Calculating luck

A couple of months ago, after what I thought was a particularly bad run of luck,I came up with a method of quantifying luck. I wanted to make sure my run of poor results was at least partly due to bad luck.



I decided that I would analyse all pots ending in showdown, where the total pot was at least 50 times the big blind. I decided to look at these 'big' pots for a couple of reasons: (1) They were statistically the most significant factor affecting results; and (2) they were relatively few in number and could be reviewed quite quickly.



Basically my calculations determine two things:

- how well (or badly) I got my money in, and

- how was the outcome, compared with the expectation.



Its best to demonstrate my method by going through a few examples. (All examples feature $0.50 & $1 blinds with all players starting the hand with $100. Rake is ignored).



Eg1



- I am on the button with AA, and an early position players raises to $4 with KK, I reraise to $16 and he goes all-in. I call, so the pot is $201.50.



- I am an 81% favourite, so my true win is (0.81*201.5)-100 = $63.22. Or, I have bet $100 and my pot equity is $163.22



- If I lose the pot, I have been unlucky to the tune of $163.22, ie. pot equity compared with return.



- If I win the pot, I have been lucky to the tune of $38.28, again, pot equity compared with return.



Eg2 (same hands as Eg1)



- EP limps for $1, 4 callers for $1, I raise to $6, EP re-raises to $20, everybody fold round to me, who raises again to $40. EP calls and we see the flop. The flop is K82 rainbow, EP check calls my $60 flop bet.



- My EV in the hand is calculated as:

• Pre-flop: (0.81*85.50) = 69.25 +


• Flop: (0.09*120) = 10.80 [I now have a 9% chance to win the pot]


• TOTAL EV $80.05

- My true loss in the hand is $100 - $80.05 = $19.95

- If I lose the pot, I have been unlucky to the tune of $80.05

- If I win the pot, I have been lucky to the tune of $125.45

Adding up all of these hands for a day or so, it can have a huge impact on actuals results. In theory, over time, the impact on results should average out to somewhere approaching 0%.

At the time of writing, I am ahead of the curve. I have won approx $400 more than my calculated EV since 29th May.

This allows me to be more objective in reviewing my results than I might otherwise be. I can look at a good week and keep my feet on the ground because it may be largely due to winning more than my share of the big pots.

What it doesn't do is keep a track of 'situational luck' ie. the luck you need to get in a profitable situation eg. AA v KK. Obviously this should even out over time too, but its a hell of a lot more difficult to calculate than EV luck.

Also. having calculated my 'big pot results' (true and actual), I can then calculate my small pot results. As there are many more of these (approx 95:1 ratio), luck in these pots should even out more quickly.

A side benefit is that I force myself to review all big pots to see how I played them, as well as calculate how lucky (or unlucky) I was.