ROI stands for Return On Investment and in poker terms is used as a measure of player's long-term average profitability. However, in worse case, it may be also negative. The formula and examples of ROI calculation in poker are shown below.
The abbreviation and the meaning of ROI were taken from financial analysis. Apart from that there are other "Returns On ... " such as Return On Assets (ROA) or Return On Equity (ROE).
The general formula of ROI is the following:
ROI = (Net profit ÷ Investment) × 100
or (which is the same):
ROI = (Gain from investment − Cost of investment) ÷ Cost of Investment
And again the 2nd formula is to be multiplied by 100 to arrive at % value. The use and calculation of ROI in poker will be best illustrated by the examples below.
Suppose you have played 1,000 Sit and Go (SNG) tournaments with the buy-in $5+0.5. After the end of the cycle your balance shows $6,000. What is the ROI?
The investment is everything you put into the game. That is 1,000 SNGs × buy-in $5.5 = $5,500. Both parts of the buy-in are included, thereof $5 go into the prize pool and 50 cents is rake, the commission of the tournament facilitator.
The net profit is $6,000 − $5,500 = $500.
ROI = $500 ÷ $5,500 = 0.0909 = 9.09%.
Let us have another example, not a poker-related one for change. The previous example is similar as if you bought goods for $10,000 (the investment or the cost of the investment) and sold it for $12,000 (the gain from the investment). ROI = ?
The solution is very simple. First thing to do is to determine the net profit again, simply by deducting the cost of the investment from the gain of the investment (or the sales of the goods, if you like):
ROI = ($12,000 − $10,000) ÷ $10,000 = $2,000 ÷ $10,000 = 0.2 = 20%.
This example could be spiced up a bit by not including only the book costs of $10,000 to buy the goods, but by adding economic costs as well, which are also known as opportunity costs.
What can we imagine behind that? For example you spent 20 hours of your time on getting this business done and, of course, these costs are not entered into any accounting book. But instead you could have played poker with your hourly rate of $25. The opportunity (or the sacrificed) costs can be expressed in numbers as 20 hours × $25/hour = $500.
The net (economic) profit would be
$12,000 − $10,000 − $500 = $1,500 and
ROI = $1,500 ÷ $10,000 = 0.15 = 15%.
And the last example is very poker-like. Let us have a poker player, who plays Sit and Go mini-tournaments for 9 players with the buy-in $10+1 and the payout structure 50/30/20 (% of the prize pool). We will look into his statistics and find out how many times he has ended up on the first three paid positions:
1st place: 14 times;
2nd place: 13 times;
3rd place: 12 times.
It shows that he has not reached the paid position 61 times (out of 100), however, we do not need this figure in this example.
Let us calculate the prize pool and its division: 9 players × $10 = $90. The first place takes 50% of $90, or $45, the second place is 30% of $90 = $27 and finally the third place is worth 20% of $90 = $18.
Gross profit (before the buy-in deduction) alias "gain from investment" is:
14 × $45 + 13 × $27 + 12 × $18 = $630 + $351 + $216 = $1,197.
Investment, or "cost of investment", is the number of tournaments played × the buy-in of $10+1, thus
100 × $11 = $1,100.
Net profit = $1,197 − $1,100 = $97, and then
ROI = $97 ÷ $1,100 = 0.0882 = 8.82%.
ROI indicates how much you are likely to capitalize on money invested into the game from the long-term prospective. For instance if your average profitability is 10% (in other words ROI = 10%, or 0.1) and you are planning to play 1,000 tournaments with the buy in $5+0.5, your expected profit is going to be 0.1 × (1,000 × $5) = $500. Nevertheless it is need to add that your real profit can deviate from the expected profit as the phenomenon known as the variance can play its part too.
Do you want to improve your poker skill? Do not miss the following articles:
→ Rules of bankroll management – handle your poker funds safely
→ Step-by-step and commented Variance calculation based on a simple example
→ Calculation of poker variance in 9 player Sit and Go tournament
The article is based on my Czech article ROI v pokeru.