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.”

A polarized range

The following explanation gives a more concrete idea of using polarization in poker. I was always grappling with this concept.

There seems to be a general sentiment in the poker community that having a polarized range tends to be exploitable and is therefore bad.  These players tend to focus strongly on balancing and merging their ranges in an increased effort to avoid exploitation.  While balance and merging certainly have their place, and being polarized can be exploited, there are some situations where polarizing your range can have the highest expectation and also be difficult to exploit.
Before I go on, let me take a moment and define specifically what I mean by polarized range in the context of this article.  I consider a polarized range to have two components:

1. It contains only very strong and very weak hands.
2. It has similar proportions of strong and weak hands.

Situations in which you or an opponent has 90% bluffs and 10% nuts are not considered polarized by this definition, because they are disproportionately weighted towards bluffs.
Some conditions which need to be met before having a polarized range becomes a good response are:

1. The percentage of strong value hands in your opponent's range which can beat the value portion of your polarized range is very small.  Generally, this is because he is too loose.
2. Your opponent is tough.
3. You are out of position.
4. You cannot outplay your opponent by simply having a strong value range which on average beats him.

These factors are indicative of the following generalized situation:  Your opponent is too loose and you want to exploit that, but you cannot exploit him easily because he is tough or in position, or he otherwise has an advantage which makes simply playing a better value range difficult.  Thus, the best way to widen your range while still protecting yourself and being able to play as close to the Fundamental Theorem of Poker as possible is to keep your value range strong, and add in some of your worst hands, polarizing your range to the very best and very worst of your hands.  This allows you to exploit his looseness while still being able to play well.
If you are betting a very strong hand, you know you are likely ahead and can try to extract value.  If you are betting a very weak hand, you know you are behind and that you are bluffing.  You avoid being in a difficult situation because you always know where you are at.  In addition, your opponent has difficultly responding because the best of his middle strength hands lose value, since they all fair the same against your range.  (To take a contrived example, if your range includes only AA or 54s, 66 and KK have similar all-in preflop equity.)  You make extra money by bluffing your opponent, thus taking advantage of his looseness, but you protect yourself from being re-exploited.  A significant portion of your range is still very strong, and you can play near-perfectly, since you always know whether you are bluffing or value betting.  So while against a bad and loose opponent you would simply try to get the money in with a wider value range, against a tough and loose opponent you may opt to polarize your range.
There are two main times when a polarized range is generally used:

1. Preflop re-raising wars
2. Betting or raising big on the river

Fortunately, the nature of hold ‘em allows for very frequent river opportunities for polarization.  When an obvious draw misses, a river bet or raise can be polarized by having either a missed draw or a strong two pair or set.  When a draw hits, a river bet or raise can be polarized by having the nuts or near nuts, as well as a weak pair-turned-bluff or a missed non-obvious draw (like a straight draw when the flush comes in).  These situations are highly context-dependent and occur frequently, so tread with caution when deciding what situations and opponents warrant a polarized range.  Preflop polarization opportunities are less frequent because while even a tough opponent may often be too light on the river (sometimes without realizing it), most half way competent players these days are not prone to egregious preflop errors. If you start playing back at them, they will notice and adapt.  (And if the player is not competent preflop, polarizing your range is unnecessary and costing your profit.)
Flop and turn polarization is generally unnecessary.  Assuming you are a generally tight player, on a very dry flop, like K62 of different suits, a value raise usually represents only a set, ace-king, or aces, and maybe KQ or KJ.  There are no other hands that you can have which are “monsters”.  Therefore, an opponent who is not good enough to adjust his hand's value based on the board texture will often be forced to give up to pressure on such a board.  However, your raising range on that flop against such an opponent is not polarized; it is almost entirely bluffs unless you just happen to have a set.  Against a good opponent, you may indeed have to polarize your range on a flop like that, cutting your bluffing frequency to a very low number, since the hands you can play for value on that flop are also very low.
On a drawy flop, like 965 with a flush draw, against most opponents, you should generally refrain from out-right bluffing with no equity, since with such a coordinated texture, you often have, and your opponent will often have, hands with a lot of equity.  All kinds of flush draws, straight draws, overpairs, and pair plus draws are possible on that board, and thus high equity semi-bluffing opportunities abound.  This gives you ample bluffing opportunities against even tough players, and rather than having a polarized range to make your decisions easier against a difficult player, you should instead bet or raise an amount that makes your decision easy with a non-polarized range that has decent equity.
Turn play, for the purposes of discussing polarization, can be related to both flop play and river play.  Like the flop, the board texture and opponent will tell you whether you should have a polarized rage and how to proceed, and like the river, obvious draws and scare cards may come which allow you to represent a specific and narrow range of value hands.  But, as noted earlier, most flop and turn play is not going to require any polarization against even good players.  Polarizing your range is a one-move tactic because all play on later streets is made in the context of having a very narrow value range, and barreling future streets is merely a continuation of that story.  Most of the time, postflop play will tell a different story than “I either have a monster or nothing.”
It is important to reiterate that in order to have a properly polarized range, you must have similar amounts of bluffs as value hands, and the frequency of your bets must not be too high or too low.  In the K62 rainbow flop example given above, when you raise, even though you are representing only bluffs or very strong hands, you are going to be bluffing far more often than you are going to have a real hand.  In that situation, your range isn't polarized, it's just mostly bluffs.  If you are against a tough opponent who knows how few value hands like that flop, then you might cut your bluffing frequency down to match how often you have a big hand.  At that point, your range is polarized.
Another example of a non-polarized range would be when your value range is very wide, and then you add in a proportional amount of bluffs.  At that point, your range, while technically “polarized,” is simply super wide and subject to being exploited by waiting for a hand.  That is, if you play the top 30% and the bottom 30% of hands, you're not so much polarized as super-loose.  And if you're playing against an opponent where you can get value from the top 30% of hands, bluffing him is not going to be wise!
Polarization only occurs when the frequency of your bluffing and value betting is similar, but not so tight or loose that you can still be directly exploited by your opponent based on the frequency of your betting.  For example, if you are “polarized” but too tight (playing only aces, kings, and 52o), he can steal your blinds incessantly.  If you're too loose (top 30% and bottom 30%), he can afford to just wait for a decent hand and figure to profit by the fact that you are putting money in the pot too often.  In order to be polarized in a given situation, your total frequency of betting should not in itself be open to exploitation.
As with all poker, you want to have the most equity possible, so when you polarize your range, you want bluffing hands (the bottom pole of our polarized range) to be as high equity as possible while still being “bluffs”.  Thus preflop, instead of a range akin to (QQ+,AK,72o,62o,52o), a range of (QQ+,AK,53s-86s,43s-87s) is preferable.  Each range has the same number of combos, but against a value range of (TT+,AK), the bluffing range of (72o,62o,52o) has equity of 20.2%, while (53s-86s,43s-87s) has 27.7%.  Both ranges are fairing poorly—they are bluffs after all—but having the suited-connectors is far better, and not just for the extra 7.5% equity.  Assuming a deep enough game with money behind after a polarized three- or four-bet, if the bet is called, at least some of our postflop betting frequency can be based on if we flop or turn some kind of a draw.  This tempers our betting frequency and strengthens our overall range (since even our bluffing equity is higher), and makes it that much more difficult for an opponent to play back at you light.  While bad players may espouse “being suited is only worth four percent,” what they fail to realize is that being able to stay aggressive with a strong draw, and having that added equity in your range, is worth far more than just the equity-value of the hand.  Similarly, if you are against a tough opponent and have a polarized range on the K62 flop listed above, you want to have all those low gutshots (54 and 43) in the bluffing portion of your range.  Turning a complete loss into a big win, even occasionally, is worth a lot.

A strong finish to an up and down week

yeah! I solved all the software problems, the last one being an annoying "aero peek" option in windows 7 themes that is on by default. if you dont know what it is, it can drive you crazy.. what happens is when you move your mouse unknowingly past the right corner of your screen.. the focus is taken off your active window.

Turn it off by right clicking in the bottom right corner pane, next to the time.


Things are going along much much smoother, and im twelve tabling the .01/02 games on fulltilt.
It takes forever to make any money at these, cause even if you play almost perfectly (assuming 95 percent of the players are loose passive),, most of them are too tight by the river to call anything of value.


so now i make the big jump to the next buy in.. 2 NL.  I think ill stay there for a while.. 50k hands, and see how it goes.  I will either 9 table or 12 table, depending on how the games play.

The software I ended up using for poker, is holdem manager and tableninja. they make playing and reviewing hands so much easier.  I can assume a very comfortable position in my chair , and make minimum mouse movements to use my thinking time the most in tougher spots.  Im keeping all my decisions really easy..
basically raise until they fight back, or I have the nuts.. then all in. It will be interesting to get a large 2nl sample of hands to see if I can be as comfortable in that game.
Im starting each session with 45 minutes or so of study.  now im studying milwauki 2 videos at 100 nl, to prepare my self for tougher decisions as I move up in stakes.