In previous posts, I looked at how variance affects players who play large-field MTTs, smaller-field MTTs, and NLHE 6-max cash. Now, I thought I’d grab some low-hanging fruit in the form of sit-n-gos. It turns out that 9-handed and 6-handed STTs are very similar statistically, so I’ll lump them together below (I justify this in my assumptions section). HU SnGs are next in line, and should be done in a day or two (no promises).

If you’re a fellow nerd, you might want to read about [slider title=”my assumptions”]

1. I’m only going to consider Poker Stars $114 9-mans and $119 6-mans. Some sites have different payout structures. In particular, some sites spread 10-mans and/or 5-mans instead, which obviously changes the payout structure and changes the numbers as well. This analysis will still give a decent picture for all roughly similar games, but keep in mind that it is explicitly an analysis of the Stars $114s and $119s.
2. I’m going to assume normality. STTs are pretty close to normal over samples of 100+ tourneys and essentially indistinguishable over 500+ tourneys, so that shouldn’t be a problem. This follows directly from properties of the binomial distribution.
3. I’m going to assume constant standard deviations. In theory, standard deviation for an STT player is dependent on her win distribution. So, players with different ROIs can be expected to have different standard deviations, and even players with the same ROI could have different standard deviations. In practice, these effects are tiny: Standard deviations vary by only about 20% in 9-man STTs and only about 10% in 6-max STTs over reasonable finish distributions for serious players. I’m not looking to estimate confidence intervals within 10 or 20%, so this should be fine.
4. I’m going lump 9-man and 6-man SnGs together, with a 1.5 BIs/tourney standard deviation for both 6-max and 9-man STTs. I didn’t initially plan on doing this, but it turns out that the numbers are almost identical for the two. Typical standard deviations are about 0.05 BIs/tourney higher for 9-man STTs and about 0.05 BIs/tourney lower for 6-man. So obviously this approximation is good enough for my purposes.

(Of course, if you know basic statistics, everything in this post is derivable easily from the above. So, the real meat of this post is contained in the assumptions, which are all justified by a bit of behind-the-scenes research with sharkscope and windows calculator and some discussions with friends of mine. The rest is essentially just watching me divide by SQRT(n) and plug in to my favorite z-score calculator repeatedly)[/slider].

In my previous posts, I didn’t consider rakeback because it typically varies by stake and becomes much less important at the higher stakes. STT players make a large percentage of their income from rakeback, VIP programs, and bonuses, even at the highest stakes, and it doesn’t vary much by stakes. So in this post, I’m going to talk about “effective ROI”, not ROI. Effective ROI is a phrase (that I made up) that means your ROI after you consider rakeback, bonuses, VIP rewards, etc. In other words,

[latex] \displaystyle (\mathrm{Effective\ ROI}) = (\mathrm{Raw\ ROI}) + \frac{(\mathrm{Rakeback\ etc.}) }{(\mathrm{Buyins,\ including\ all\ rake)}} [/latex]

With that housekeeping out of the way, let’s look at the numbers. Take a player with an effective ROI of 7%. (He might, for example, play $114s with a raw ROI of 4% and earn an additional 3% from Stars VIP program and bonuses–equivalent to a RB % of about 38%.) What happens if he and his 99,999 identical grinder twins (!) play 1,000 STTs each? Well… this does:

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