winning and losing streaks.. BE PREPARED!

We have all experienced seemingly ridiculous runs of dead cards, bad beats, and tournament crash outs. It is natural to begin to feel that our luck must turn around, if for no other reason than the simple “law of averages”. Well, it turns out that these streaks of bad luck should, in fact, occur more often than we may believe possible.  It is all a matter of probability and statistics.  For the sake of your own sanity, and bankroll, it is wise to be aware of the probabilities behind different streaks in poker.
Winning and losing streaks in poker occur at all aspects of the game: from actual “game-level” wins and losses, to individual hands, and everything in between.  I will approach each instance where streaks come into play from the “top-down”, starting with streaks during individual playing sessions, and then drilling down to streaks as they occur during actual card play.
We will begin with what I will call playing “sessions”. For the purposes of this article, I define a session as a single, uninterrupted, poker sitting. For on-line players, this may constitute several hours, and many simultaneous tables. For live players, it could be 24 hours or more of continuous play.  It is natural that we measure our success at the session level.  I, for one, keep a detailed spreadsheet which begins with my results at the session level.  Of course, this top level of analysis will ultimately have the most significance on our total bankroll, since wide swings of playing equity will be involved. To analyze how streaks occur at this level, it is first necessary to define an expected winning percentage (EWP). The EWP is simply the percent of time we “win”, or come out ahead in a session.  When interpreting our overall performance, though, it is also important to consider how muchwe win or lose during a session. After all, if you have an EWP of just 40% but the average haul is $1000, and your average losing session is just $100, you will come out smelling like roses. For purposes of this article, however, I am assuming that your average winning session is comparable to your average losing session.
Now, how bad a losing streak should you be prepared for?  Five or six sessions?  What are the odds that you lose ten in a row? These are very important questions that are often overlooked by many players. After all, could you psychologically continue to play after ten losing sessions, even if your bankroll allowed for it? Again, I am not implying this is the only metric that should be looked at, as I mentioned above the total dollar amount of your wins and losses are more critical than your EWP, but I know that I (perhaps subconsciously) tend to think of a session as either a “win” or a “loss”, without regard to the actual dollar amount.
Below is a table showing the probabilities of sustaining losing streaks of various lengths, assuming a 50%, 60% and 70% EWP. The calculations were based on playing 1,000 sessions.
                                    Table 1: Losing Streaks at various EWPs

Losing Streak Length	50%	60%	70%
1	100.00%	100.00%	100.00%
2	100.00%	100.00%	100.00%
3	100.00%	100.00%	100.00%
4	100.00%	100.00%	99.69%
5	100.00%	99.82%	81.88%
6	99.97%	91.63%	39.91%
7	98.15%	62.62%	14.14%
8	86.06%	32.42%	4.46%
9	62.39%	14.47%	1.36%
10	38.53%	6.05%	0.41%
11	21.54%	2.46%	0.12%
12	11.40%	0.99%	0.04%
13	5.86%	0.40%	0.01%
14	2.97%	0.16%	0.003%
15	1.50%	0.06%	0.001%

These results assume that each session is “independent” of one another. For this purpose, independent means that each poker session is not in any way related to, or affected by, any other playing session. In reality, however, we know that this is probably not the case. Many players, after a significant series of losses will experience negative effects in their play. Mentally, a losing streak can wreck havoc on one’s play. Conversely, a long winning streak may also adversely affect one’s play. Some players begin to play more recklessly, or at higher limits, after a series of wins. Elite players, however, continue to play their game, paying little attention to streaks.
You might be surprised at the results. Streaks of significant length can, and do, occur with higher frequency than many of us expect and plan for. Knowing these probabilities won’t make you a better player at the table, but they will help in your overall bankroll management and profit expectations. Are you prepared to lose ten sessions in a row? The table shows that if you win 50% of your sessions there is a nearly 40% chance that you will experience a losing streak of ten. How would that affect your confidence, and thus your play?  Ideally, the answer is that it would have no effect, but that is easier said than done.
Another aspect in poker where streaks come into play is at the individual hand level. This tends to play out in one of two ways: A couple dozen hands go by, and the best you see is a J7o, or the player to your left has raised pre-flop 5 straight hands. In the first example, we will look at the probabilities of getting streaks of “unplayable” hands (the following calculations assume 1,000 randomly generated hands). While there is no absolute consensus on “playable” starting hands, for the purpose of this article, I am deferring to poker expert David Sklansky who devised the following table of “playable starting hands”.
          Table 2: David Sklansky’s “Playable Starting Hands”

Rank	Hole Cards
1	AA, KK, QQ, JJ, AKs
2	TT, AQs, AJs, KQs, AK
3	99, JTs, QJs, KJs, ATs, AQ
4	T9s, KQ, 88, QTs, 98s, J9s, AJ, KTs
5	77, 87s, Q9s, T8s, KJ, QJ, JT, 76s, 97s, Axs, 65s
6	66, AT, 55, 86s, KT, QT, 54s, K9s, J8s, 75s
7	44, J9, 64s, T9, 53s, 33, 98, 43s, 22, Kxs, T7s, Q8s

Sklansky recommends playing the hands in Ranks 1-4 regardless of position, but for Ranks 5-7 the playability is based on position and previous table action.  If you are a tight player you may consider only playing the top 4 Ranks.  If so, then the probability of getting one of these hands is only 11.3%, or about 1 in 9 hands. A looser player may choose to play all 7 Ranks regardless of position. In this case, your odds of being dealt a playable hand jump to 31.5%.
Knowing these odds is critical so your play doesn’t become compromised.  For example, you are sitting at a table with an impossibly cold deck. You have mucked forty straight hands, with none of them belonging to the above table of “playable” hands.  What are the odds of this happening? Well, if you are a tight player (playing Sklansky’s top 4 Ranks) then the probability of seeing forty consecutive “bad” hands is just over 60%. So it’s not necessarily a cold deck after all. Note how the streak lengths change dramatically as your play gets looser. If you are seeing 31.5% of the flops (Sklansky’s entire “playable hands”) then you will rarely experience a cold streak of over 20 hands. Quite a difference from what the tight player experiences.
                Table 3: Streaks of “unplayable” hands at various pre-flop playing percentages

Streak Length	11.3% (tight)	Streak Length	20.0%	Streak Length	31.5% (loose)
1-20	100.00%	1-10	100.00%	1-9	100.00%
25	99.85%	15	99.96%	10	99.95%
30	96.48%	20	90.74%	11	99.42%
35	82.80%	25	52.97%	12	96.88%
40	60.89%	30	21.59%	13	90.45%
45	39.67%	35	7.59%	14	79.70%
50	23.93%	40	2.54%	15	66.21%
55	13.81%	45	0.83%	20	14.85%
60	7.70%	50	0.27%	25	2.38%
65	4.31%	55	0.10%	30	0.36%
70	2.38%	60	0.03%	35	0.05%
75	1.30%	65	0.01%	40	0.01%
100	0.06%	70+	0.00%	45+	0.00%

So next time you sit through hand after hand of utter junk, remember that it may not be outside the realm of expectations. Awareness of this will help you remain patient and wait for your hands. This will protect your bankroll and help keep your emotions in check.
On the flip side, let’s look at streaks of playable cards. The guy next to you (who you thought was a tight player) suddenly raises five straight hands. Is he bluffing or has he hit each time? Of course you can’t know for sure, but having the probabilities in mind will give you an edge on interpreting his play. In this example we see that the odds of him hitting five straight is only about 2%, so chances are he is trying to change up his play. Below is the table showing the odds of getting playable streaks of different lengths.
                Table 4: Streaks of “playable” hands at various pre-flop playing percentages

Streak Length	11.3% (tight)	Streak Length	20.0%	Streak Length	31.5% (loose)
1	100.00%	1	100.00%	1-3	100.00%
2	100.00%	2	100.00%	4	99.90%
3	72.24%	3	99.85%	5	88.20%
4	13.44%	4	72.26%	6	48.76%
5	1.62%	5	22.53%	7	18.94%
6	0.18%	6	4.97%	8	6.39%
7	0.02%	7	1.01%	9	2.06%
		8	0.20%	10	0.65%
		9	0.04%	11	0.21%
				12	0.07%
				13	0.02%

Now that you see these odds, it may change your feelings next time the player next to you continues to raise pre-flop.  Like the previous examples, this really boils down to emotions. When you are faced with continued raises, it begins to gnaw at your psyche. Is he bluffing? Am I playing too tight? Can he really be getting the cards? And so on. Having these probabilities at your disposal will give you a leg up on your competition. If for no other reason, you will be able to play without second guessing yourself at every turn. Further, it is likely the other players at the table are not familiar with these probabilities.
While this article strives to be objective and statistical, poker is also a game of subjectivity. Knowing the probabilities of sitting through hand after hand of dead cards, or crashing out of ten straight tournaments is extremely useful to your overall playing mindset. You might think the “card gods” are conspiring against you, forcing you to play more aggressively than you normally would in hopes of ending your losing streak. You may find yourself playing weak pre-flop hands just to get a taste of the action, or making a weak call on an opponent making raise after raise.  These all boil down to mental mistakes. As we all know, to be truly successful at the game of poker we cannot let emotions get the better of us- during a losing streak, or a winning streak. Mike Caro summed up poker streaks very well when he said: “There is never anything in the cards that will dictate that the streak either will or won't continue. So, you're always starting fresh. Just as every hand is a new start, every session is a new start. Never give a streak the importance of something that has influence over your future.”