*Originally posted by Lacas84*

Hi,

Thx for the reply. But i still don't know what to make of these results. It doesn't show variance or luck but expectation. Ok, but what that does really mean?

The terms Luck, Expectation, and Variance are used in statistics applications, they are defined by statisticians and mathematicians, we must use these precise definitions accordingly. The best resource for you would be to review a statistics course on these topics if you want to learn more above and beyond what we discuss in this post, but I predict you will be able to follow along.

A results-oriented measurement of luck could be perceived if you look at street by street equity. This is not really luck, but the brain can certainly use this to comprehend how lucky your results are even though this does not account for the luck included in card distribution or the opponent's decision tree (Collin Moshman has written about this in great detail in his great book

**The Math of Hold'em**). Additionally PT4 can only calculate all-in equity adjusted winnings when all hands that had equity in the pot are known at showdown, this cannot be calculated when the pot is multiway and a player folded such as an all-in preflop, 2 calls, followed by an all-in and a fold on the flop. This results in a bias where only some hands are calculated unless you are playing purely headsup games.

When you convert all-in equity into currency, then we are only discussing the use of expectation. Note that this is not EV (Expected Value), many players wrongly assume this is true. EV is measurement of future results vs an opponent's range (and it is not only during all-ins), where as all-in equity is a results oriented measurement of the share of the pot that we are expected to win - without factoring in skill, range, or fold equity. EV cannot be calculated by a tracker, only a human being can determine the range needed.

All-In Equity is measured in Chips. In a cash game the value of chips is equal to the value of currency that you can win, but in a tournament a one to one correlation does not exist between the number of chips and the prize pool which means we must use ICM (Independent Chip Modeling) to determine the value of each chip, and then incorporate that value with the equity adjusted expectation of the pot to result in your Net Adjusted Winnings. ICM is a complicated topic outside of the scope of this post, it is only calculated at the final table assuming payout structure is know for the event, and it is recalculated as stack sizes change and players bust out.

To reiterate, Net Adjusted Winnings is calculated by correlating the ICM value of each chip, the size of the pot, and the all-in equity adjusted winnings in chips to determine the Net Adjusted Winnings in a currency format - to verify that PT4 is accurate you must review each specific all-in situation at the final table rather than looking at the summed results. For example lets take a situation that is easy to calculate such as a $20 + $1 HUSNG where we know the prize pool is $40 and there are 3,000 chip at play so 40/3000 = .01333333, this means the value of each chip at play is $.0133 for our purposes. Next we consider the total size of the pot - lets say it is 2,202 chips (the villain already took 798 chips from you) this means the total prize pool value of this pot is $29.3599. Then we consider the all-in equity percentage preflop, lets use an example where you are expected to win 81.97% of the time. When you win you will get a pot valued at $29.29, when you lose then the hand cost you $21 (the price of the buyin + fee). The Net Adjusted Winnings stat is calculated by adding the expectation of the hand with the actual results, therefore the calculation is (29.3599 * .8197 - 21 = $3.06631003 which is rounded up to $3.07.

And that is why Net Expectation results can be so confusing, even though they are mathematically correct. In that example your Net Expectation is only $3.07, even though you have 81.97% equity because your stack size is too small, and your opponents stack size is too large, to increase your expectation. As you can see, this is a VERY complicated topic!

I mean if there are 3 black and a white ball in a bag and I get one out without looking I expected it to be black I know theres a chance its gonna be white. Now lets say i do this 4 times and everytime i pull out the white ball even though i expect it to be black every time but somehow i always get the white one. Does that mean im really unlucky?

You are confusing probability with Net Expectation in your example, I feel its better to just use the mathematical analysis shown above than to try to use your simplified example.