This data is based on a simulation of 100,000 hold'em poker deals with 5 players, with a cap of one pot-sized raise per round (to allow a large number of hands to complete in 8 hours). Although the player strategies were probably far from optimal, I believe that the play frequencies computed at the end of 100,000 deals are probably fairly accurate.
19% of deals are decided preflop.
32% of deals are decided on the flop.
18% of deals are decided on the turn.
31% of deals are decided on the river.
On the flop, 47% of deals are heads-up, 27% are 3-way, 6% are 4-way, and 1% are 5-way.
On the turn, 38% of deals are heads-up, 9% are 3-way, 2% are 4-way, and 0% are 5-way.
On the river, 24% of deals are heads-up, 6% are 3-way, 1% are 4-way, and 0% are 5-way.
Since 100% of deals are multi-way preflop, it's important to know preflop play cold.
The next most common situations are a heads-up flop (47%), a heads-up turn (38%), a 3-way flop (27%), a heads-up river (24%), a 3-way turn (9%), a 3-way river and a 4-way flop (6%).
In other words, improve your heads-up flop/turn play before worrying about 3-way play, and 4-way play ought to be very rare.
Thursday, July 30, 2015
Dave Computes a System for Evaluating Flops in Hold'em Poker
Here is a simple but effective system for giving a rough estimate of how good your Hold'em poker hand is on the flop. We'll group hands by how likely they are to win a showdown in a heads-up game. A hand that scores a 9 should win a heads-up showdown 90-100% of the time. A hand that scores an 8 should win a heads-up showdown 80 - 89% of the time, and so on. When a pair is made, this system awards more points for higher pairs--regardless of the presence of overcards in the flop or the strength of kickers. This surprising aspect of the system is nonetheless consistent with probabilities of winning a hand, as determined empirically. Of course, overcards and kickers do matter, but they don't often move a hand out from winning 75% of the time (say) to winning 65% or 85% of the time.
The Flop Scoring System
+9 for trips
The Flop Scoring System
+9 for trips
+8 points for KK
+7 points for 99
+6 points for 66
+5 points for 22, 4-flush, open-ended straight, A on a paired flop
+4 high cards, gutshot
-1 for single-suit flop with no flush draw
-1 for no-gap (e.g. 987) or one-gap (e.g. 976) with no straight draw
9-Point Hands
These are made hands, like A5 with a flop of 432. Most 9-point hands are trips, like 33 with a flop of K73, or 52 with a flop of 554.
8-Point Hands
J6 with a flop of JT6 scores 8 points for making 2 pairs. AA with a flop of KT7 scores 8 for making a pair of aces, as does A2 with a flop of AQK (despite the weak kicker and threatening board). So does K4 with a flop of K53 for making a pair of kings.
7-Point Hands
Q5 with a flop of QTT scores 7 for making a pair of queens (no credit awarded for making 2-pair on a paired board). Likewise, J6 with a flop of AJ5 scores 7 for making a pair of jacks.
6-Point Hands
83 with a flop of A82 scores 7, as does 77 with a flop of 954.
5-Point Hands
54 with a flop of QT5 scores 5, as does J3 with a flop of 763. Jc8h with a flop of Qh9h5h scores 5 for a 4-flush. Likewise, KT with a flop of QJ4 scores 5 for an open-ended straight. A5 with a flop of KK4 scores 5 for holding an ace on a paired flop. Th6h with a flop of Ks6s3s scores 5 points: 6 for a pair of sixes and -1 for a single-suit flop. Likewise, Q6 with a flop of 764 scores 5 points: 6 for a pair of sixes and -1 for a single-gap flop.
4-Point Hands
J2 with a flop of 432 scores 4 points: 5 for a pair of twos and -1 for a no-gap flop. Nearly any other vaguely playable hand scores 4 points. These are generally hands with an ace or a couple of high cards, like KJ with a flop of Q32, or A2 with a flop of 974. Gutshots also score 4 points, like T4 with a flop of KQ9.
4-and-Lower
4-point hands are generally worthless. These are hands you hope will improve for free, but you should probably not invest any money in them (even as bluffs). Because of this, there's no sense in developing a rule to distinguish 4-point hands from 3-point hands. The very worst hands score 1 point. (All hands have at least a 10% chance on the flop of winning a heads-up showdown.) 1-point and 2-point hands have virtually no possibility of improving. These hands are probably worth a single bluff given the right circumstances, but should otherwise be discarded.
Turn Scores
Regarding the dream of a scoring system for turn and river holdings, turn evaluation is very subtle. It appears to depend about equally on both the strength of the hand you made and the number of single cards that an opponent could hold that would beat your hand. Maybe the best way to evaluate the turn is simply to start with your flop score and then decide whether the turn card itself ought to bump the value of your hand up or down. A formula would certainly be welcome, as evaluating your hand at the turn is quite critical.
River Scores
Evaluating at the river is probably less critical, as few hands ought to reach the river, and you can usually tell whether you made your hand or not and whether your opponent is likely to have made a better hand. The single most important aspect of evaluating a hand at the river is the number of single cards that your opponent might hold that would beat your hand.
+7 points for 99
+6 points for 66
+5 points for 22, 4-flush, open-ended straight, A on a paired flop
+4 high cards, gutshot
-1 for single-suit flop with no flush draw
-1 for no-gap (e.g. 987) or one-gap (e.g. 976) with no straight draw
9-Point Hands
These are made hands, like A5 with a flop of 432. Most 9-point hands are trips, like 33 with a flop of K73, or 52 with a flop of 554.
8-Point Hands
J6 with a flop of JT6 scores 8 points for making 2 pairs. AA with a flop of KT7 scores 8 for making a pair of aces, as does A2 with a flop of AQK (despite the weak kicker and threatening board). So does K4 with a flop of K53 for making a pair of kings.
7-Point Hands
Q5 with a flop of QTT scores 7 for making a pair of queens (no credit awarded for making 2-pair on a paired board). Likewise, J6 with a flop of AJ5 scores 7 for making a pair of jacks.
6-Point Hands
83 with a flop of A82 scores 7, as does 77 with a flop of 954.
5-Point Hands
54 with a flop of QT5 scores 5, as does J3 with a flop of 763. Jc8h with a flop of Qh9h5h scores 5 for a 4-flush. Likewise, KT with a flop of QJ4 scores 5 for an open-ended straight. A5 with a flop of KK4 scores 5 for holding an ace on a paired flop. Th6h with a flop of Ks6s3s scores 5 points: 6 for a pair of sixes and -1 for a single-suit flop. Likewise, Q6 with a flop of 764 scores 5 points: 6 for a pair of sixes and -1 for a single-gap flop.
4-Point Hands
J2 with a flop of 432 scores 4 points: 5 for a pair of twos and -1 for a no-gap flop. Nearly any other vaguely playable hand scores 4 points. These are generally hands with an ace or a couple of high cards, like KJ with a flop of Q32, or A2 with a flop of 974. Gutshots also score 4 points, like T4 with a flop of KQ9.
4-and-Lower
4-point hands are generally worthless. These are hands you hope will improve for free, but you should probably not invest any money in them (even as bluffs). Because of this, there's no sense in developing a rule to distinguish 4-point hands from 3-point hands. The very worst hands score 1 point. (All hands have at least a 10% chance on the flop of winning a heads-up showdown.) 1-point and 2-point hands have virtually no possibility of improving. These hands are probably worth a single bluff given the right circumstances, but should otherwise be discarded.
Turn Scores
Regarding the dream of a scoring system for turn and river holdings, turn evaluation is very subtle. It appears to depend about equally on both the strength of the hand you made and the number of single cards that an opponent could hold that would beat your hand. Maybe the best way to evaluate the turn is simply to start with your flop score and then decide whether the turn card itself ought to bump the value of your hand up or down. A formula would certainly be welcome, as evaluating your hand at the turn is quite critical.
River Scores
Evaluating at the river is probably less critical, as few hands ought to reach the river, and you can usually tell whether you made your hand or not and whether your opponent is likely to have made a better hand. The single most important aspect of evaluating a hand at the river is the number of single cards that your opponent might hold that would beat your hand.
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