You need the Luck Calculator
So you've been running bad. You read all the best books, study hard, apply the techniques, and you're still a loser.
You know variance is huge, and you know that your last 10,000 hands are really a small sample when it comes to results, but you really want to know whether you've just been unlucky, or whether you're a bad player. You want the luck calulator; you want to plug in your hand history and be told "You are unlucky."
I totally feel where you're coming from. . . you know you need tens of thousands of more hands before you know your long-term expectation, and you really want to get some kind of measure of your relative performance between now and then. . . but it just ain't gonna happen, and although many have tried to devise a method for a luck calculator, I really feel efforts in this direction are misdirected.
There are so many variables that dictate your luck that it's hard to encompass them. No simple rubric of statistics captures it.
Let's say you come in with JTo. You flop two more tens! There's also an ace on the board, and two to an opposing flush. You slow play. The turn puts a flush card on the board. Were you unlucky because the flush came, or stupid because you slowplayed? Someone bets out; you fear the flush but call. River, another flush card. You lose to what was a back-door flush semi-bluffing the turn. Were you unlucky? Or were you stupid to allow the free card on the flop?
What is lucky?
Let's say you come in with QJs. You flop QJ3. You bet. All fold. You won. Tiny pot. Were you lucky or not? Lucky to catch it, lucky to win, but unlucky not to get paid off? Which matter more? Netlucky, or unlucky?
You flop quads. Can't get luckier, right? Unpaid. Feel lucky now? If the other players have cards that just can't call on any street, no skillful choice of when to bet would have helped. You were just unlucky to have made a monster without any playable opposition cards.
You flop top set, bet all the way, and win a really big pot against three opponents with top pair, second set, etc. Were you lucky? Not lucky to win; top set holding up is the "expected" result, but you were certainly lucky to have opponents who were second best giving you action or caught in the middle.
Is getting KK as a starter lucky? Not if others got AA. Is geting AA lucky? Sure. But it's LUCKIER if others got KK at the same time; that's really lucky. Unless they board a king, of course, in which case it's phenomenally unlucky.
You should get the idea - there's luck in getting starting cards, lucky in making boards, luck in taking down pots, luck in getting paid off, luck in getting away cheaply on a loss, and then there's always the concern that regardless what you calculate as luck, a lack of skillful play actually ruin it for you. . .
Now, I know the first reponse to statements like mine from people who actually understand me: "I understand that, but I've been running bad. Even a general indicator would be a lot of help." To which I say this:
No, you don't, because a luck calculator can't work
It won't help. . . Because there's not just luck, there's the variance of luck. Variance in poker is so huge that one lucky hand can outweigh many, many unlucky hands -- or vice versa. You would need a very, very large sample to get a meaningful read on your luck, at which point luck is no longer a measurable factor, because you have a very, very large sample.
I'm going to say that again, because it's a profoundly important point to understand, yet it's incredibly subtle.
Any time you measure something statistically, you need a large enough sample size for your statistic to start to overwhelm variance. If not, your reading for that sample may be way off, and you can't tell how much. If you came up with a formula that measures a specific aspect of luck you would inevitably have some amount of variance in that luck statistic itself. And, from the very nature of poker, that variance would be very large. So to get a meanginful read on that luck, you would need a very large sample. And if you have a very large sample to determine your luck with any accuracy. . . well, then you have enough hands to know your actaul win rate with some accuracy, and you don't really care about your relative luck so much.
In a nutshell: luck is so incredibly sensitive in the short term that you can not measure it with any accuracy.
I'll prove it
Try this in PokerTracker. I'll use my numbers; I've been running bad this week. I've got a filter-by-date set which captures my last 8544 hands. I'm down 33.30 BB on 8544 hands, or -.39 BB/100.
I bring up all my hands in Game Notes and sort by my Net, descending order. I now see my biggest losers. Let's make me luckier on those losing hands. How many do I have to convert to turn my 8544-hand unlucky streak into a winner?
Worst hand was -10BB (nut flush down to a boat); if I won instead, I would have picked up a 30 BB pot. So changing my luck on one hand out of 8544 takes me from a -33BB run to a -3BB run. If I change my luck on my TWO worst hands, I'm a winner overall!
8544 hands, two change, I'm a winner. It's that sensitive.
If I change my luck on my 8 worst hands, I pick up 171BB. That would make me a +138BB player, or a 1.6 BB/100 player. Still weak for my actual average, but much better than a losing streak. Changing .09% of my hands turns it all around. That's right; less than 1% of hands. You'll find that for any sample size, if you usually take the 1% of hands with the biggest pots and reverse them, you will turn your fortunes around. You can reverse your big winners and make yourself a net loser, too.
Luck is the impossible measure
Luck is something which should average out over time. But to measure it, you need a larger sample. Over that larger sample, it will have averaged out! Luck will only be sizable in the short term, but then you can't measure it. . .
The only way to measure luck short-term is to already know what your average ought to be. For example, if you've been dealt 2,652 hands, you should, on average, have been dealt aces 12 times. If you've only been dealt 10 pairs of aces, you've been unlucky, and if you've been dealt 14 pairs, you've been lucky. . . but as we saw earlier, you've been lucky/unlucky only in the strictest sense of getting aces. That doesn't mean that the aces you've gotten were lucky - they may have lost, or been unpaid.
So the basic idea: if you know, with some accuracy, what your result should have been, you can tell how far ahead or behind you are in a short sample. That ahead/behind figure would then be your luck.
But to measure the effect of luck with some accuracy, you need a formula which will add up the number of times you got aces, how well they held up, how well they paid off, etc. . . and you also need to know how many you should have gotten, how well they should have held up, how well they should have paid off for your particular style and skill at playing.
But coming up with one big formula which encompasses all the various aspects of luck -- how the cards fall on different streets, whether opponents held enough strenght to pay off, and so on -- is no easy task. Consider the multitude of variables!
Here's a secret
And I'll let you in on it. There is a statistic that encompasses all the varying effects which cause you to win or lose more dollars. And when you compare that statistic to the expected value, you have a perfect measure of your luck.
The 100% most accurate measure of your luck is the number of dollars you win or lose. If you get crappy starters but manage to win money, you have been lucky. If you get great starters but come out behind, you've been unlucky. It's the dollars that tell you, not the cards. The only figure that encompasses all the varying effects of luck is dollars won!
But to use your dollars won to determine your short-term luck, you need to know your long-term expectation. Compare your current Dollars Won to your long-term expectation, and you know if you've been lucky or unlucky with much more reliability than any other possible method.
The irony is, of course, you wanted to know your short-term luck because you don't have a big enough sample to know your long-term expectation yet. But the only way to measure luck in the short-term is to subtract your short-term results from your long-term expectation!
The cold, hard truth
Short-term variance: Luck. Yes, variance is luck.
Long-term result: Skill.
Incidentally, Dollars Won is also the only statistic that encompasses all aspects of skillful play. Look at your long-term Dollars Won and you'll see if you're skillful.
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