Luck factor

[jordyun]

I mainly play DON and I just figured out how $EV won works. However I don't really think that value represents your luck or you can see your luck from that value. I'm really confused with the session I played yesterday:

70 games, I got 2 outer-ed 4 times (preflop, preflop, flop, flop all in), 1 outer-ed 1 time (flop), AA lost to J2 (preflop), and countless times that my overpair all in on the flop and lost to top pair who pairs his kicker on the turn. Not to mention my KK always loses to Ax. On the other end, I was rarely all in with the worse hand and sucked out. I definitely think that today is a bad day. But I manage to have 6% ROI, +52 profit. And surprisingly, I found that it shows my luck adjusted winnings is 49. WTF? I'm so unlucky the whole session, but I'm still considered lucky and win more than I am expected to win???

As a winning player in the level I play, I think that number almost always under-estimates a winning player's winning. For example in the session that I run like god, win 100+ dollars, it says I win 40 more than expected. Ok this is fine, but in the sessions that I run bad, since I can manage to lose only a little, say -20, it will show that the expected value is 0, that I only lose 20 dollars because of bad luck. But if you sum up the good days and bad days, then it doesn't make sense. After 600 games my lines always show that I won more than I expected. This actually isn't accurate at all.

As a mathematics genius I tried to see where the offset occurs. I'm not quite sure that I'm correct but here are a few points that I found:

1.Say 6 people left, you are the chip leader, and sitting on BB. A short stack with 2BB shove, fold to you, and you call with any trash based on pot odds. If you win, you're considered "lucky" and the "$EV won" is low. In luck-adjusted-winnings it looks like you're running hot but It really doesn't matter much whether you win this hand or not. And calling is definitely a +EV move, but it makes your stat showing that you are lucky in the long run.

2.6 handed too, the blind is huge, and there's one chip leader when all others are short. You're one of the short stack and shove UTG with a marginal hand because the next hand you'll go on the blind and get crippled. And the $EV won doesn't make sense again in this case, whether you won or not. The ICM model still thinks that you have good equity based on the chips counts. But the blind is too huge that you're actually the most dangerous one so you have to move. Again this is a +EV move but once again it makes you look like a luckbox when you win.

3.You were the chip leader and you lost a 70-30% favor and was crippled. Then you won a 30-70% underdog to come back and win. This is only average luck. But in ICM model it shows that you are lucky.

4.Sometimes you won without any all in showdowns. And I'm not sure what $EV win will be, but I know it will be a ridiculous number which either makes you look very lucky or very unlucky.

To sum up, I believe the ICM models are distorted when the blinds are huge. I don't have a solution/suggestion for this, but I do think we can use other values to represent luck at the same time as well. I suggest the following ones:

1.Normalized expectation vs Real Winning
Average of all the expectation when you all in. And see how many pots did you really win. For example, you are all in 5 times with 80%, 50%, 50%, 50% 40% respectively. Then the averaged expectation shows 54%. And if you won 3 of them, you are actually 3/5=60% and is considered lucky. This value can also help you to see if you're all in with the best hand or not.

2.Chips expectation vs Real Winning
Similar to the above, but weighted with chips. So it shows that in all all-in confrontations, how many chips are you expected to win. And of course we can compare this with the actual chips that you win. This is very close to the cEV which is already in the tool, but I don't know why you abandoned this and choose $EV in tourneys calculation. I of course know they're different. But this value is more important to me as it reflects the luck the most.

The above numbers may only be used for HERO. In another word, if two others are all in then it doesn't count. (Well I don't know how to define it if we want to include it. There may be some ways to do it too.)

And the $EV could be kept.

I wanna know how you guys feel about this. If it makes sense then I will post this to http://holdemmanager.uservoice.com/ , thanks.

Jordyun

[netsrak]

I'll forward it to Roy

[Rvg72]

Hi, the method we use is completely accurate. We use ICM which is the independant chip model to determine your hand value. With ICM you can see exactly how much each seat is worth. When you start a $20 SNG your ICM is $20. if you lose a couple of blinds it might be $19.25. If there are 6 players left in a DON and you all have the exact same stack then each player will have a value of $33.33

Now, when you go all-in we determine what your expected value in the hand should be. So we figure out all the calculations and determine the expected ICM value. Then we look at the actual ICM value after the hand and that determines luck.

So in that spot where there are 6 people left and you all are $33.33 and you get all-in and it is exactly 50/50 then your expected ICM is actually $20 since there is a 50% chance you will have a value of $0 after the hand and a 50% chance you will have a value of $40 after the hand. If you lose then you were $20 unlucky. If you win then you were $20 lucky.

This is how it is done and it is the only way to do this properly.

Roy

[Rvg72]

This is very close to the cEV which is already in the tool, but I don't know why you abandoned this and choose $EV in tourneys calculation. I of course know they're different. But this value is more important to me as it reflects the luck the most.

This is actually completely wrong - cEV is a very poor way of measuring luck. In a DON it is not as bad a measure but in most SNG's it is terrible because being 1500 chips unlucky on the first hand is nowhere near as bad as being 1500 chips unlucky when you are on the bubble. $EV captures this accurately

[jordyun]

I understand how $EV works. But ICM model really can't mean anything when the blinds is large compared to your chips. Say 6 people left all with the same amount of chips, and you only have 1.5 big blind left and you are UTG. The ICM will think that you have 5/6 chance to win this, but actually you're the next to post blind so that you are the most dangerous one who at best has 2/3 chance of making it.

The normalized EV and cEV will not be accurate for the result and luck-adjusted winning, but it's accurate for luck only. In fact, luck has many different aspect. As I said, people define luck the way different from the way based on $EV winning. It's not conditional probability. If in a session I am all in 10 times, each time it's a 50%, and I only win 4 times, I'm considered to be unlucky, no matter when I'm all in. You can't say that the times I win is more crucial so I'm lucky. When you get unlucky is another kind of luck for sure, but that's not what people will say about luck. I myself feel sick when I got two outered, but I feel ok if the same session I also sucked out on others. So I prefer a value who can directly reflect what happened when you are all in. I of course feel more sick if I got two outered on the bubble, but everyone feels differently. So I don't think the definition you have on luck is good for everyone. $EV win itself is a weighted factor, so why not let user define their way to weight luck? As a winning player, I just wanted to make sure I'm really unlucky after a session that I think I was sucked out 5 times, rather than winning or losing. In another word, when I win 50 dollars but I got sucked out so many times I still feel sick. If I don't get any suckout and am not winning, I don't feel sick (about luck, but I do feel sick about playing bad :P).

Again, I'm NOT saying that we shouldn't use $EV win. But you cannot use this value to conclude all the luck. Even the two numbers I provided have two different meanings. My suggestion is that keep the original settings while adding the two I provided as optional. Let the user define how they interpret luck. I believe those ones are very easy to include.

jordyun

[henri44]

and a 50% chance you will have a value of $40 after the hand.
Roy

that's surely not what icm would say, and i hope it's not the way hm calculates it. with 5 people to go, if they all had the same stacksize, the value would be 40$ for each player. but in your example you have double the stack of your opponents, but still only 40$ in value? you screwed up somewhere.

[Rvg72]

that's surely not what icm would say, and i hope it's not the way hm calculates it. with 5 people to go, if they all had the same stacksize, the value would be 40$ for each player. but in your example you have double the stack of your opponents, but still only 40$ in value? you screwed up somewhere.

It's a double or nothing. Once it is down to 5 everyone wins $40 regardless of stack size.

[Rvg72]

If in a session I am all in 10 times, each time it's a 50%, and I only win 4 times, I'm considered to be unlucky, no matter when I'm all in. You can't say that the times I win is more crucial so I'm lucky.

$EV doesn't necessarily correspond to "luck". It is expected earnings based on ICM and that is definitely affected by luck.

But... if I was all-in 10 times and the first 9 times I lost and it cost me a $20 buyin each time and the last time it was heads up on the final table of a tourney where the difference between winning and losing could be thousands or tens of thousands of dollars then of course I would feel lucky on the session despite losing 9 of 10 coin flips.

Roy