# ROI Expectations vs Winning Players

## Finding the most profitable SNG tables involves avoiding winning players. This article shows you the math of how playing other winners reduced your ROI.

One of the biggest factors in assessing your potential profitability in SNGs is the skill level of your opponents. It makes sense that you opponents get proportionally better as you move up levels - and your ROI thus decreases. But what about the medium levels? On many of the main sites - these are often populated by several winning multi-tablers. This article looks at how playing against other winning players affects your ROI expectation - even when you feel you have an edge against those other winners!

Firstly let us briefly look at where your profit comes from in SNGs. This part is easy, it comes from your opponents mistakes. If everyone played 'perfect' poker then over a large sample you'd all break even and the 'house' would be the only winner (due to the rake).

In the first example we will look at a 10 player SNG where 3 of your opponents are winning players - they make the same number of errors as you! We will exclude rake from the calculations to keep the numbers simple. We will look at it from 3 angles:

### 1) Reduced prize pool accounting for the winning player's profits

10 player SNG - \$100 pool - on 'average' your 3 winning opponents will take home \$12 each, remaining 7 (including you) now fight over 64 / 7 = \$9.1 each - your ROI = 20% so you now can expect \$1.8 + 9.1 or an average of \$10.9 (so your ROI is now 9%)... of course this is simplified - your ROI also affects the other winners.

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### 2) From the perspective of your ROI expectations vs individual players averaged for the table

Expectation vs table. If your ROI of 20% comes from losing players and you now put winners on the table... so vs 9 donks you have 20%, vs 3 winners you have 0% over time. so we reduce your 20% by 1/3rd to reflect your average against the whole table - thats 13.33%

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### 3) Strategy Considerations

Winning SNG players know that profits come from the bubble! The key point here is that winning players make less bubble mistakes. Conversely losing players make plenty - once you have a critical mass of bad opponents at the bubble then your expectation increases. 1 bad player at the SNG bubble may make a loose call and spread your equity to the rest of the table, 2 or 3 bad players are more likely to do this to each other - increasing your profits.

A common response on forums is that the key is to get better than the other winning players – ‘improve to survive’. This advice is well meant but it is wrong. The key should be to avoid other winners when possible instead. The second example below will explain... this one is based on a 'Super-Player' someone so good they have an edge over the other winners!!

## ROI Against Winning Players Part #2 - The Mythical 'Super Player'

First the baseline... 10 players, \$100 prize pool (50/30/20).... our super-player has a 40% ROI (probably not achievable long term but for this example we use it), this is vs the 'average player). Thus for every \$10 invested he makes \$4.

Next we add in 3 winners but exclude the edge against them from our super-player for now. If we give the 3 winners a 25% ROI then \$37.50 is gone from the prize pool (on average) leaving \$62.50 for the remaining 7 players or \$8.90 each... out winner has +40% and so makes (again on average) \$12.46 per game. His ROI with 6 average and 3 winning opponents is 24.6%.

We can then factor in our super-players edge vs the opposition. Here we have to calculate that edge by doing the math backward from the above example.... if our super-player takes \$14 from the prize pool we have \$86 left for the other 9 = \$9.5 each - our 3 winners have 25% so \$11.85 per game or 18.5% ROI - thus the edge of the super player against the 3 winners is 6.5%.

Now we get to the key question - what is the true ROI of the super player vs the 3 winners and 6 losers. Well it is all in the calculations above (40% *6)+(6.5%*3)/9 = 28.8%

So his edge vs the winners has increased his expectation from 24.6% to 28.8%... not much.

The numbers above are simplified but hopefully still make a valid point - winning players at your SNG table are bad for your ROI - whether you are better than them or not!

The solution is two-fold. You need to practice good table selection, that is avoid other winners where possible. If this means spending 10 minutes making a coffee before you start to play then do so - your increased profits will more than make up for it.

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