Long term breakeven stretch statistically unlikely for a winner

    • howard182
      howard182
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      Joined: 30.10.2006 Posts: 416
      (BB is poker tracker big bets in this post, the convention is now unnecessary for NL but we're stuck with it because it's been used this way for so long.)

      I've been in a break even stretch for a while (over 20k hands) and only recently stopped to consider how likely this is if I'm still the few BB/100 winner I was in my poker career until this started. Unfortunately I can't break down my results into full ring, short stack versus deep stack etc. easily, but assuming a SD of 40BB/100 should be good enough. If assume that I'm a fairly small winner, say 3BB/100 (which I could live with) and that I've been breaking even for 28.9k hands (that's about right and gives us a nice round figure, 289 is 17 squared) my expectation over that sample would be 867BB and my SD 680BB, giving a result of 0BB a z-score of -867/680 = -1.275 or almost exactly on the 10th percentile. Could happen, but it's not a very comforting figure.

      Now I don't remember enough statistics to say how likely it is that the actual win rate for my strategies in the games I played in that sample is less than 3BB/100, but intuitively it's going to be pretty high. Now is the time to start getting worried that I've lost my edge, but I don't know what's changed. I've played the limit I'm on since about the 55k mark so I don't think it's just that the games are tougher.

      For reference, here's my lifetime NL graph:

  • 28 replies
    • Puschkin81
      Puschkin81
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      Joined: 14.04.2006 Posts: 4,786
      Hi howard182!

      Don't worry! A break even streak over 20k hands is more than normal. I started with a 20k hands break even streak on NL200 myself before I moved up. It's just the variance which influences your winrate. Your graph indicates that you are a NL winning player on the limits you have played so far because you won 4400BB over 100k hands, which is a winrate of 4,4BB/100. So don't worry: you will move up again. But nevertheless you should work on your game, read articles, post your hands and discuss about the game.

      Good luck at the tables!
      Puschkin81
    • howard182
      howard182
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      Joined: 30.10.2006 Posts: 416
      The point is that it isn't normal, I did the maths to prove it.
    • Puschkin81
      Puschkin81
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      Joined: 14.04.2006 Posts: 4,786
      A winrate in No Limit becomes significant when you have played 100k hands at least. If you only look at 20k hands the variance plays a bigger role than anything else. There are so many factors and situations at the poker table which influence your calculation that you cannot simply assume a SD of 40BB/100. Your calculation itself might be correct but it doesn't consider all the factors (bad beats, run of good cards, streaks of bad luck, strength of your opponents, your condition while you play, etc.). Only if the sample size is big enough you can make an assumption about how good you really are.

      Good luck at the tables!
      Puschkin81
    • ciRith
      ciRith
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      Joined: 25.03.2005 Posts: 18,556
      Ther must be something wrong in your calculation because a break even streak is normal. Even 40k hands can happen.

      You have 4,4BB/100 over more than 100k hands and maybe you are only a 3BB/100 winner. So the luck evens out maybe? :)

      Of course it can be that you don't beat the limit yet but a sample size below 50k for one limit isn't enough to say that you don't beat it yet. Do you use the SD from PT or did you just say that you think you have 40?
    • howard182
      howard182
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      Joined: 30.10.2006 Posts: 416
      40BB/100 is pretty standard for full ring NL and since I've got a mix of that, 6 max (higher, about 50) and short stacking (lower, maybe 20) I decided it would do as an estimate. Getting the SD for the last N hands is a bit of a pain but I'll go ahead and check... okay, this should do for a sample. 32411 hands, +45BB and pokertracker says that the SD/100 is 39.5. As you can see, I didn't just pick 40 randomly ;)

      Over that sample, SD is 711BB, expected win for 3BB/100 winner is 972BB, (45 - 972)/711 ~= -1.3. Slightly worse than my "easy numbers and lotsa rounding" figure.

      This maths is all perfectly standard, there's nothing wrong with it. What's wrong is my game, somehow.
    • ciRith
      ciRith
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      Joined: 25.03.2005 Posts: 18,556
      I'm not that good at this SD math stuff. (And too lazy to reread it in mathematics of poker.) Can you explain me what you calculate? -1.3 is what? :)

      Could it be that PTBB != SD BB? maybe it's 80BB. :)
    • howard182
      howard182
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      Joined: 30.10.2006 Posts: 416
      Obviously all units are the same, it wouldn't be very sound otherwise :P (The breakeven stretch would be even _more_ unlikely if the SD was in big blinds anyway.)

      The -1.3 (or -1.275 in the original calculation) is the "z-score", which is where the result lies on the normal distribution (you do know about the normal distribution, right?) It is simply the measured value minus the expectation divided by the standard deviation. A -1 SD event has a z-score of -1. 68% of the normal distribution is between -1 and 1, 95% between -2 and 2 etc. There are tables to convert z-scores to percentiles.
    • ciRith
      ciRith
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      Joined: 25.03.2005 Posts: 18,556
      Hmm to be honest the special words are too much for my eglish. ;)

      To know what is what with the SD I have to reread it. (Yeah I forget things too fast. ^^)

      I know that you can say how likely an event is with the SD. Can you convert it too percenttages?

      Like: The probability of your break even streak is 5%. (Which would be very high. ^^)

      EDIT: I reread your post. Everything between -2 and 2 is for 95% likely? So -1,3 (or -1.275) is even more likely?

      If this is the case and the math is correct then your break even streak should be just normal.
    • Nunki
      Nunki
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      Joined: 25.10.2006 Posts: 865
      Originally posted by Puschkin81
      Hi howard182!

      Don't worry! A break even streak over 20k hands is more than normal.
      Suppose there is a Hero who wins at 3 PTBB/100. We also know that Hero
      has a break-even stretch of 30k hands about 10% of the time. We can be sure of this since Hero has played millions of hands.

      What is the likelihood if we randomly select a sample of 120k concurrent hands that Hero endures at least one breakeven stretch of 30k hands?

      Answer:= 1-(9/10)^4=34%

      (assuming we are able to choose three consecutive 30k intervals and that the fourth interval consists of a concatenation of the remaining hands).

      Don't obsess with win-rates (unless you are close to broke). Go through your hands and see where the money has been coming and going.
    • howard182
      howard182
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      Joined: 30.10.2006 Posts: 416
      Of course I'm looking at my games, I know that one's win rate is just the product of good or bad play combined with fortune. The problem is that there's nothing I can put my finger on but my results remain dismal and seem to be getting worse by the day.

      I played a bit over 1400 hands of short stack NL200 today (what can go wrong with short stacking, right? Simplest way to play poker), lost $425. Lost yesterday too, although close to break even. Lost the day before too, $300.

      I even played some damn .05/.10 limit hold'em a while ago just to see how I'd do, lost at that too.

      There is something horribly and fundamentally wrong with my play and I can't find it!

      It's getting to the point where I'm having to think about when to cash out my bankroll and call the last year a failed experiment, because I have no interest in being a losing gambler.
    • howard182
      howard182
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      Joined: 30.10.2006 Posts: 416
      To give you an idea of why this looks so dire to me, here's my graph in DOLLARS:



      As it happens, the graph also currently corresponds to my bankroll almost precisely.
    • ciRith
      ciRith
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      Joined: 25.03.2005 Posts: 18,556
      I know how you feel. I am 40k hands worse than break even at 5/10$. I'm currently playing 3/6$ just to get my confidence back. :/
    • Puschkin81
      Puschkin81
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      Joined: 14.04.2006 Posts: 4,786
      Hi howard182!

      Sorry to hear that. I recommend that you go down one or two limits and start again. It's definitely better than switching from BSS to SSS to FL. Keep with your favourite variant and go down one or two limits to get your confidence back - like CiRith already mentioned.

      Good luck at the tables!
      Puschkin81
    • howard182
      howard182
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      Joined: 30.10.2006 Posts: 416
      I haven't been "switching", I've frequently mixed some SSS play in, particularly when clearing bonuses. It's been profitable too, until recently, when nothing has been.

      Certainly there's a temptation to run away to a fresh game, but I know that's not a formula for overcoming this. NLHE, whatever stack size, is my main game and should remain so for now. It is all poker though, and seeing the same results outside of deep NLHE is worrying.
    • howard182
      howard182
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      Joined: 30.10.2006 Posts: 416
      After yet more losing my bankroll is nudging at the $2000 mark, so I'll be moving down regardless it seems.

      Winning the bad beat jackpot's about my best hope.
    • Puschkin81
      Puschkin81
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      Joined: 14.04.2006 Posts: 4,786
      Hi howard!

      Moving down might be the best decision.

      Good luck at the tables and for the Bad Beat Jackpot! :D
      Puschkin81
    • howard182
      howard182
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      Joined: 30.10.2006 Posts: 416
      Well, I've found a silver lining to all this: I'm loving NL50.

      I can't say that table selection is entirely redundant because sitting at a table full of nits isn't very profitable and sitting with a buddy (by NL50 standards!) is hugely profitable, but... flop set, stack donk seems to be a sufficient as a winning formula, and can be improved on still. I only played full ring NL50 before, but this gives me some insight into how I beat NL25 SH without knowing anything about typical short handed play.

      These are a few choice hands from today :D : (actual AFs are... bah, just fix grab'em already please)

      Known players: (for a description of vp$ip, pfr, ats, folded bb, af, wts, wsd or hands click here)   
      Position:
      Stack
      CO:
      $55.99
      Hero:
      $50

      0.25/0.50 No-Limit Hold'em (5 handed)
      Hand recorder used for this poker hand: Texas Grabem 1.7 by www.pokerstrategy.cc.

      Preflop: Hero is BU with 3:heart: , 3:diamond:
      MP3 folds, CO raises to $2.00, Hero calls $2.00, 2 folds.

      Flop: ($4.75) 8:diamond: , 3:spade: , 9:heart: (2 players)
      CO bets $3, Hero raises to $7.00, CO raises to $21.00, Hero calls $14.00.

      Turn: ($46.75) 2:spade: (2 players)
      CO bets $27, Hero raises to $27.00 (All-In).

      River: ($100.75) 5:diamond:


      Final Pot: $100.75

      Results follow (highlight to see):
      CO shows [ Th, Td ] a pair of Tens
      Hero shows [ 3h, 3d ] three of a kind, Threes
      Hero wins $98.75 USD with three of a kind, Threes.

      (Next one I didn't play well... except the river.)

      Known players: (for a description of vp$ip, pfr, ats, folded bb, af, wts, wsd or hands click here)   
      Position:
      Stack
      CO:
      $84.31
      Hero:
      $50
      SB:
      $49.25

      0.25/0.50 No-Limit Hold'em (6 handed)
      Hand recorder used for this poker hand: Texas Grabem 1.7 by www.pokerstrategy.cc.

      Preflop: Hero is BB with 9:heart: , 8:spade:
      2 folds, CO calls $0.50, BU folds, SB calls $0.25, Hero checks.

      Flop: ($1.50) 3:heart: , 9:club: , 9:spade: (3 players)
      SB checks, Hero checks, CO checks.

      Turn: ($1.50) J:diamond: (3 players)
      SB checks, Hero bets $1, CO folds, SB calls $1.00.

      River: ($3.50) 8:heart: (2 players)
      SB bets $3, Hero raises to $48.50 (All-In), SB raises to $47.75 (All-In).

      Final Pot: $99.75

      Results follow (highlight to see):
      Hero shows [ 9h, 8s ] a full house, Nines full of Eights
      SB shows [ Qc, Td ] a straight Eight to Queen
      Hero wins $0.75 USD with a full house, Nines full of Eights.
      Hero wins $96 USD with a full house, Nines full of Eights.


      Known players: (for a description of vp$ip, pfr, ats, folded bb, af, wts, wsd or hands click here)  
      Position:
      Stack
      MP3:
      $109.79
      Hero:
      $86.49
      BU:
      $16.49

      0.25/0.50 No-Limit Hold'em (6 handed)
      Hand recorder used for this poker hand: Texas Grabem 1.7 by www.pokerstrategy.cc.

      Preflop: Hero is SB with 8:spade: , 8:heart:
      MP2 folds, MP3 calls $0.50, CO folds, BU calls $0.50, Hero calls $0.25, BB checks.

      Flop: ($2.00) 6:heart: , 8:club: , 4:heart: (4 players)
      Hero bets $2, BB folds, MP3 calls $2.00, BU folds.

      Turn: ($6.00) 7:club: (2 players)
      Hero checks, MP3 bets $5, Hero calls $5.00.

      River: ($16.00) 6:club: (2 players)
      Hero checks, MP3 bets $8, Hero raises to $78.99 (All-In), MP3 calls $70.99.

      Final Pot: $173.98

      Results follow (highlight to see):
      MP3 shows [ 5h, 5s ] a straight Four to Eight
      Hero shows [ 8s, 8h ] a full house, Eights full of Sixes
      Hero wins $170.98 USD with a full house, Eights full of Sixes.

      MP3 in the last hand is a 70% VPIP donk and obviously hit my buddy list before this hand :)
    • undercover82
      undercover82
      Bronze
      Joined: 09.12.2006 Posts: 813
      how can you find people who call these huge overbets :rolleyes:
      A bit weird that you checkraised the river on last hand , most players will check behind there with that dangerous card and you will lose value :D
    • howard182
      howard182
      Bronze
      Joined: 30.10.2006 Posts: 416
      The right people will call, even good players will call in the right circumstances. And that guy doesn't check behind, I had a read :D I also thought, but was less certain of this, that he'd be more inclined to call if I let him bet first. (He also hardly ever raises, so anything less than an all in really loses value, put all that together and I had check/raise all in as the maximal line.)
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