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Server Time: 8/28/2008 8:23:41 PM PACIFIC |
 Losing Streaks and Daily Expectation, NiceFella, 6. Apr 2003 01:06 | ||
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| I recently had a rough day at the poker table where I seemed to lose every hand for hours on end. What else is new, right? Well, I broke out the pocket protector and slide rule tonight to try to figure out just how unlucky you have to be to feel sorry for yourself, and what sort of losing day should be considered unusual. What I did was write a little computer program to simulate a year of playing poker. The program didn't really play poker, it just generated random numbers and distributed wins randomly to one of ten "players". You could argue that this doesn't reflect the skill of a player, etc., but it does at least fairly represent who got dealt the best cards. I simulated 200 8-hour days of this simple "poker". At 50 hands per hour, that means 400 hands are played per day. 200 days make 50 weeks of 5 days-a-week play. I wanted to determine how long a losing streak could be for a player, how many wins and losses could occur in a day, and how bad it can really get. Here's what I found. Playing 400 hands a day, with a 10% chance to win a hand, you'd expect to win 40 hands every day. Over the course of a year, my simulated player had a worst day where he won only 25 hands and lost 375, and a best day where he won 55 hands and lost 345. That's a swing of plus or minus 15. The standard deviation for daily hands won was 5.5. Notice that this means 2/3 of your poker days, just through blind luck, will have winnings which vary by the difference between winning and losing 11 average pots. If an ideal expectation of excellent play is less than 2 big bets per hour, that means the random luck factor on any day (11 pots lost instead of won -- fill in your estimated size here) dwarfs an expectation of 16 big bets. Even at $4/8 holdem this can mean several hundred dollars. More interesting to me, because I'm feeling sorry for myself tonight, were the losing streaks. I tracked the longest losing streak the player suffered every day. Over the course of the year, the simulated player had a worst losing streak of 74 hands in a row. That's about 90 minutes of continuously being dealt a losing hand. On average, a day's worst losing streak was 40 hands. EVERY DAY of play, one should expect to go through at least one hour-long period of continuous losses. The standard deviation for a day's worst losing streak was about 10 -- so a 50-hand losing streak is not at all unusual. So how should this make me feel about my bad day at the tables? Well, I think it's entirely normal to break even for several hours, go on a losing streak where you lose every hand for an hour, get a small hand and win a tiny pot, then lose every hand for another hour, get demoralized, and go home 5 or 6 pots short of your expectation. You've lost several hundred dollars, had no fun, and you complain, complain complain. And you know what? It's entirely typical, you haven't been unlucky, and you shouldn't read anything into it. Get over it, cheer up, and come back tomorrow. I think this is something that committed casino seat-warmers already know instinctively. I get a kick out of seeing beginners to the game start griping about bad cards about 20 minutes into their session. :-) I realize that my results were crudely generated. But I ran the sim a few times, got similar results, and I'm satisfied that I've learned something interesting about poker that gives me some perspective on my rough days. I hope it helps out some others. NiceFella | ||
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| Re: Losing Streaks and Daily Expectation, Kevin J, 6. Apr 2003 06:33 | ||
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| I suck at math so I could be wrong, but it seems to me you went through a lot of work for nothing. Isn't this what standard deviation is supposed to tell you? When your results start approaching 3 standard deviations, you'll know you've been very lucky or unlucky. It's pretty simple. | ||
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| Provided you are playing well, Kevin J, 6. Apr 2003 06:41 | ||
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| I should've add this. Approaching 3 standard deviations is unlucky provided youare playing well. One good thing about SD is that when your results exceed 3, you can be very sure it's not just luck. | ||
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| Re: Losing Streaks and Daily Expectation, flintsword, 6. Apr 2003 15:57 | ||
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| A lot of work, thanks for going to the effort! Kevin J mentioned that Standard Deviation (SD) addresses the variance everyone goes through as well as the "clue" you are doing well if you are positive more than three SD. Is there a very real difference between pro poker players and beginners with respect to their expectation of wins? I hear a lot about bad run of cards yet whenever I do well in a tournament, I do not bet that often, but feel I should. Any other beginners out there face good results when you are disciplined and NOT playing every second hand that trots by, but feel they should "play" more? | ||
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| Re: Losing Streaks and Daily Expectation, stdioh, 7. Apr 2003 09:28 | ||
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| I don't mean to prick your balloon, but this is a little bit simplistic for poker. To say that any one player has a 10% chance on a hand of winning 9 bets and a 90% chance of losing one bet just doesn't come close to simulating poker. Generally, a winning player is going to play few hands and win big pots (assuming low limit games at least). For many reasons, this sort of simulation is an excercise in futility as you're using poor axioms in the system. | ||
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| Re: Losing Streaks and Daily Expectation, NiceFella, 7. Apr 2003 12:38 | ||
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| I appreciate the comments. I'm naive and did a lot of work (yeah, about 45 minutes with Excel), but I know computers better than I know statistics. I attacked the problem in a way I could understand. I'm eager to learn elegant solutions if anyone cares to share. It's fine to say "more than 3 standard deviations is unlucky", but just I don't know what 3 standard deviations should be in holdem. I'm sure there's a formula to give the standard deviation of a 10% trial... anyone care to share? In the real world, measuring the standard deviation comes from measuring hundreds of actual results, which I don't have yet. I certainly don't have data about how often I was or wasn't dealt the best cards in a day. I figured empirical measurments of a random number generator would get me most of the way there. But beyond just knowing the standard deviation for the number of wins in a day, what I was especially interested in was how long a typical day's worst losing streak would be. In the span of 400 deals, how many times in a row can you expect to be dealt a loser? In a year of play, what would your longest bad-cards streak be? I don't think these are trivial questions easily dismissed. My brute force method gave me an answer I'm happy with, but would some more elegant calculation I don't know about give a similar answer? Yes, stdioh, I know that dropping 10% wins into a bucket isn't any way at all to simulate poker. However, I think it's still a fair exercise as an exploration of how often you'll get the best cards. Yes, sometimes you'll muck a winner and sometimes you'll convince the winner to fold. I'm not too concerned with the quality of play or actual cash results. What I wanted to know is whether that frustrating situation of getting had really bad cards for hours on end is unusual or par for the course. There are times at the table when I haven't won a pot in hours, and can't recall having mucked a winner. That's the situation I wanted to examine. More input always welcome, I want to keep learning. Thanks, NiceFella | ||
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