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Flush and flush draw probabilities

  
 
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DrivingDog
Old 11-22-2007, 09:12 PM     Post subject: Flush and flush draw probabilities #1 (permalink)  
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DrivingDog
I've calculated the likelihood of facing a flush draw and/or made flush on different boards, depending on how many opponents saw the flop. Some of you may find this useful and/or wish to comment.

Three important points:

1) The likelihood of someone who sees a flop having a suited hand is estimated at 33% (1/3). This may differ in practice - e.g., some players will limp with ATC as long as they are suited; early raisers are relatively more likely to have big unsuited cards or pps; players in the BB are more likely to call a preflop raise with two or more opponents when they have suited cards, etc.

2) The figures in the tables make no allowances for betting or folding that goes on after the flop. For example, a single opponent capping a turn with 3 suited cards is typically more likely to have a flush than the tables would indicate. The point is not to look at the chart and think "probability he has a flush is <50%, so i must be ahead with my two pair". Nor is it to determine the chance of an opponent completing the flush draw should they have one, as this is already common knowledge. The sole purpose is to provide some information about a priori probabilities at a given point in the hand.

3) The possibilities of multiple opponents having a flush draw and/or made flush on the same board are beyond my ambition to get my head around at this point. At the risk of being glib, don't worry about it. Suffice it to say that these are mutually dependent but not mutually exclusive probabilities - whereas one opponent having a made flush decreases the likelihood of another having a made flush or flush draw, it is possible for more than one opponent to have either a made flush or flush draw on the same board, or for multiple opponents to have a made flush. These probabilities are quite small, however, and generally if one opponent is beating you with a made flush it doesn't much matter if another one has a made flush as well.



The leftmost column is the number of opponents who see the flop. The next three columns indicate how many (0, 1, or 2) cards you possess that are the same suit as the flush cards (your opponents are less likely to have a flush if you hold one of the flush cards yourself and less likely still if you hold two flush cards yourself). The values in the table indicate the % chance that at least one opponent has said hand. Backdoor draws are not considered.

For example, on a two-suited flop with 2 opponents (second row), if you have one card of the flush suit (middle column), there is an 11% chance that at least one of your opponents has a flush draw.


TWO SUITED FLOP

Q 8 J

% chance one or more opponents has a flush DRAW

.............................--------------------------you hold---------------------------
Opponents..............A K.............A K............A K
1..................................7.............. ..........6.......................5
2.................................14.............. .........11......................9
3.................................20.............. .........17.....................13
4.................................26.............. .........22.....................17
5.................................31.............. .........26.....................21




THREE SUITED FLOP

Q, 8, 4

% chance one or more opponents has a MADE flush

.............................--------------------------you hold---------------------------
Opponents..............A K.............A K............A K
1....................................6............ .............5.......................4
2..................................11............. ............9.......................7
3..................................17............. ..........13......................11
4..................................22............. ..........17......................14
5..................................26............. ..........21......................18


% chance one or more opponents has a flush DRAW

.............................--------------------------you hold---------------------------
Opponents..............A K.............A K............A K
1..................................37............. ..........33.....................30
2..................................60............. ..........55.....................51
3..................................75............. ..........70.....................65
4..................................84............. ..........80.....................76
5..................................90............. ..........87.....................83




TWO SUITED TURN

Q, 8, J, 6

% chance one or more opponents has a flush DRAW

.............................--------------------------you hold---------------------------
Opponents..............A K.............A K............A K
1....................................8............ ............6.......................5
2..................................15............. ..........12.......................9
3..................................21............. ..........17.....................13
4..................................27............. ..........22.....................17
5..................................33............. ..........27.....................21




DOUBLE SUITED TURN

Q, 8, 6, 3

% chance one or more opponents has a flush DRAW

.............................--------------------------you hold---------------------------
Opponents..............A K.............A K............A K
1...................................15............ ...........14......................12
2..................................28............. ..........25......................23
3..................................39............. ..........36......................33
4..................................48............. ..........44......................41
5..................................56............. ..........52.......................48




THREE SUITED TURN

Q, 8, 4, J

% chance one or more opponents has a MADE flush

.............................--------------------------you hold---------------------------
Opponents..............A K.............A K............A K
1....................................7............ .............6.......................4
2..................................14............. ...........11......................7
3..................................20............. ..........16......................11
4..................................26............. ..........21......................15
5..................................31............. ..........25......................19


% chance one or more opponents has a flush DRAW

.............................--------------------------you hold---------------------------
Opponents..............A K.............A K............A K
1..................................37............. ..........34.....................30
2..................................61............. ..........56.....................51
3..................................75............. ..........71.....................66
4..................................85............. ..........81.....................76
5..................................90............. ..........87.....................83




FOUR SUITED TURN

Q, 8, 4, 9

% chance one or more opponents has a MADE flush

.............................--------------------------you hold---------------------------
Opponents..............A K.............A K............A K
1..................................35............. ..........32.....................28
2..................................58............. ..........53.....................48
3..................................73............. ..........68.....................63
4..................................82............. ..........78.....................73
5..................................89............. ..........85.....................81




THREE SUITED RIVER

Q, 8, 4, J, 3

% chance one or more opponents has a MADE flush

.............................--------------------------you hold---------------------------
Opponents..............A K.............A K............A K
1....................................6............ .............5.......................4
2..................................13............. ...........10......................8
3..................................18............. ..........15......................12
4..................................23............. ..........19.....................16
5..................................28............. ..........23.....................20




FOUR SUITED RIVER

Q, 8, 4, 9, J

% chance one or more opponents has a MADE flush

.............................--------------------------you hold---------------------------
Opponents..............A K.............A K............A K
1..................................36............. ..........32.....................29
2..................................59............. ..........54.....................49
3..................................74............. ..........69.....................64
4..................................83............. ..........79.....................74
5..................................89............. ..........86.....................82




Conclusions:

1) Even against mutliple opponents, the a priori probability of one having a flush draw/made flush on a three flush board tends to be low on all streets. Again this does not take into account betting or folding after the flop.

2) HU, your opponent is <10% likely to have a flush draw on a two-suited flop. Even with two opponents, the probability is < 15%. Naturally, the chance that they will have a made flush should a third suited card come on the turn or river is correspondingly low.

3) The 3 suited flop table nicely illustrates why flopped flushes should almost never be slowplayed, especially without the nut flush. With two opponents, there is a >50% chance one of them has a flush draw and this number increases with more opponents.

4) Four suited turns and rivers offer good bluffing opportunities against tight opponents. E.g., on a four-suited river with two opponents it is 41% likely that neither has a flush, and a +EV bluff could often be made here.
"You can fool some of the people all of the time, and those are the ones you want to concentrate on." (George Bush).
 
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mk84
Old 11-29-2007, 06:01 PM #2 (permalink)  
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good info
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