How Many Winning Players Are in Cash Games? It Depends on Rake

Original Post on Reddit

How Many Players Actually Win at Poker?

I've put together a chart showing player pool win rates for 6-Max NLHE cash games, from NL10 up to NL500 over tracked sites:

Notice how many more winners there are at NL500? That's because the rake is lower. Reminder that your biggest villain is the house. If you're playing full time, do whatever you can to escape the low-stakes rake trap.

Bayesian Adjustment

As we all know, win rates are noisy as hell. A player's "true" win rate takes a huge sample size to converge. If I were to simply filter out low-volume players, it would bias the data towards stronger regs.

To get a more realistic picture, I've applied a Bayesian adjustment. In simple terms, this method reins in the crazy results from small sample sizes by gently pulling a player's observed win rate toward the population average (which is negative, thanks to rake). The more hands a player has in the database, the more we trust their results, and the less their win rate gets adjusted. This helps correct for luck.

(For the stats nerds: the prior mean is set to the stake's rake, with a standard deviation between players of 8 bb/100)

What Percentage of Players Are Actually Winning?

Definitions:

• Winners: Players with a win rate >0 bb/100 after rake.
• Pre-Rake Winners: Players who would be winning if we ignore rake.

Table 1: Bayesian-Adjusted

Now remember, the Bayesian win rates are pessimistic by design. Bayes pulls winners with small sample sizes down into the negatives (towards rake), so winners here need a good volume AND good results.

Table 2: Raw Win Rates

This is the raw data without any corrections applied. I only filtered out players with less than 100 hands.

In short: about 25-30% of players are winning at poker. Far fewer of them are proven winners over a decent sample. But to be fair, that's not necessarily because they can't win; they simply haven't put in the volume to prove it.

U-Shaped Difficulty Curve

This is the part I find fascinating. If you look at the 'Pre-Rake Winners' in either table, you see a U-shape. The highest percentage of pre-rake winners are at the very bottom (NL10) and the top (NL500), while the middle stakes (NL25-NL200) seem to be a tougher grind.

My theory:

As you move up, two things happen simultaneously:

• Competition gets tougher
• Rake gets lower

As you move up from NL10 -> NL200 you tend to get tougher competition without a big discount on the rake, so the game gets harder. But once you break through that NL500 barrier the game gets easier because all of a sudden you get a huge discount on the rake, and the competition isn't *that* much tougher between NL200 and NL500.

Now to be clear, the "break point" depends on the operator. You can look up the approximate rake by stake in bb/100 using this free resource:

The Discussion

Redditors scanned the post, and chimed in with their thoughts.

— "Interesting stat. I don’t think I’ve ever considered someone to be a winner if they have a negative winrate post-rake. For some reason I thought that the pre-rake winner stat would be higher. Love it."

The pre-rake winner is an "above average" player in some sense. I wanted some rake-neutral measurement.

— "Does adding in the rakeback winners into the equation add anything interesting to the sample?"

Definitely. For simplicity if we assume every player gets 3bb/100 in rakeback, it would shift the entire curve to the right by that amount.

— "What about looking at reg data? Anyone with say, 5k+ hands in a month played. I’m finding a lot of players who I consider regs losing at a rate of something like -1 to -10 bb/100. With rakeback a good amount of them are break even or just slightly winning. This is with samples of only 10-30k hands though."

Volume is strongly correlated with skill. Filtering for players with 5k+ hands (in my total sample on them, not just in one month):

• Pre-Rake Winners: 31.8%% → 70.8%
• Winners: 28.8% → 49.2%
• Avg. win rate of 1.2 bb/100

I don't really have a nice chart prepared for this one, but here's a quick graph. There's definitely some negative skew -- long left tail of losing players but not so many crushers on the right end.

Bayesian Update:

Plugging that avg. win rate into my priors, we can calculate a Bayesian stats for regs:

• Pre-Rake winners: 89.3%
• Winners: 53%

– Pre-rake winners 90% post-rake winners 53%. Jeeeeeezus, the house takes everything.

It actually does, yeah.

If you're sitting at an NL100 6-max table, on average each players loses 7.3 bb/100, which means the house makes 43.8 bb/100 per table.

IDK if it's corporate greed or just like, the amount of unnecessary regulation driving up operating costs, but this much rake is non-sustainable to the ecosystem, which is why so much online poker is moving towards unregulated sites.

— It also means 10% of losing players feed 90% of the population, which TBH sounds sus ...

Yep, not surprising though. The entire poker ecosystem is propped up by a few high volume whales.

— High volume whales that play micro stakes?

Ever heard the legend of Paisting?

News

Player Has First Winning Month in Almost 20 Years (Paisting)

Read

A player named "Paisting" has finally brought a near-20-year downswing to an end, thanks to his own strategy and "fair RNG."

Read

— "Why would you expect to see 20 bb/100 winners? I would be skeptical of anyone claiming to win at that rate in an online pool, the games are too tough."

20 bb/100 is like three standard deviations above the mean so no surprise that it's uncommon.

I think you're objection stems from the fact that a Bayesian correction to win rate is pessimistic. So let's explore without that correction.

Here's a graph (no Bayesian correction) that shows the win rates of NL100 players who've played at least 5k hands [N=2181], well call this the "reg" cohort. This biases the data towards players with higher win rates, but at least their win rates are less noisy.

• 23.6% of regs have a win rate >= 5 bb/100
• 7.2% of regs have a win rate >= 10 bb/100
• 0.69% of regs have a win rate >= 20 bb/100

Regarding my extraction methods: I uploaded hands into Poker Tracker 4, ran a population report, and exported that report into to a spreadsheet.

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