How to think about hand ranges for beginners (long)
Disclaimed: I'm a noob and this thing could be based on critical misunderstandings, but I think it's sound.
Warning. This post is extremely long and ALSO extremely simplified. It provides a possible way to start constructing study exercises for beginners who are not used to this sort of studying. It outlines the method by which this process is carried out and does not pretend to constitute a fully valid example (especially as many complexities are ignored and the opponent is a super exploitable caricature)
This could be said to be a companion piece to Robb's excellent range practice post - just starting at an even lower level of understanding and holding more hands.
Ok, what is a hand range? A hand range is the total pocket holdings with which a given action is pursued.
The interesting thing about hand ranges is that it instantly changes the focus from the cards you are actually holding to the situation as a whole including the tendencies of your opponents and the lines taken in a hand. The hand range is the result of analysing the situation. The actual hand is almost incidental.
In this post I will endeavour to outline a map of one line taken in a hand against a caricature opponent.
First, let us establish the situation. The hero is playing 6max 2nl, for this hand is sitting on the button with the action folded to him and the small blind is a set miner and the big blind is a semi-loose calling station. I will explain both of these in some detail. Stacks are 100bb.
Caricature opponent 1: Set miner. Plays AA-22, AK, AQs only. Raises all hands first in every time. 3bets, 4bets and 5bet shoves AA only and every time. Bets (regardless of whether he raised) every flop which is A or K high (as a bluff when necessary) and every time he hits a set, TPTK, TPGK and overpairs. Shuts down all bluffs past the flop and stacks off with all sets, TPTK, TPGK and overpairs TT+. Will bet, bet, bet with sets and overpairs TT+. Bets overpairs 99-, TPGK and TPTK for two streets only (flop and river). Will call 3 streets with TPTK and TPGK, but not overpairs 99- (they call 2). Will raise with any hand that will bet (on that street) and call with any hand that will fold if facing a bet that is below 1/2 pot. Will call betting hands and fold folding hands if bet is 1/2 pot or above and additionally raise river if not already all-in (and holding set or TT+ overpair.) Not situationally aware at all. Not board texture aware at all. Never bluffs outside of cbetting.
Caricature opponent 2: Calling station. Never raises preflop. Limps and calls PFR with all pocket pairs, any ace, any suited K, Q, J and T and any hand were the lowest card is 9 or higher. (40.9%) . For bets below 2/3 PSB will call 3 streets with second pair or better. Will call 2 streets with any pair and any 6+ out draw. Will call 1 street with A-high and any draw. For bets above 2/3 PSB will call 3 streets with top pair or better, 2 streets with second pair and any 10+ out draw and 1 street with A-high and any 6+ out draw. Bets any 2 pair and better. Never bluffs.
Ok, situation again. Hero on BTN folded to him, SB is a set miner (caricature above) and BB is a calling station (caricature above). Due to their extremely caricaturish playing tendencies you could well argue that you are +EV to raise ATC because these two can be outplayed after any flop. For the sake of this post we will assume we don't know the opponents as well as described above, but only has a decent idea what their stats are and as a result conclude that we cannot open ATC for a steal but need to confine ourselves to around 40% of hands.
These 40% are our preflop opening hand range, and the way to play hand ranges is to first determine what our hand range is for taking a certain action, and then determine if our current holding fits inside that range.
Our BNT opening range against specifically these two blinds, assuming a good image:
22+,A2s+,K9s+,Q9s+,J8s+,T7s+,96s+,85s+,74s+,64s+,5 3s+,42s+,32s,A2o+,KTo+,QTo+,J9o+,T8o+,98o,87o,76o
Now, how much should we bet? In this situation I'd like to argue that we should bet 5bb. None of the opponents defend by 3betting and both are extremely predictable post-flop. This means any money that goes in after the flop will be sized relative to the pot and we will basically only put in money after the flop when we are pretty certain that we win. With the set miner he should fold way too much so we can just steal the pot. With the calling station we'll only put money in when we are ahead of his calling range. The assumption is that they will react preflop to a 3bb, 4bb and 5bb raise the same - with the same range of hands.
Action to this point ($2 effective stacks - 100bb):
Pre-flop: Fold to BTN. BTN raises to $0.10. SB calls, BB folds.
Flop: Pot is $0.22.
Time for the flop? No, why rush it. Remind yourself of the SBs playing tendencies and imagine which flops he hits hard.
Set miner PF calling range: KK-22, AK, AQs (92 hand combinations)
For the sake of simplicity I will overlook flush, straight and full house options throughout this hand. I am looking to make sets, pairs, two pair and ace-high only.
A-high: A blocker eliminates 4 AK and 1 AQ hand combination. 2 other blockers eliminates 3 pair combos each. 11 combos lost, 81 remaining. 15 combos TPTK, TPGK (bet/call, check/call, bet/call), 6 combos sets (bet/call, bet/call, bet/call), 60 combos of others (bet/fold, check/fold (unimproved).
K-high: K blocker eliminates 4 AK and all cards block 3 pocket pair combos each for 13 combos lost and 79 remaining. 12 combos TPTK (b/c, c/c, b/c), 9 combos sets (b/c *3). 58 others (b/f, c/f unimproved)
Q-high: 1 AQ eliminated. 9 pocket pairs eliminated. 82 remaining. 6 overpairs (b/c *3), 9 sets (b/c * 3), 3 TPTK (b/c, c/c, b/c), 64 others (c/f*3 unimproved)
J-high: 9 pocket pairs eliminated, 83 remaining. 12 overpairs (b/c *3), 9 sets (b/c *3), 62 others (c/f *3 unimproved)
T-high: 9 pocket pairs eliminated, 83 remaining. 18 overpairs (b/c *3), 9 sets (b/c *3), 56 others (c/f *3 unimproved)
9-high: 9 pocket pairs eliminated, 83 remaining. 24 overpairs (b/c *3), 9 sets (b/c *3), 50 others (c/f *3 unimproved)
8-high: 9 pocket pairs eliminated, 83 remaining. 24 overpairs TT+ (b/c *3), 6 overpairs 99- (b/c, c/c, b/c) 9 sets (b/c *3), 44 others (c/f *3 unimproved)
7-high: 9 pocket pairs eliminated, 83 remaining. 24 overpairs TT+ (b/c *3), 12 overpairs 99- (b/c, c/c, b/c) 9 sets (b/c *3), 38 others (c/f *3 unimproved)
It's interesting to note that flops with only low cards actually hits a narrow range pretty well. Going through these possible flops should give us an idea what kinds of lines it is profitable to take against this opponent - when is it profitable to call a bet with the intent of bluffing on a later street, when is it profitable to bet or raise as a bluff, and how strong a hand we need to have (or be drawing to) for us to commit money for straight value.
A thing that is immediately obvious is that if the opponent checks to us we can bet ATC any small amount and take down the pot every time. While in reality there may be occasionally slowplayed monsters and sets checked that will still be fundamentally true.
Ok, let's have a flop. Going with a super dry one.
Action to this point ($2 effective stacks - 100bb):
Pre-flop: Fold to BTN. BTN raises to $0.10. SB calls, BB folds.
Flop: Pot is $0.22. Board is K:c: 8:h: 3:d:. SB bets $0.20.
Ok, we now have a wealth of information that we can start reading things into.
1) We know the flop
2) We know our opponent tendencies
3) We know the line taken by the opponent
We know that the line taken by our opponent is taken by every single hand in our opponents range. We also know that 58 of 79 (73.4%) hand combinations taking this action are bluffing and will fold to a turn bet if they do not improve. Remember we likely have blockers for these hand combinations.
Let's consider the value realised when we call flop and bet turn 1/2 PSB when checked to and assume we have two blank cards in front of us (no showdown equity).
We call $0.20 79 times and bet $0.31 70 times. Total expenditure $37.5
We win $0.42 58 times. Total gain $24.36
This calculation really needs to be redone for each of our pocket holdings taking our blockers into account, but it is indicative that we need to extract value some other way than just betting the turn when checked to as that is not profitable as a pure bluff.
An alternative line we can take is to call flop, check behind turn and bet river if checked to a second time.
We call $0.20 79 times and bet $0.31 58 times. Total expenditure $33.78
We win $0.42 58 times. Total gain $24.36
Ok, so we assume a (single) bluff doesn't do the trick. Maybe we need to consider a different line - betting for value. We could call with hands that either have good current showdown equity against the b/f, c/f, c/f range or have decent draws to good equity and then bet them on turn or river or both just below 1/2 PSB so they are called and extract value.
Kx hands are obvious for this as they are ahead of all the pocket pairs that did not become sets already. Pairs down to 99 definitely also qualify. Below that it becomes a question of how often they bet and end up being up against a better pair. Probably 77 and a couple more pairs are also good, but they're more borderline. They could of course all become sets and stack off against AK (which will be easy if he checks the turn because then we know what he has) so even though they only have two outs the implied odds value of setting up should more than make up for the call, check behind, bet river (full 1/2 PSB as bluff to fold worse) line as outlined above itself being -EV.
Other candidates for this line are hands that can improve to beat the pocket pairs. Meaning high cards and pairs. AQ is an obvious example - if the opponent is holding AQ and hits the A or the Q he will bet the river and we can adjust as if he's holding AQ/AK. 98 is another good example. We have 5 outs to a two-pair hand that is likely to be best. AQ-A9 I would probably also accept.
In the real world proper draws and backdoor flush draws etc also qualify on this type of criteria, but I'm doing a limited analysis and not acknowledging those.
So, what I've tried to do above is to plan my hand. I've considered my opponents range, my range, the flop texture, the EV of certain obvious plays and I've decided on lines that I think will be profitable with certain types of hands. Now I'm going to properly populate these lines with hand ranges and THAT is how you think about hand ranges when you play.
Let's first define our continuation range:
AA-22, A3, A8+, K9s+, KTo+, J8s, T8, 98, 87, 86s, 85s, 53s, 43s, 32s
This is 23.7% of hands, so that's about 59% of our opening range. Defensively this feels like a good place to start.
In a normal hand we would be looking to split these out into ABCD ranges for every decision, but this simplistic case can probably handle the flop decision without. In terms of folding, that is already our D range. Our raising range here there are two reasons we can probably do without. One is that implied odds are granted to us on TPTK hands that are willing to call any bet on any street to get all in if we think we can beat TPTK and we're assuming even min-raises will see folds from all bluffs. This makes raising for value unnecessary. The other is that raising the flop as a bluff is less profitable than just waiting for the next street and the opponent to tell us what he has through his actions. Even if a min-raise gets full folds from the bluffing handseEffectively we would be putting $0.11 less at risk 58 times where it has zero impact on our EV, 12 times when we lose $0.11 less by it and 9 times where we lose $0.20 more by it.
So for this flop we have already defined our fold range, we do not need a raising range and the calling range will be split based on what card comes and what happens on the turn. So that will be ABCD ranges for the turn only and on.
Action to this point ($2 effective stacks - 100bb):
Pre-flop: Fold to BTN. BTN raises to $0.10. SB calls, BB folds.
Flop: Pot is $0.22. Board is K:c: 8:h: 3:d:. SB bets $0.20. BTN calls.
Turn: Pot is $0.62. Board is K:c: 8:h: 3:d: T:s:. SB checks
Ts is a blocker for TT in the opponents range. That eliminates 3 hand combos leaving the opponent with 76 hand combos in his range. Check is done by all hands except sets. Sets are now 12 combos (KK/TT/88/33), 12 combos are the checked AK and 52 combos are other stuff.
SB Turn check range: AK, QQ, JJ, 99, 77-44, 22, AQs
Ok, now it's time to implement our plan and define for each of the hands in our range which line they are following to maximise the EV of our hand range. I'm going to label my lines with letters and it might not follow the basic ABCD outline that Renton presented, but it's a similar principle.
A: Pure value range contains AA, KK, TT, 88, 33, KT, T8, AK. Turn bet $0.30. If called, plan to bet river $0.60. If raised that means AK 100% of the time so that is a turn shove. AK splits.
B: Secondary value range is KQ, KJ, K9s, QQ, JJ. Turn bet $0.30. If raised, fold.
C: Betting to improve (with outs): AQ, AJ, AT, A8, A3, J8s, 98, 87, 86s, 85s, 53s, 43s, 32s
D: 99, 77-44, 33, Ax checks behind.
Action to this point ($2 effective stacks - 100bb):
Pre-flop: Fold to BTN. BTN raises to $0.10. SB calls, BB folds.
Flop: Pot is $0.22. Board is K:c: 8:h: 3:d:. SB bets $0.20. BTN calls.
Turn: Pot is $0.62. Board is K:c: 8:h: 3:d: T:s:. SB checks. BTN bets $0.30. SB calls
River: Pot is $1.22. Board is K:c: 8:h: 3:d: T:s: 2:s:. SB checks.
AK is no longer possible due to the turn call. 3 combos of 22 are eliminated by the river card. 3 combos of 22 are eliminated by the river check.
SB river check range: QQ, JJ, 99, 77-44, AQs
Since my caricature says that he folds to any 1/2 PSB any of our hands can now be turned into a bluff if it is not more profitable to be called by this range. EV of betting any hand $0.61 is +$1.22 because we win the full pot 100% of the time. Our alternative is to bet $0.60 to win $1.82. So any hand that has more than 1.82/2.42 (75.2%) equity against the opponents hand range should bet $0.60 instead.
A: Betting $0.30 for value: AA, KK, TT, 88, 33, KT, T8, AK, KQ, KJ, K9s, QQ, JJ, 32s
B: Bettng $0.31 as a bluff: AQ, AJ, AT, A8, A3, J8s, 98, 87, 86s, 85s, 53s, 43s
Ok, the end? The point of this post is to get me (and you) thinking more and more correctly about hand ranges. A situation is analysed, different lines are considered and types of hands are considered for those lines with rough estimates done to assess their relative profitability. Then a decision is made with regards to which lines are profitable - these lines are populated, then balanced and then and only then do we check our pocket holding.
This sounds awfully complex if you're not used to doing it, but it's important to keep doing these kinds of exercises so the brain gets better and more efficient at it - this is the real skill that I think I need to put into my head. The ability to juggle hand ranges and assess factors and form reasonable hand ranges for myself. And doing it in the head in a very short period of time.
When you go the full ring, 6 max, heads up or high stakes forum and read hand histories and someone mentions that he never takes that line in the situation or plays this hand for balance or something else - more often than not this person will have a whole map of a hand as outlined in this post in his head and it's based on that that he is making his observations. This map of a hand with hand ranges and lines is absolutely crucial for any deep understanding of poker. Best get practicing putting these things in the head imo.
For a simpler way of starting this exercise - start posting hand histories without showing your own cards.
Another simple way of doing this is to take any part of this example and tweaking it. Change opponent tendencies so he calls less then 1/2 PSB with missed cards first time and only less than 1/3 PSB the second time. Change it so he only calls second pair or better, or calls different bet sizes with different types of hands. Change the lines actually taken in the hand and fully populate the tree that the hand then becomes with all its branches. Change opponent type from one caricature to another. Define your own opponent types (simplied or complex) and try to analyse hands against them. Ultimately you want to be doing this with real opponents, but for practicing the technique it may be easier to work with caricatures.
