Creating first Stat: Won Fair Share Ratio

[silver_nz]

Hi Guys,

I'd like to create a stat to show the number of times I win a pot vs the number of times I should win given how many people are involved.
e.g if every one is playing the same optimal strat, in a Heads-up pot hero should win 50% of time. In a 3 way (sexy) hero should win 33%. In a 4way 25%, etc

so in a 3way, say I am winning 40% of pots, it's 40% / 33.3% = 1.2 - great
If I was only winning 20% of pots it's 20% / 33.3% = 0.6 - not so hot
A raito of 1.0 would indicate winning exactly my fair share of pots, given number of players in the hand.

I thought I might be able to do this by diving the Win% stat by the theoritical optimal %'s.
And use the column cnt_players_ttl to get the average numbers of players in the hands used to generate the win%. Then just need to divide 100 / cnt_players_ttl to get my optimal percentages

so custom stat comes out to be
( ( cnt_hands_won / cnt_hands ) * 100 ) / ( 100 / cnt_players_ttl )



Everything look legit? Anything that I have missed? Any better way to do it?

Cheers for any feedback.

[kraada]

Your formula is unfortunately not quite right - mathematically (X * 100) / (100 / Y) is the same as X / Y. Also (X / Y) / ( 1 / Z) is the same as (X * Z) / Y.

So your formula simplifies down to: (cnt_hands_won * cnt_players_ttl) / cnt_hands. Say you won 15 hands out of 100 that were 10 handed (which has a total of 1000 players). You would expect to win 10 and get 15 / 10 or 1.5 as your ratio. In this formula we get 15 * 1000 / 100. We can see this is not correct.

Instead we want: cnt_hands_won * (cnt_hands / cnt_players_ttl). We can see this checks out on our quick example 15 * (100 / 1000) = 15 * 1/10 = 1.5.

Intuitively, what we're taking is the number of hands we actually won and multiplying it by the expected winrate (there's no need for percentages, that just makes the math more complicated). The result will be exactly what you are looking for.

[silver_nz]

Ah, I see! Great explanation, thanks Kraada.

[silver_nz]

Hmm, actually, seems the formula is not working, I get some very big numbers in reports.

For example, say you won 300 hands out of 1000 that were 3 handed (which has a total of 3000 players)
using: cnt_hands_won * (cnt_hands / cnt_players_ttl)
300 * (1000 / 3000) = 100
^ not a ratio because first number is just the total count of hands won. it only works for 2 digit number of hands.

Instead I played around with ratio divided by ratio:
(cnt_hands_won / cnt_hands) / (cnt_hands / cnt_players_ttl)
( 300 / 1000 ) / (1000 / 3000) = 0.9
which seems right.

also works for orginal example:
won 15 hands out of 100 that were 10 handed (which has a total of 1000 players)
( 15/ 100 ) / (100 / 1000) = 1.5

so its ( x / y ) / (y / z)
I can simplify this down to:
x*z / y^2
Which I also tested and I seems to give legit answers in reports.

Should I simplify for sake of computational speed? or leave it as ratio of ratios for readability?

Does all this look right?

[WhiteRider]

I'm not sure that will work correctly for different numbers of players.
As an extreme example, say you play 10 hands heads up and win 5 and 10 hands 10-handed and win 1 (your "expected" amounts) that would make your expression:

(6 / 20) / (20 / 120)

or:
(6 * 120) / (20 *20)

which is 720 / 400.
Since you won the "correct" number of hands, you'd want this number to be 1, right?

I wonder if this stat might be more use if you split it by number of active players, so you can see if you're winning (for example) more than your share in short-handed hands and less in full ring (and then your expression should work).

Although of course how many pots you win depends on your style of play, and winning more than the average number of hands doesn't necessarily mean you're playing well. If you go all-in every hand you'll win nearly every hand, but you'll probably still lose money. The same sort of thing applies if you play very aggressively (but within a more normal range) - you'll win more pots than a very tight player, but that is no indication of win-rate.

[silver_nz]

Ah, good point, that could have been a nasty hidden problem.

To make the stat properly robust might need to split by active players and then recombine as an average? idk.
Atm I am only using it for zoom poker though, so garunteed to always have 9 players.

Agree, that stat is mostly useful in conjunction with winrate and VPIP. In the same way win% is useful, this is just like win% on steroids?

Cheers for having a look.

[WhiteRider]

Ah yes, for Zoom I think your stat should be fine.