The Affect of Rake, No Rake, and Rakeback on Preflop Strategy

[Benjamin]

[ QUOTE ]
My numbers indicate that in full ring limit hold 'em rake as a percentage of the pot is:

5/10: 3.47%
10/20: 1.30%
20/40 .94%
30/60 .71%
50/100 .67%

To my way of thinking, and bearing in mind the playing adjustments described in the Stox book which makes very fine playability distinctions based on equity considerations, the dfferences here are too small in 10/20 and above to promote looser play. A gifted quant. might be able to show profitability change of one pip of strength if the rake distribution were changed but to my way of thinking it doesn't follow that the effect on ten players would have any marked impact on the looseness of the games. Its too small a shift.

[/ QUOTE ]

Thank you for the numbers. May I ask where they come from? Are they from WPEX alone, or a broader sample? Does the figure come from all hands, or only raked ones? Do you know the average pot-size? Average seeing the flop?

We can probably improve on my numbers above with more exact data.

[jfk]

I pulled the numbers right from PT. They are 100% WPX and cover all hands. I have two DB's and the numbers are slightly different between the two so there is a degree of wiggle.

Also, the 50/100 is all 6 max. I'm not sure there's ever been a bona fide 10 person full ring 50/100 or larger game at WPX.

30/60 has a player average of 7.5, avg. pot of $392.42, SF% 22.8
20/40 has a player average of 8, avg. pot of $243.67, SF% 22.77
10/20 has a player average of 8.23, avg. pot of $117.54, SF% 20.12
5/10 has a player average of 8.66, avg. pot of $57.96, SF% 19.64

Hope this helps.

[Benjamin]

You got the figures from the Summary tab, I take it?

Hmm, the summary tab avg. pot size is significantly bigger than that found on the session notes tab. I have a question posted to the PT forum to see if the summary tab avg. pot is pulled from hands that saw a flop.

For comparison with your numbers, my full ring 10/20 stats from this year at WPEX:

Hands-21.9k, Raked-17.3k Players-7.1, SF%-25.7, Avg rake-2.57, Avg pot-118, % of pot-2.17.

Meanwhile on the Session Notes tab, I see the same number of total hands, average players, sf%, but the Avg. pot is $97.3.

The $97 avg pot seems more in line with what you see on the site. It's rare to find a 10/20 table with a $118 pot average, and I'm sure that's not the long term average, so the summary tab figure must be pulling only from hands that see a flop. I'll confirm when I hear back from PT.

[Benjamin]

OK, heard from PT Pat, and the Avg. Pot number on the Summary tab is derived from:

1) Hands that see the flop.
2) Rake is added back in.

I will have to think about this some more and I will try to improve my model.

[Benjamin]

[ QUOTE ]
Assume 10/20 fixed limit holdem, 10 players, with sufficient looseness that we can say that every pot sees the $3 rake taken from the pot. Assume that these rake conditions are similar to those in effect for this EV chart.

[/ QUOTE ]

Revisiting these assumptions ...

The assumption that every hand goes to flop and is raked is not true in WPEX games. All players will fold to a raise with some regularity. When this is the case you win the blinds and do not get any extra EV from the contributed rakeback.

From my stats about 20% of pots at full ring 10/20 WPEX are unraked.

The assumption that rake will be capped at $3 is also incorrect. PT tells me that the avg. rake over my last 1.5 years at WPEX 10/20 when we see a flop is $2.77.

The assumption that rake conditions similar those I posit, were in effect for the EV chart I link to is clearly incorrect, but it's not really necessary. The EV Chart just gives us a measuring mark to identify a set of marginal hands, so we can more clearly see how their EV changes in the absence of rake.

The EV Chart was probably derived from a game raked 5% up to $3, as is fairly standard online, but it is derived from many limits and table sizes. Most of the hands almost certainly came from lower limits where the impact of rake is more severe than 10/20. So, my estimate, derived from 10/20, may underestimate the lift provided to the marginal hands by removing rake at, say, 1/2. And, it will overestimate the lift at, say, 30/60.

[ QUOTE ]
To make calculations easier, I will consider the scenario of changing the rake/rakeback structure to a contributed calculation where if you see the flop, you split the rake with others who also saw the flop.

[/ QUOTE ]

This method of calculating rakeback is contrived to make calculations easier. It matches neither a rake free scheme (which would reward all rake on a hand to the winner), nor does it match the contributed rakeback scheme used by some online sites where any contribution to the pot earns you a share of the rakeback for that hand (i.e. a folded small blind is enough for a share).

The rakefree scheme introduces the complexity of estimating how often a given hand will win the pot if you play it. The marginal hands that we consider playing are better than hands they will get action from out of the big blind, but they are worse than many hands that they will get action from from the rest of the table. If we assume that the marginal hand will win an equal share of pots vs opponents who see flops with it, then we arrive back to the same situation as my contrived rakeback scheme.

In looking at my personal stats with some of these marginal hands, like 55, J8s, KTo, I find that their 'won money when seeing the flop' percentages range from roughly 35-50%, with most in the low 40s.

The average number of opponents that I see the flop with is not available directly in PT. PT has the See Flop % figure, for instance my recent 10/20 hands featured an average of 7.1 players getting cards and a See Flop % of 25.8%. An average of 1.8 players seeing the flop.

To derive the number of players who see the flop when there is a flop, and using my earlier observation that 20% of the time it's folded around. .2*0 + .8*x = 1.8 and x=2.25.

Equal share with 2.25 people seeing the flop is 44%.

I believe that an assumption that these marginal hands win an equal share vs opponents who see a flop with them is OK. Not exact, but not far enough off to worry about. That means that my contrived scheme of equal payment to those seeing a flop is an OK representation of a rakefree game.

[ QUOTE ]
And I will assume an average of 3 players to the flop. This structure awards 1/3 of the rake, or $1, to us when we see the flop. That is .05 BB. So, the EV of any hand we see the flop with goes up by .05 BB.

[/ QUOTE ]

Putting together previous observations into an EV calc:

20% of the time the hand folds around and you get no benefit from the rake reduction. 80% of the time, we see the flop with an average of 2.25 seeing the flop and a rake of $2.77.

Dividing 2.77 equally by 2.25, we get $1.23 rakeback when we see the flop.

Extra EV from rake absence: .2*0 + .8*$1.23 = $.98

This is basically equivalent to the $1 derived from my first, rougher, effort. So we would see the same set of hands moving up into the playable range, and the same large increase going from 17% of hands played to 24%.

Shocking.

I again welcome reasoned criticism.