I've actually won more than I realised...

The PLO has been going great since I made the switch down to $200 max. I have managed to play a decent game on 3 and sometimes 4 tables, although probably 2-3 is best.

When reviewing my results I made an interesting discovery. Well, it interested me anyway, but I like numbers and theories about them. For those who have little interest in this, it’s been nice having you along. Maybe you should spend your spare time reading something decent: maybe a political autobiography or a thrusting novel full of espionage and intrigue.

Anyway, here goes. It’s to do with the calculation of EV in pots that make it to showdown. Here are some assumptions that I have made previously when determining how to estimate my EV (in both showdown pots and otherwise):

Non-showdown wins and losses are ‘pure.’

If you manage to win a pot without showing your cards, the EV is simply your net return. If you lose, your EV is negative to the value of the amount you put into the pot. To this end, the over-riding factor in determining your EV is the result. The number of players seeing the flop, turn or river is irrelevant because your ‘pure wins’ come as a direct result of your actions (betting, raising, check-raising). Your ‘pure losses’ come as a result of folding after having invested money in the pot.

Show-down wins and losses are ‘partial’

They are calculated based on pot equity at the point of betting. For instance, if my AA beats my opponents KK and all the money goes in pre-flop (in NLHE) then my equity is 81% of the pot. If all the money goes in on the turn, my pot equity is 90%

Pot equity

I had calculated pot equity as MB x %W
(where MB = the total money bet on a specific betting round, and %W is the chance that the hand will win by showdown).

On the face of it this seems OK. However, something I never even considered as an option was this: between how many ways do we split the equity on any given betting round? Do we split it between all players who put money in on that betting round? Just those who see the next card? Or just those who see the showdown?

I had been splitting the equity between all players seeing the next card, but this is wrong. When a player folds, either on the current betting round, or on a future betting round, they forfeit their equity in the pot. Therefore, it makes no sense to do anything except allocate pot equity between only those players making it to showdown. I had been calculating equity split amongst all players seeing the next betting round.

In heads-up pots, as most are in NLHE, this makes no difference at all. But in multi-way pots, as many more are in PLO, this understates EV of players making the showdown quite significantly.

Effectively, by betting or raising on the flop, we can thin the field and improve our equity in the pre-flop pot. Obviously, this could mean that we are putting money in at –EV on the flop, but that it a separate matter. If 3 players see the flop but only 2 players go to showdown, it means that the pre-flop pot is ‘owned by’ the 2 players going to showdown.

Conclusion

I realised that I had been under-stating my EV in many pots and have since gone back and re-calculated for all hands in my database.

My 2007 profit figure of $39.65 is now actually $49.35 – a huge increase that has made me feel really good about my play. Obviously, no more money has changed hands but I now realise that I haven’t been as lucky in 2007 as I first calculated. More of my bankroll increase was caused by +EV play than previously thought.

2008

The start to 2008 has been great too, and I have increased my cumulative win-rate to $51.57 thanks to a $100.00 per hour win-rate at PLO $200max (playing on average 2.31 tables)