In previous posts, I looked at how variance affects players who play large-field MTTs, smaller-field MTTs, NLHE 6-max cash, and 6-man and 9-man STTs, and I found quite a bit of difference. Next up: HU SnGs. (Still to come: HU NLHE, FR NLHE, HU PLO, 6-max PLO, HU LHE, 6-max LHE, and FR LHE. I’m going to be quite busy for at least the next couple weeks, so please don’t hold your breath. Follow me on twitter if you’d like to know when these posts go up.)
HU SnGs are quite simple statistically, so I will make exactly one assumption: rake that is 1/22 of the rake-free buy-in. This is the standard rake for turbos on Stars and FTP at most stakes (e.g. $110+$5), so everything that I say will be exact for those games, but if you play games with a different rake:buy-in ratio, the numbers will be a bit different. To get most of the results, I won’t even bother to assume a normal distribution; I’ll just use the binomial distribution, which is an exact statistical representation of a HU SnG. (This won’t actually change the numbers at all after rounding, but it just requires a bit of extra algebra from me, and it’ll appease some of the statistical purists in the audience.)
Anyway, with that out of the way, let’s jump in. Say you’re a HU SnG pro with a solid ROI of 3% at the Stars $115s. You’re also moonlight as the world’s greatest physicist, and you invent a cloning machine that you planned to use to resurrect Einstein, Lincoln, Ghandi, etc., thus ushering in a new era of global age of peace and prosperity. But, then you remember that rent’s due soon, so instead you make 99,999 clones of yourself and get to grinding. You figure 1k HU SnGs each should cover rent plus some standard expenses. (Trips to the Rhino get expensive when there are 100,000 of you…)
How does this HU clone army fare? Good question!
Well, it’s pretty gross. Almost 16% of the clones lose, and 31% of them earn less than 15 buy-ins (half their equity of 30 buy-ins each). This is worse than what I found in comparable situations for STT players, 6-max cash game players, and small-field MTT players. (It should go without saying that the picture is much worse for large-field MTT players.)
But, hang on. What if the clones were smart enough to get 33% effective rakeback? (Next ethics post: “Should Identical Clones Be Allowed to Create New accounts for Rakeback Purposes?”) Well, let’s look:
Well, it adds a bit over 1.4% to their ROI, and that money is now variance free. Now, instead of 16% of the clones losing, only 7% do. Instead of 31% earning less than 15 buy-ins, only 17% do, and almost 78% of the clones earn over 22 buy-ins (just under half their equity of 44.3 buy-ins). Indeed, the numbers are almost exactly the same as the numbers for 9-man and 6-man STT players. And, 33% effective rakeback is much lower than what the hardcore grinders on Stars make. (I know nothing about FTP’s Iron Man and Black Card programs.)
So, rakeback is pretty awesome for SnG players. I think that a lot of 9-man and 6-man STT players are very aware of this fact, but a lot of HU SnG players are not. Obviously, the rake is about half as high at HU SnGs, so rakeback gives you about half the money, but it still adds up to a lot. If you don’t have rakeback (or the equivalent like a good VIP program or good bonuses), that might change your mind about playing. If you do, they’re a very reasonable option and probably the best choice for a lot of players.
So say you’re grinding HU SnGs for a living, 4-tabling the $115s continuously (which is somewhere between really easy and really hard to do) with a 3% ROI and 33% rakeback . From the time that you finish one to the time that you finish its replacement takes about 12 mins (This might even be a high estimate), so you play 20 per hour. Playing a lazy average of 15 hours per week, you manage about 1,250 SnGs per month, which earns you a comfortable living of about $77k/year. Variance is fairly low, with a roughly 42% chance of no losing months in a year and about a 20% chance of having more than one losing month in a year. Of course, double the stakes, and suddenly you’re making a very substantial living. Double the time commitment (You’ll still be making money playing a card game less than the average working man slaves away at his job), and suddenly you’re making a very substantial living with very low variance.
But, if you’ve read my other posts on this subject, you know that this is when I start depressing you by pointing out that you can never really estimate your winrate. The same is certainly true of HU SnGs. Indeed, the 95% confidence interval for someone with a 3% ROI (before rakeback) goes from -3% to 9%. So, you might be a losing player even after rakeback, or you might be one of the best HU SnG players in the world. The 75% confidence interval is runs from about -0.5% to 6.5%. Still pretty gross, huh?
Can a larger sample help? Well… No. If you want to know your winrate within 1% (e.g. 3% +/- 1% or 2% to 4%) at 95% confidence, you need to play about 34,500 SnGs. To know your ROI within 1% with 75% confidence, you need to play just under 12k SnGs. You can get a 75% confidence interval of +/- 2% (e.g. 3% +/- 2% or 1% to 5%) over 3k SnGs, so that’s sort of some silver lining, but 75% confidence ain’t great and +/- 2% really ain’t great either.
Plus, HU SnGs are constantly in flux. The games can change dramatically depending on who’s playing in any given week. So, extrapolating your winrate from the past to the future in these games is even more risky than in other games. And, HU SnGs are sufficiently complicated that you have basically no chance of estimating your own winrate by comparing yourself to other players (like I suggested in STTs). And, of course, you will be incredibly biased when you estimate your own winrate in general.
So, use of these types of statistics is risky because for many reasons, you might not know what your future winrate will be. The way to combat all of this is to be conservative with your estimates. If your ROI over your last 3k HU SnGs is 4%, then prepare for the possibility that your expected winrate over the next 3k HU SnGs will be, say, 1.5%.
One more caveat, and then the data dump. I’m going to list a few absurdly high ROIs as well because, well, some people table select heavily and some people specialize in goofy games like NL O8 or whatever. The highest I’ve seen over a decent sample at NLHE over the last year that wasn’t heavily table selected was about 6%.
No Rakeback | 33% Effective Rakeback | |||||||||
ROI | n | EV in Buy-Ins | Chance of Losing | Chance of Earning < .5x EV | ROI | n | EV in Buy-Ins | Chance of Losing | Chance of Earning < .5x EV | |
1% | 500 | 5 | 41% | 45% | 1% | 500 | 12 | 28% | 31% | |
1% | 1000 | 10 | 36% | 44% | 1% | 1000 | 24 | 22% | 25% | |
1% | 2000 | 20 | 32% | 40% | 1% | 2000 | 49 | 13% | 18% | |
1% | 5000 | 50 | 23% | 35% | 1% | 5000 | 122 | 4% | 8% | |
1% | 10000 | 100 | 15% | 30% | 1% | 10000 | 243 | 1% | 2% | |
2% | 500 | 10 | 32% | 39% | 2% | 500 | 17 | 21% | 29% | |
2% | 1000 | 20 | 25% | 36% | 2% | 1000 | 34 | 13% | 21% | |
2% | 2000 | 40 | 17% | 31% | 2% | 2000 | 69 | 5% | 12% | |
2% | 5000 | 100 | 7% | 23% | 2% | 5000 | 172 | 1% | 4% | |
2% | 10000 | 200 | 2% | 15% | 2% | 10000 | 343 | One in 6095 | 1% | |
4% | 500 | 20 | 18% | 32% | 4% | 500 | 27 | 10% | 20% | |
4% | 1000 | 40 | 9% | 26% | 4% | 1000 | 54 | 4% | 12% | |
4% | 2000 | 80 | 3% | 18% | 4% | 2000 | 109 | 1% | 5% | |
4% | 5000 | 200 | 0.1% | 7% | 4% | 5000 | 272 | One in 34000 | 1% | |
4% | 10000 | 400 | One in 71387 | 2% | 4% | 10000 | 543 | One in 158676578 | One in 6479 | |
6% | 500 | 30 | 8% | 25% | 6% | 500 | 37 | 4% | 15% | |
6% | 1000 | 60 | 2% | 16% | 6% | 1000 | 74 | 1% | 7% | |
6% | 2000 | 120 | 0.2% | 8% | 6% | 2000 | 149 | One in 4096 | 2% | |
6% | 5000 | 300 | 0% | 1% | 6% | 5000 | 372 | One in 54458250 | One in 2029 | |
6% | 10000 | 600 | 0% | 0% | 6% | 10000 | 743 | Effectively 0 | One in 599125 | |
10% | 500 | 50 | 1% | 12% | 10% | 500 | 57 | 0.3% | 6% | |
10% | 1000 | 100 | One in 2430 | 5% | 10% | 1000 | 114 | One in 13227 | 2% | |
10% | 2000 | 200 | One in 2430 | 1% | 10% | 2000 | 229 | One in 26863766 | 0.1% | |
10% | 5000 | 500 | One in 796102 | One in 10237 | 10% | 5000 | 572 | Effectively 0 | One in 1301633 | |
10% | 10000 | 1000 | Effectively 0 | One in 15269303 | 10% | 10000 | 1143 | Effectively 0 | Effectively 0 | |
20% | 500 | 100 | One in 1007468 | One in 122 | 20% | 500 | 107 | One in 6386830 | 0.3% | |
20% | 1000 | 200 | Effectively 0 | One in 2570 | 20% | 1000 | 214 | Effectively 0 | One in 18754 | |
20% | 2000 | 400 | Effectively 0 | One in 1103626 | 20% | 2000 | 429 | Effectively 0 | One in 40969643 | |
20% | 5000 | 1000 | Effectively 0 | Effectively 0 | 20% | 5000 | 1072 | Effectively 0 | Effectively 0 | |
20% | 10000 | 2000 | Effectively 0 | Effectively 0 | 20% | 10000 | 2143 | Effectively 0 | Effectively 0 | |
30% | 500 | 150 | Effectively 0 | One in 9257 | 30% | 500 | 157 | Effectively 0 | One in 42403 | |
30% | 1000 | 300 | Effectively 0 | One in 9797726 | 30% | 1000 | 314 | Effectively 0 | One in 186234006 | |
30% | 2000 | 600 | Effectively 0 | Effectively 0 | 30% | 2000 | 629 | Effectively 0 | Effectively 0 | |
30% | 5000 | 1500 | Effectively 0 | Effectively 0 | 30% | 5000 | 1572 | Effectively 0 | Effectively 0 | |
30% | 10000 | 3000 | Effectively 0 | Effectively 0 | 30% | 10000 | 3143 | Effectively 0 | Effectively 0 |
(Sorry for the ugly formatting.)
So, once again, your ROI and rakeback (or just your ROI after accounting for rakeback) have a huge effect on how much variance can hurt you. If you have a 2% ROI without rakeback (or equivalently, a 2% effective ROI after rakeback/bonuses/VIP rewards), you’ll lose 25% of the time over 1k tournaments and still 7% of the time over 5k SnGs. That’s obviously pretty gross. Compare that to someone with a 4% ROI and a decent rakeback (or equivalent) deal, who loses only 4% of the time over 1k tournaments and basically never over 5k.
In fact, if you’re really good (i.e. 6%+ ROI) and have decent rakeback, you can make 6 figures a year at these things lazily, at low stakes, and with a pretty negligible bankroll, and extremely low variance. In 92% of years, you won’t experience a losing month if you play at least 1k SnGs per month.. If you’re not very good and don’t have rakeback, these won’t be so fun, and even over very large samples, you’ll be a slave to variance.
If you play HU SnGs for a living or are considering doing that, take a careful look at this table. There’s a lot of information there, and a lot of it will probably be quite surprising.
One teaser of a closing note: HU SnGs are actually remarkably easy to compare to other forms of STTs. In spite of the completely different format, you can play about as many 9-man STTs in an hour as HU SnGs, and ROIs are roughly comparable. Obviously these comparisons aren’t perfect, but this happy coincidence makes this comparison a good rough example to illustrate where I’m going with this: Say you’re choosing between playing 1k 9-mans with a 6% effective ROI and 1k HU matches with the same effective ROI. Which would you rather do? Well, look at the tables: The 9-man option will lead to a 10% chance of loss, whereas the HU options will lead to only a 2% chance of loss.
Of course, this is not the only thing that you should consider when choosing your game of choice, and that example was concocted specifically to illustrate a point. It’s also obviously oversimplified and ignores important questions, like bankroll requirements, skill discrepancies, etc. Of course, it certainly doesn’t mean that HU SnGs are a better choice in general than 9-man STTs, but it sure is suggestive…
I haven’t crunched the numbers yet to do a thorough study comparing the different games. But, that’s where I’m going. Stay tuned.
Great post as always.
for next post FR TAG with 3BB/100 winrate stats would be awesome.
Can’t wait for PLO SH!!! If you would speak about Bankroll requirements it would be even better because i think about PLO BRM isn’t much information available
nice analysis. one of these for hu cash would be awesome =)
thanks for ur work !
Thank you for this!
HU cash, and PLO please
Getting your hands on such a valuable poker advice and experience can help you to gain the edge over other poker players online or offline.Great article post I like it thanks
Hi!
can u make a statistic test about “Life as a NLHE 9” ?
Very very impressive post. This is a must read for anyone playing poker seriously…