Module 4 · Lesson 23 of 39 · Free
Suited connectors and broadway cards
Being suited adds less than most players think. Against a random hand 7♠ 6♠ has 45.4% equity and 7♠ 6♥ has 42.3%, only 3.1 points more. Across all 78 kinds of hands with two different ranks, being suited adds from 1.7 points (AK) to 3.7 points (32).
The hand
The same hand two ways: 7♠ 6♠, suited, or 7♠ 6♥, offsuit.
Predict first
By the river, how often does 7♠ 6♠ end with a flush?
- About one hand in 16
- About one hand in 5
- About one hand in 3
Show the answer
Answer: About one hand in 16
It needs three more spades among the five board cards: 135,597 of the 2,118,760 possible boards, 6.4%, about one in 16. Offsuit, 7♠ 6♥ needs four cards of one of its suits: 1.9%.
Working it out
Being suited buys flushes: 6.4% of boards against 1.9% offsuit. Being connected buys straights: a 7 and a 6 fit in four different straights, from 3-4-5-6-7 to 6-7-8-9-T, and by the river the board gives 7-6 a straight with at least one of its cards 9.0% of the time. Each gap between the cards loses one straight: 7-5 makes a straight 7.7% of the time, 7-4 5.9%, 7-3 4.2%, and 7-2, in no straight with both cards, 2.4%. Together, 7♠ 6♠ ends with a straight or a flush 14.7% of the time, about one deal in seven. Otherwise it usually ends with one pair or nothing, which is why it has only 45.4% against a random hand.
Broadway cards, ten to ace, work the other way: they win with high pairs. K♠ Q♦ has 61.5% against a random hand, 16.1 points more than 7♠ 6♠, but K and Q fit in only two straights and make one 4.8% of the time. Small suited connectors earn their money from rare big hands, so they need what set mining needs: cheap flops, deep stacks and position. Big cards earn theirs with top pairs, so they need care against raises that can dominate them.
Formula
Suited bonus = suited equity − offsuit equity: 45.4% − 42.3% = 3.1 points
Check your understanding
Against a random hand J♠ T♠ has 57.5% equity and J♠ T♦ has 55.2%. How many percentage points does being suited add?
Show the answer
Answer: 2.3
57.5 − 55.2 = 2.3 points.
How many different straights contain both a 9 and a 7?
Show the answer
Answer: 3
5-6-7-8-9, 6-7-8-9-T and 7-8-9-T-J: one gap leaves three straights.
Which makes a straight by the river more often: 8♠ 7♦ or K♠ Q♦?
- 8♠ 7♦
- K♠ Q♦
- Both the same: two cards in a row
Show the answer
Answer: 8♠ 7♦
An 8 and a 7 fit in four straights, a king and a queen in only two, since no card ranks above the ace: 9.0% of boards against 4.8%.