limit Hold’em, 6-max, online. The game has been particularly aggressive, and you have stats on each poker player seeing as though you’re playing with a HUD, and you’ve encountered them multiple times. You consider most players to be at least level 1 thinkers, if not greater.
You’re at the river with A5dd on a board of T942A. Can you value bet here? And if so what do you bet to get the MOST value?
Well the first question you may ask yourself about how to extract the max value from a poker hand is, “where is the rest of the information?” Well, I’m glad that came to mind. (Hopefully.) Whenever you’re considering extracting value, you should incorporate all information available. What was your stack size? What was your opponent’s stack size? What were the pre-flop positions of both you and your opponent? Who raised pre-flop and to how much? What’s the general dynamic of the poker game? What notes do you have on this player? What notes or reads does he have on you? Does he view you as tight? Passive? Loose? Aggressive? Ultimately, I could go on and on about the ideas that should enter your mind. But it’s more essential to understand the plethora of information available to make this decision.
Let’s go back now.
$2/$4 No-Limit Hold’em. You have A5dd on a board of 2742A. This online poker session after about 200 hands, the players at the table have viewed you as loose, despite your overall HUD statistics depicting otherwise. The one hand you’ve shown down thus far was a turned two pair, after calling an UTG raise in position. You’re normally much tighter than this, playing VPIP and PFR numbers of 18/14. You’ve noticed, however, after considerable play, that the rest of the table is just as tight and aggressive, if not tighter than you. So you’ve planned to adjust by playing much looser to provoke mistakes.
The villain you’re involved with opened the button for $12 while you’re in the big blind, and you three-bet to $40. He started the hand with $800. You started with $900. He’s playing 12/10, in most opinions absurdly nitty for a small to mid-stakes regular. Although he should be focused on adjusting to your loosened poker starting hand requirements, light 3-betting ranges may not be his focus at the moment seeing as though he’s mass multi-tabling. While he’s capable of being deceptive, most of the time, he’s on auto-pilot. Villain decided to call.
You lead for $50 into $82, and villain calls on a board of 274dd.
Turn – 2s.
You bet $135, he calls.
River – Ah.
Well let’s see our options here. The pot is $452, and the effective stack is $574. Because of the bet sizing, you couldn’t get your opponent pot-committed by the river. We could check, but in all likelihood if our opponent decides to bet can we call profitability? Maybe. But villain could also decide to check back with his hands of showdown value. Should we bet $300? Just shove? Hmm, let’s see actually.
This will take some time mathematically, so bare with me. Our opponent could hold a variety of things, but given this villain statistics we’ll estimate that it’s exclusively pocket pairs. Some of those pairs are obviously sets. We would guess that since this player is multi-tabling, he would normally 4-bet his premium pairs QQ-AA. So we will safely exclude those for now. (If he did show up with one of those hands, we would take a note.)
This leaves 22-JJ – or 60 hand combos – all of which are feasible given the stack sizes. However, 33, 55, and 66 should never get to this river card given the action, which will narrow our hand combos to 42. So let’s look at what our bets might bring given the narrowed range.
We bet $300:
Our opponent will put in $300 to win $752, or ~2.5-to-1. We can reasonably expect our opponent to fold 88, 99, TT, and JJ to a bet of this size fairly frequently. Our villain could choose to bluff-raise, but it would be for his whole stack, and we don’t believe that the villain would put his entire stack at risk with such an unconventional line. Because of the stack size, our bet-sizing, and the fact that our opponent would have to be correct in picking off our bluff 40% of the time to be profitable (optimistic), we’re in good shape against most of villain’s poker hand range. Those 4 hands equate to 24 hand combos of the total 42, or 57% of his range. The other 43% (22, 44, and 77) have obviously made quads or a full house, and we’re getting called or raised. So 57% of the time we bet $300, we’ll win $452. 43% of the time, we’ll lose $300. So let’s calculate our expected value.
($452 x .57) + (-$300 x .43) = ($257.64) + (-$129) = +$128.64!
So if we decided to bet $300 on this river, although we’d win $452 in this particular example, we would average a profit of $128.64 in this situation over time.
Now let’s examine a shove:
If we decide to go all-in on this river, although we probably still inspire a ton of folds, we lose a lot more when we’re beat. Surprisingly, this still remains a trivial river spot for our opponent, as all of their decisions will likely remain the same. So, our opponent only has $574 left on the river, which would be our effective all-in bet.
($452 x .57) + (-$574 x .43) = ($257.64) + (-$246.82) = +$10.82
So looking at the results of shoving the river, although we’ll continue to make money over time if our opponent folds, we tend to make less on average when he does call, making this $117.82 less profitable than just betting $300.
The key ingredient of these equations is to accurately estimate what our opponent will do in both situations. With our example, if our opponent reacts similarly regardless of bet size, we’re better off risking less money, since we’ll achieve the same outcome regardless.
So to extract the most money over time, we want to bet the minimum amount of money that maximizes our fold equity. If our villain makes an error by calling with a hand that he should be folding, our EV only looks to improve!
While the process can be complicated, it’s useful to look at everyday poker hands and see if you’ve made the highest +EV play possible – or maximized your value. It’s tough to implement at the table, but with enough side practice, you’ll be able to apply your new poker knowledge more frequently and know how to extract the max value from a poker hand.
Good luck, and hopefully I’ll see you at the tables.