Poker — pre flop hand evaluation
One of the first things that a beginner chess player learns is the value of the pieces: pawn = 1, knight = 3, bishop = 3, rook = 5 and queen = 9. This is so ingrained that it takes many hours of play to recognise that this is just a guideline. Sometimes it might make sense to, say, give up rook for knight (the exchange sacrifice) for purely positional reasons.
Similarly, the very first thing a bridge player learns is how to value their hand, with points credited for holding the ace and ‘picture’ cards, and for having a long suit. Opening conventions might require you to have a hand worth 15 to 17 points to open 1 no trump. Your partner will expect you to have 15 to 17 points, and be upset if you don’t …
Turning (finally) to poker - while there are opening range charts, players are not taught how to assign a value to their starting two cards and to make their pre flop actions based on the value of their hand. So here is a ranking algorithm developed by Steve Selbrede, for the game of Texas no limit holdem (TNLH).
Steps to place a value on your starting hand
In TNLH each player receives 2 cards from a standard deck.
- Assign a value of 2 to 10 to the hole cards 2 to 10. The picture cards jack, queen and king score 11, 12 and 13 respectively. The Ace earns 15 points; think of it that the Ace can be both high (14) and low (1).
- Take 2 times the higher card plus 1 times the lower card. Some examples: K7 scores 13 * 2 + 7 = 33; A9 scores 15 * 2 + 9 = 39; while 88 gets card value points of 8 * 2 + 8 = 24.
- Then assign bonus points for suitedness: if the hole cards are the same suit add 8 points.
- Assign bonus points for connectedness: if the cards could flop a straight in 4 ways, add 8 points. For example, 65 can flop a 9, 8, 7 or 6 high straight, so gets 4 * 2 = 8 points. If the cards can flop a straight in 3 ways, add 6 points, if 2 ways add 4 points, and if 1 way add 2 points. So for example, T6 can only flop the 10 high straight, so gets just 2 points. Note that the connectedness scoring normally just involves considering the size of the gap between the cards, but be careful in the case of low or high holdings. A3 is a 1-gapper so would ordinarily be worth 6 points; but only a wheel straight is possible on the flop (5,4,3,2,A), so A3 gets only 2 points for connectedness.
- Broadway bonus rule: if the hole cards are AK, AQ or KQ, round up step 4. to 8 points (i.e. these get 8 points in lieu of the connectedness bonus).
- Assign points for having a pocket pair: add 28 points. This sounds generous, but a pocket pair naturally gets no points for suitedness or connectedness.
This valuation system gives the following total scores.
Suited hands are in blue, pocket pairs in green and unsuited hands in orange. For example, AQs scores 15 * 2 (ace) + 12 (queen) + 8 (suited) + 8 (broadway bonus) = 58. Meanwhile 72o scores 7 * 2 (the 7) + 2 (2) = 16.
So what do we open?
Position is very important in TNLH, as play proceeds clockwise from the blinds round to the button on each of the 4 streets of play. Players in later position get to see what the earlier players do first.
The weighted average hand with this scoring has 32.6 points. If everyone has folded to you, then the button needs 36 points or more on the Selbrede scoring system to open. Add 2 points for each seat to the button’s right: 38, 40, 42 for the CO, HJ and LJ respectively in a 6-max game. Selbrede concluded this by comparing the result to a game theory optimal (GTO) solver output and also empirically, by looking at a database of millions of online games and determining the opening choices that maximised expected value. His recommendation is a compromise between simplicity and goodness of fit.
Importantly, the computer solvers and empirical evidence both show that raising (or folding) is always more profitable than ‘limping in’ for 1 big blind.
Comparing the Selbrede opening requirement in the Lojack seat (viz. 42 points or more) with a GTO raise first in range (RFI — per J Little) gives:
Hands labeled 0 are opened by neither range; 1s are opened by the GTO range only; 2s are opened in the Selbrede range only; 3s are opened in both ranges. Both ranges represent about 17% of possible starting hands. There’s a reasonable overlap.
Other preflop actions
In a 6 minute blog I won’t be able to cover all possibilities. For that you will need to read Steve Selbrede’s preflop GTO cash game strategy. But broadly speaking:
· As noted above, never open limp except in the small blind. Limping behind (i.e. after an earlier limper) is a lesser sin, but is still the less profitable play, except in the small blind. Never flat (i.e. call) an open, except from the button or the blinds. Generally it’s 3-bet or fold.
· You need a stronger hand to open raise when there have been limpers, but only by a point or two per limper. Also, add 1 BB per limper to your opening bet size.
· To 3-bet an open, add about 6 points to their perceived opening range. For example, the CO needs 38 points to open, so you need 44+ points to 3-bet them. If they’re loose players and would open with 30 points, however, you only need 36 points to 3-bet.
Will this evaluation system catch on?
I guess it depends on how many people buy Selbrede’s book! It has some interesting analysis in it, though would have benefited from a better proof-reader: the very first table showing the output of his scoring system for each starting hand has mistakes in it. I found it difficult to know what his baseline recommendation actually was in each situation.
My brief book review aside, I think explaining this scoring system to a new poker player would be much more useful to them than supplying a series of opening range charts, which are almost impossible to learn by rote. The new player immediately learns to appreciate the importance of high cards, suitedness, connectness and table position.
One could simplify the thresholds still further by instructing our beginner to count their points and just fold if they have less than 30. Only open in late position with 30 something points. Only open in early position with 40 something points, especially in a full ring game (i.e. 9 players). Facing 3-bets, or if the beginner wants to 3-bet themselves, they really need 50 something points. Basically, to play the game well they will learn to fold a lot.
The other issue is whether the 6 step process to calculating the hand score is too complicated for most people. I certainly don’t think it’s more complicated than bridge, though maybe that’s a bad example: it takes many hours to master even a basic convention system in that game.
After a bit of practice most people will be able to calculate the score of their hand in real time, before the action is on them. It’s only really required in marginal cases anyway; you don’t need to look down at KK and calculate that is worth 13 * 2 + 13 + 28 = 67 points, before deciding what to do!
I do suspect that it will be too much hassle for most recreational players. Players sitting down to play chess or bridge have steeled themselves to do a bit of thinking. Players sitting down to an evening of low stakes poker don’t want to do much mental arithmetic. If their hand is worth only 25 points, let’s say 65o: 6 * 2 + 5 + 8 (for connectedness) = 25, then they want to limp in with it anyway. They came to play not fold :)