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 Anatomy of a Poker Hand
Ok, so in another line of needlessly long posts I'm submitting my notes from todays poker study/meditation session.
1. Introduction
In this text I map out a poker hand in a way that is conducive to and indeed the requirement for any serious analysis. The content is simply a reflection on how to implement Renton’s ABCD Theorem. I noticed on 2+2 someone called RedJoker explaining randomization by hand equity, which is exactly the same concept. I explain some things that may have gone assumed and try to structure it in a way that I think gives a well rounded tour of the whole thing and how it can be used.
2. Situational thinking and hand strategy
I think the term situation is central to thinking about poker. A hand flows through decisions and actions and when you freeze this flow at one point and consider the hand in more detail you are looking at a situation. A situation is defined by everything you know about your opponents and the actions taken. An incomplete list of what defines a situation is this:
- o The stack sizes of the people involved in the hand and the positional setup
[list:1c9453b60a]o This dictates which strategy is optimal to play and starting hand values my go up or down accordingly
o The playing tendencies of the people involved in the hand
- o This tells us which actions they take with which parts of their hand range.
o This includes knowledge of whether they are playing a profitable strategy or an exploitable strategy etc.
o This includes bet/raises sizes when they bet, whether the opponent understands relative hand strength, position etc.
o The actions in the hand to this point
- o This combined with the playing tendencies allows us to narrow down the hand range of each player
o The board
- o This needs to be considered along with the playing tendencies of the players in the hand (do they bet when they miss or hit or have draws and how much in each situation) and the actions in the hand to this point. It also acts as blockers to parts of hand ranges.
[/list:u:1c9453b60a]This may all seem very obvious, but the salient point is that when coming to it cold people tend to get hung up in unimportant details, such as what cards they’ve been dealt and whether or not they hit the flop. From a strategic, holistic and EV point of view this is not particularly important. Or to be specific it’s not important whether our actual hand is in our A, B, C or D range – what’s important is whether we have put together our A, B, C and D ranges intelligently.
We have a situation defined very often when someone posts a hand. We started with this many chips. Then this happened, followed by that. Now what? The ideal description of a situation will include reads, history – both long term and recent, game flow etc. Typically stacks, bet sizes and actions are a minimum for any meaningful examination of a situation, but there is no reason to stop there.
As in so many cases the better we describe the problem, the more obvious the solution becomes. If we in our description make sure to include all the relevant factors needed to arrive at the right conclusion, actually getting to the right conclusion will suddenly seem a pathetically small step.
We can then go iteratively over all the component parts of the situation and investigate each for obvious strategic flaws that can be exploited in this situation. Based on this and falling back on what is game theory optimal we then define A, B, C and D ranges along with appropriate bet sizes for the betting/raising parts of the range. Then we test our ABCD ranges for exploitability – are we folding too often are we spewing too often – and we make appropriate adjustments to our ranges. Maybe we find that we are too easy to read and tipping off our hand strength too heavily and with observant opponents we can make adjustments for that too. Finally with a set of ABCD ranges defined we see in which part of the range our actual hand falls and take the action associated with that hand range.
The key here is that we’re not looking for our play with our current holding to be maximum EV – we are looking for our strategy for this situation to have the highest possible EV, and then for our current hand it’s just a question of following what we have defined as our best strategy.
Similarly when we read our opponent as having the nuts 50% of the time and a bluff (that we beat) 50% of the time, we call and he shows the nuts – we didn’t misread him. We just ran into that part of his range. It’s tempting based on situations like this to second-guess our read, and there’s nothing wrong with that – if we do it analytically. We cannot emotionally decide that our reads are off and we have to disregard them – then we stop playing poker and start gambling. If we genuinely doubt our read we need to sit down, work through the hand ranges, find out if there are enough believable bluffs in his range given the action and maybe end up concluding that in this case there actually was a much smaller bluff chance – or a much bigger bluff chance – and take that information into account next time we run into a similar situation against that opponent.
3. Solitaire poker
This section describes a solitaire version of 6-handed no limit texas hold’em and leads into discussion of hand analysis. It’s pretty simple to see how the same principles can be used to create a solitaire version of any other game. I am presenting here the random form of the game. The game simulates a heads up situation after the flop. The only real value in using this game rather than any hand posted on the forums is that you’re not confused by an actual holding.
Game pieces: 1 die, 1 deck of cards
Setup:
- o Optionally decide player profiles and stack sizes – alternately go on assumptions (both players play like me, 100bb stacks)
How to play the game:
- o Randomly determine the full set of actions for the hand. Note down the full set of actions for analysis.
[list:1c9453b60a]o Define SB as position 1, BTN as position 6, roll a die for each of the players to find their position.
o Imagine play of hand – action is on the first player. Roll the die. 1: He limps. 2-6: He raises
o Action is on the second player. Roll the die. 1-5: He calls. 6: He 3bets.
o If 3bet continue in same vein until pre-flop is resolved. Alternately decide that you want to examine a raised pot, or a 3bet pot, or a 4bet pot etc and just decide on the pre-flop action.
o Shuffle the deck, deal a flop.
o Randomly determine the actions for the flop in a similar way to pre-flop – though maybe not using 1 in 6 for each type of action. A standard bet size of 2/3 PSB can be used for simplicity.
o Repeat for turn and river
[/list:u:1c9453b60a]This gives you a map for a hand. Now for each player, define some rough ABCD ranges at every step (including defining the ranges for the actions they didn’t end up taking). Do this based on gut instinct or what you consider standard for the situation without too much initial reflection. I’m not saying don’t reflect on it – the whole rest of this and the majority of your time should be reflection – I merely want to encourage being true to decisions you might take if you were in the hand.
Assume that both players know the exact ranges the opponent is playing and want to play the optimal counterstrategy to the opponent. The initial opener doesn’t know who he ends up in a hand with, so we assume he opens a range that is standard for him based on his stack size and position. Now we interrogate that range. Categorise the different parts of the range and determine the proportions of it. Is it a narrow range heavy with pocket pairs, a wide range heavy with suited connectors, a wide range heavy with high cards? Do not simply describe it verbally but for each hand in the range define what kinds of flops it wants to hit and what kinds of flops it wants to continue on. One simplified example could be: 24 combinations JJ+ - hit over pair or set and continue for value. 54 combinations 22-TT – set it or forget it. 40 combinations AK, AQ, AJs, KQs – hit TPTK, or TPGK and continue for value. 36 combinations Axs – hit flush draw and get all in, hit top pair and pot control, try to steal with a backdoor flush draw and an over card. 28 combinations QJs-65s – flop big or fold.
Go through the same process for the other player. This time make sure that he is playing hands that he expect will be profitable to play against the opponents opening range taking into account whether this player will be in position or out of position. Make sure for each hand in their ranges that you understand at least one reason for thinking they might find +EV situations in which to play the hand.
Once the flop comes this is a large amount of information to incorporate. First go back to the hand ranges and eliminate all the hands that you now have blockers for. Then characterise for each hand what it has now become. AA on a Q72r flop is an over pair on a dry board for instance. 8s7s on a board of JsTc2s is a gut-shot non-nut flush draw with 12 outs, possibly discounted. KcQc on a board of Th5d2c is two over cards with back door flush and straight draws. Having done this, assign each hand to an A, B, C or D range and then look critically at it. Ok, so we continue with our sets and over pairs – fair enough. Does that mean we are looking to fold 80+% of our hand range? Does that make us easy to bluff off our hand? Are we realistically betting (cbetting) 80+% of our hand range here, and does that mean that anyone can simply raise us with any two cards for profit when we fold the weak part of our range? Count the combinations for each part of the range, compare it to the total combinations we arrive on the street with and consider if there is a simple counter-strategy to how we arrive here that is +EV for our opponent. In other words – are we exploitable?
To continue with the example of folding 80+% of our hand combinations to a bluff (like a cbet) there are two main avenues we need to consider. First we need to consider if we simply played too many hands pre-flop. Are we continuing pre-flop with hands that simply don’t flop that well so when, as in this case, they don’t flop well we end up having to fold them? Second, are there any hands we initially wanted to discard that we have to promote to a playable hand simply to prevent us being too bluffable? Note that if we follow the second principle a typical sequence of events could be that we promote some weak top pair hands from our B range to our A range, some 8+out draws from our C range to our B range and some 4-7 out draws from our D (fold) to our C (semi-bluff) range. Be especially aware of backdoor flush draws. A backdoor flush draw means you need to hit both one out of 10/47 and one out of 9/46. If we assume that both flush cards are good (not discounted, not making full houses etc) a backdoor flush draw on the flop is worth 1.9 outs twice. By comparison backdoor straight draws are often closer to 1 out. Remember over cards are sometimes outs.
Once we’ve gone through that level of analysis we can break out PokerStove for some more fun. For each of our ranges we run a stove analysis against the likely opponent ranges. We then weight the equity according to how many hand combinations we have in each part of the range and try to reality check if we are establishing an equity edge or we are playing so loosely that we are going to be –EV. Remember to consider fold equity and implied odds (as well as reverse implied odds).
Of course we end up doing the same analysis for each decision on each street up to and including value betting the river. One interesting thing to consider is if we on the flop continue with a large proportion of drawing hands where that may make us have an exploitable range on the turn if the draw doesn’t come in – similar if we have a range with a low proportion of drawing hands where we are exploitable on any flush card completing three to a flush on the turn.
These are just the first few basic ideas off the top of my head of what we can analyse when we use this tool, but I think there are many more perspectives to take and leaks to identify and fix through such analyses. I think this kind of approach is the key to developing a winning strategy – now having described it I of course need to spend hundreds of hours working through actual hand examples. To hark back towards the beginning of this text I’d like to reiterate that we find ourselves in a situation and the important thing in any poker situation is to have a strategy for this situation (or kind of situation) that is solidly based on an analysis as outlined here that we can assert with confidence is +EV. The only important thing about our hand is for us not to misplay it according to our profitable strategy.
4. Links
Renton’s ABCD theorem: http://www.flopturnriver.com/phpBB2/...em-t70711.html
I think this was linked in an operation post that I can no longer find. Here’s another way of saying the same thing that I call having a profitable strategy for the situation – it also encourages us not to get too caught up in the actual cards we hold: http://blogs.cardrunners.com/interne...ore-1232943829
5. Cliff's Notes
Even acknowledging your cards is results oriented. You need a strategy that works for the full range of possible hands. The actual hand is incidental.
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