Thursday, December 6, 2012

Heads-Up Flush Draw Odds

Question #1:  Playing heads up, if you set 2-4 flush cards, how often will you complete a flush?  

The following chart gives the odds (in heads-up open face) of making a flush draw given how many flush cards you have set, how many flush cards are in the other player's hand, and how many draws remain.

The first column of the table gives the odds of completing the flush by the end of the hand if you have 8 draws left (that is, immediately after the set), then 7 draws, etc., until the last column, which is the odds with a single card left to draw and set.  So, for example, if you have set three hearts in the back hand, and your opponent has two hearts, and there are six draws left, you have a 37.0% chance of making the flush by the end of the hand.

Chance of completing a flush with 4 suited cards set, 2 players

Dead
cards
Draw 1
Draw 2
Draw 3
Draw 4
Draw 5
Draw 6
Draw 7
Last Draw
0
88.2%
85.9%
82.8%
78.7%
72.8%
64.3%
51.5%
32.1%
1
84.6%
82.2%
78.4%
73.9%
67.8%
59.0%
46.8%
28.4%
2
80.1%
77.1%
73.4%
68.6%
61.9%
53.7%
41.9%
24.8%
3
74.6%
71.0%
67.3%
62.1%
55.7%
47.6%
36.3%
21.5%
4
67.3%
63.8%
59.9%
54.8%
48.9%
41.2%
31.0%
17.6%
5
58.4%
55.2%
51.4%
46.6%
40.9%
33.8%
25.2%
14.1%

Chance of completing a flush with 3 suited cards set, 2 players  

Dead cards
Draw 1
Draw 2
Draw 3
Draw 4
Draw 5
Draw 6
Draw 7
Last Draw
0
62.7%
57.1%
50.7%
42.9%
33.3%
22.4%
10.4%
0.0%
1
55.6%
50.5%
44.1%
36.9%
28.2%
18.4%
8.1%
0.0%
2
48.0%
42.9%
37.0%
30.5%
22.8%
14.6%
6.5%
0.0%
3
40.4%
35.2%
30.3%
24.4%
17.9%
11.3%
4.8%
0.0%
4
32.1%
27.7%
23.3%
18.6%
13.3%
8.3%
3.5%
0.0%
5
23.8%
20.2%
17.2%
13.3%
9.5%
5.7%
2.3%
0.0%

Chance of completing a flush with 2 suited cards set, 2 players

Dead Cards
Draw 1
Draw 2
Draw 3
Draw 4
Draw 5
Draw 6
Draw 7
Last Draw
0
34.3%
28.6%
22.1%
15.3%
8.8%
3.4%
0.0%
0.0%
1
28.1%
22.7%
17.6%
11.9%
6.8%
2.5%
0.0%
0.0%
2
21.9%
17.7%
13.3%
8.8%
4.8%
1.6%
0.0%
0.0%
3
16.2%
12.7%
9.3%
6.1%
3.3%
1.2%
0.0%
0.0%
4
11.3%
8.8%
6.3%
4.0%
2.0%
0.7%
0.0%
0.0%
5
7.1%
5.4%
3.9%
2.5%
1.2%
0.4%
0.0%
0.0%


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