Luck adjusted winnings in SNGs

[PJs Ronin]

I have a conceptual problem trying to quantify a concept like 'luck'.

[pavels4444]

How is this possible. My graph of only 15s HU SnG (2-man only). Once I'm below and once above EV. What's the explanation? Thanks

Here is the graph in chips (below EV)

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Here is the same graph in tournaments with the new EV (overley net adjusted) (above EV)

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To me, it doesn't make sense in husng

[WhiteRider]

Please see this post earlier in this thread - the development team are discussing these issues.
If you could attach the hand history files for these tournaments to a Support Ticket and post your ticket number here we'll make sure the development team see them - examples are always useful in cases like this.
Thanks.

[Yogi Rob]

How is this possible. My graph of only 15s HU SnG (2-man only). Once I'm below and once above EV. What's the explanation? Thanks

To me, it doesn't make sense in husng

1) Chip EV is hand-by-hand, 2) Tourney "Net Adjusted" is the ICM of the EV adjusted chip stacks of the final hand. For Heads up, 1 is much more important. Please see earlier posts in the thread.

[Yogi Rob]

There does exist a perfect method for luck adjusted winnings in all single table tournaments..<clip> fanagle that with the prizepool and you get a perfect result (easy for HU lol).

I disagree with using the word 'perfect' here esp for non HU, or using that word in any EV discussion, ..but we'll get this method in ASAP.

[Voyeurism]

I disagree with using the word 'perfect' here esp for non HU, or using that word in any EV discussion, ..but we'll get this method in ASAP.

Any news yet on when we are likely to see a beta with this fixed?

[Parket]

I was told in a different thread to wait for the next beta to see the luck adjusted results fixed. But I wonder whether it will fix my actual issue. From reading this thread, it doesn't look like it.

Above I read that for HU SNGs it makes more sense to do a hand-per-hand cEV calculation. But that would still be incorrect as it could lead to results that are bigger than the actual prizepool.
Simple example. Suppose both players have 500 chips.

H1: I win 250 chips at showdown, so cEV = actual result = +250.
H2: We flip and I loose, and we're back at 500 chips each. cEV = 0 (flip).
H3: I again win 250 chips at showdown, so again cEV = +250.
H4: We flip and I again loose, and we're back at 500 chips each. cEV = 0.
H5: etc

So repeat this enough and you see that the total cEV may easily be way bigger than the max. number of chips that can be won. This is also why the cEV per hand graph is also not usable for HU SNGs.

The proper way to calculate this, is to iterate over all all-in hands. In algorithmic terms, this is the recursive definition :
EV (series of hands) =
if (hand is not an all-in) : EV (series of hands - hand 1)
else :
if (our stack is bigger) :
if (we win) : p(win) * prize + (1-p(win)) * prize * (startstack - our stack)/startstack # chip equity when lost
else : p(win) * prize + (1-p(win)) * EV (series of hands - hand 1)
else :
if (we loose) : p(win) * prize * our stack / startstack # chip equity when we won
else : p(win) * EV (series of hands - hand 1)

E.g. if you had a huge chiplead after a number of big showdowns, and then loose 3 flips in a row, this means your EV is already 87.5% of the prize, because you had 3 times 50% to win the tournament.

For +2 players, a similar approach can be taken, but then using ICM values for the moment you bust out of the tournament.

[WhiteRider]

I will make sure Rob sees your reply.

[Zangeeph]

I was told in a different thread to wait for the next beta to see the luck adjusted results fixed. But I wonder whether it will fix my actual issue. From reading this thread, it doesn't look like it.

Above I read that for HU SNGs it makes more sense to do a hand-per-hand cEV calculation. But that would still be incorrect as it could lead to results that are bigger than the actual prizepool.
Simple example. Suppose both players have 500 chips.

H1: I win 250 chips at showdown, so cEV = actual result = +250.
H2: We flip and I loose, and we're back at 500 chips each. cEV = 0 (flip).
H3: I again win 250 chips at showdown, so again cEV = +250.
H4: We flip and I again loose, and we're back at 500 chips each. cEV = 0.
H5: etc

So repeat this enough and you see that the total cEV may easily be way bigger than the max. number of chips that can be won. This is also why the cEV per hand graph is also not usable for HU SNGs.

The proper way to calculate this, is to iterate over all all-in hands. In algorithmic terms, this is the recursive definition :
EV (series of hands) =
if (hand is not an all-in) : EV (series of hands - hand 1)
else :
if (our stack is bigger) :
if (we win) : p(win) * prize + (1-p(win)) * prize * (startstack - our stack)/startstack # chip equity when lost
else : p(win) * prize + (1-p(win)) * EV (series of hands - hand 1)
else :
if (we loose) : p(win) * prize * our stack / startstack # chip equity when we won
else : p(win) * EV (series of hands - hand 1)

E.g. if you had a huge chiplead after a number of big showdowns, and then loose 3 flips in a row, this means your EV is already 87.5% of the prize, because you had 3 times 50% to win the tournament.

For +2 players, a similar approach can be taken, but then using ICM values for the moment you bust out of the tournament.

This is completely wrong. Not sure how you came up with that, but you'll find that if you used it, it wouldn't work at all.

HU SnGs and 9 man SnGs should be treated exactly the same in terms of the calculation. Because when there's two people, the ICM calculations are exactly the same as cash calculations - there's no reason to switch to any other calculation method as they will give the same result.

Also, with the correct calculation it IS possible to win more than the prize pool and lose more than the buy-in. See this topic on 2+2 of HEM's luck adjusted winnings. It has over a thousand posts in because people love to get confused by mathematical calculations. I would read the ones by jukofyork (you may end up more confused if you read posts by others as they are mostly wrong).

[Yogi Rob]

thanks Zangeeph. And thanks Parket, I too am curious as to the reference for that method. I was preparing a pm similar to what Zangeeph posted, but I wouldn't go as far to say "it wouldn't work at all". All of these methods have flaws in my opinion and at best give a rough idea of a luck-neutral result.

The consensus reached in that huge 2+2 thread is how we're going at least for the initial release. I know it's counter intuitive, but Juk explains why it's OK for this value to go beyond the scope of the normal P/L of a tourney.