~ P O K E R L E S S O N S ~
Predicting ROI in Step SNG's
Step Sit-N-Go's are fairly popular alternatives to playing standard tournaments at a number of online poker rooms. They typically consist of a few different "steps," or different level buy-ins of SNG's, of which the player can start from the very bottom level and make his or her way up to a big payout. Step SNG formats do vary from site to site, and in this specific lesson we are going to be discussing Full Tilt Poker's Tier system.
The Tier system consists of three separate levels, One, Two, and Three. At Tier One there are a number of options, from $4+.40 9-player SNG's to $13+.75 heads-up matches. The two most appealing options that I came across when starting to play these were the $6.50 6-player turbo SNG's, which pay 1st with a $26 Token and 2nd with $10, and the $8+.80 18-player SNG's, which give $26 Tokens to the top 5 and $14 to 6th place. In each case you are looking at a prize pool for the top 1/3rd, and I decided to begin by trying the $6+.50 turbo's. Our final analysis here will cover any range of Tier One buy-in costs though.
With each $26 Token won at the Tier One level, players can then buy in to a Tier Two SNG, for which there are two options - a $24+2 9-player turbo SNG (1st and 2nd get a $75 Token, 3rd get's $66), or a $24+2 18-player SNG (1st - 5th get a $75 Token, 6th gets $57). In this case we are using the latter option, and we will be using the same structure for Tier Three, a $69+6 18-player SNG, for which 1st through 5th are paid $216 Tournament Dollars, and 6th place receives $162.
I should take time to note here the different variety of values involved in this analysis. First we have Real Money - the actual cash funds we are using to buy-in to Tier One SNG's, and the occasional payouts we receive (i.e. 2nd place in a $6+.50 Tier One is $10 Real Money). Secondly there are the Tokens. Both $26 and $75 Tokens can be used as buy-ins into any tournament for their respective amounts, though they can not be turned directly into Real Money. Also, we are going to assume in this situation that these Tokens are being used only for Tier SNG's, and not for other tournaments, which is possible. I will also note that the $24+2 and $69+6 Tier SNG's can be bought directly into using Real Money, but we will not be doing that here. Finally there are the Tournament Dollars, which is the final output for cashing in the Tier Three SNG. We receive $216 Tournament Dollars for a 1st through 5th finish, and we could then use these Tournament Dollars to buy in to an even larger tournament, or several smaller ones. In this situation though we are going to assume that we convert these Tournament Dollars to Real Money, which has a 5% conversion cost. Thus we are going to treat our $216 Tournament Dollars as $205.20 in Real Money.
Now that we've touched on most of the specifics, let's get this analysis underway to see just how much ROI (Return On Investment) we can expect from playing in the Tier system.
The first thing we're going to do is define a few variables that we're going to be using throughout this analysis. Let's start with the initial cost of playing:
SS1 - Sample Size for Tier One (How many Tier One games are we going to play?)
$EC - Entry Cost (Cost per Tier One game)
$TC - Total Cost ($TC = $EC x SS1)
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All of the above variables we can define as real numbers now if we wanted to. For example, let's say we knew we were going to play 50 $6+.50 Tier One SNG's. We would evaluate our cost as follows:
SS1 = 50
$EC = 6.50
$TC = ($EC x SS1) = (6.50 x 50) = 325 (Our Total Cost, or Real Money input, is $195)
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Now let's also go ahead and define some variables that we cannot set values to at this time, but that will be essential in our ultimate ROI calculations:
SS2 - Sample Size for Tier Two (How many Tier Two games we will be able to play?)
SS3 - Sample Size for Tier Three (How many Tier Three games we will be able to play?)
$TP - Total Profit (Our total output, hopefully from Tier Three cashings)
$NP - Net Profit ($NP = $TP - $TC)
ROI - Return On Investment (ROI = $NP / $TC)
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Note that we want our Total Profit to be larger than our Total Cost, giving us a positive Net Profit. Our ROI should then also be positive, and ideally larger than our typical ROI for standard SNG's... a question which we will get to later.
Now we are getting to the tricky part of our equation - the part which will require a little speculation, estimated guesses, and some very important parameters in determining just how much Net Profit and ROI we can expect. There are two main parts to determining what these are going to be - what we are going to win and how often we will win it. Let's start with the easier part first, the "what" we are going to win. This we can easily find out by looking at the values involved. For our 3-Tiered system, there are 9 basic possibilities, 6 of which we will need to use. We can diagram them as follows:
| Tier Payouts: |
One |
Two |
Three |
| Top Finish: |
Tier Two Token |
Tier Three Token |
Real Money |
| Partial Finish: |
Real Money |
Real Money |
Real Money |
| No Finish: |
0 |
0 |
0 |
Remember that for a top Tier Three finish, we are using $205.20 Real Money value instead of the $216 Tournament Dollars value. And in knowing the games for each Tier, and their respective payouts, we can assign values accordingly:
| Tier Payouts: |
One ($6+.50 6P-T) |
Two ($24+2 18P) |
Three ($69+6 18P) |
| Top Finish: |
$26 Token |
$75 Token |
$205.20 |
| Partial Finish: |
$10 |
$57 |
$162 |
| No Finish: |
$0 |
$0 |
$0 |
In the case that we would chose to take a different path through the Tiers, which some of you may do, we would have varying values for these, so I will also go ahead and code these as variables as well, so that our eventual formula can be applied across a range of possibilities. Remember though that in this case, these variables will be set to the values listed above, and I will include them in parenthesis below as well. Also, since finishes resulting in $0 will not have any impact on our Total Profit, we can exclude them from this point on.
| Tier Payouts: |
One ($6+.50 6P-T) |
Two ($24+2 18P) |
Three ($69+6 18P) |
| Top Finish: |
$T1W ($26 Token) |
$T2W ($75 Token) |
$T3W ($205.20) |
| Partial Finish: |
$T1C ($10) |
$T2C ($57) |
$T3C ($162) |
Okay, so now comes the second, and more difficult part of predicting our winnings - the question of how often we can expect to win. If we have previous data to pull from for similar types of games we can use that in making an educated guess, but we basically just want to make sure that we're making honest and realistic measurements. So what we have to do then, is come up with values for the rates at which we will win both Tokens and Real Money. For instance, if I were a break-even Tier One player, I would win 1 out of every 4 Tier One SNG's. My rate for that variable would thus be 25%, or .25. Let's just go ahead and define all of these variables, and then we will worry about coming up with values for them:
| Tier Win Rates: |
One ($6+.50 6P-T) |
Two ($24+2 18P) |
Three ($69+6 18P) |
| Top Finish: |
%T1W |
%T2W |
%T3W |
| Partial Finish: |
%T1C |
%T2C |
%T3C |
Now for the sake of saving you a ton more of reading, I'm going to go ahead and give you the formula in a fairly straight forward explanation, rather than stepping through an entire example and showing you how to derive it. Let's first remember those two variables SS2 and SS3, which represent our sample size for Tier Two and Three, respectively, or how many games we can expect to play at that level given our initial Tier One sample size (SS1), and now combined with our win rates. We can figure these out in such a way:
SS2 = SS1 x %T1W
SS3 = SS2 x %T2W
$TP = SS3 x %T3W x $T3W
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Notice that we can now estimate our total profits by multiplying the number of Tier Three games we expect to make it to (SS3) by the percentage of those that we expect to have top cashes in (%T3W) by the value of a top cash ($T3W, which we already know is $205.20). This is the only profit value we really care about... not our profit margin after Tier One, and not after Tier Two, as that leaves us with Tokens that are not actually Real Money representations.
However, we are still missing something - all of those just-out-of-the-top-prize finishes, for example the $10 2nd place finishes at Tier One. So we must add those to the equation for each Tier, as the product of the rate that we will have a partial finish (i.e. %T1C) by the respective number of games played (i.e. SS1) by the value of that finish (i.e. $T1C, which we know is $10). Let's go ahead and right out this entire equation for the amount of partial finish profits we'll make, and then add it to the Total Profit equation. We're also going to simply our SS2 and SS3 variables in terms of %T1W and %T2W (since we deduct that SS3 = SS1 x %T1W x %T2W x %T3W):
Tier One Partial Finish Profits = SS1 x %T1C x $TIC
Tier Two Partial Finish Profits = SS1 x %T1W x %T2C x $T2C
Tier Three Partial Finish Profits = SS1 x %T1W x %T2W x %T3C x $T3C
Total Partial Finish Profits = (SS1 x %T1C x $TIC) + (SS1 x %T1W x %T2C x $T2C) + (SS1 x %T1W x %T2W x %T3C x $T3C)
$TP = (SS1 x %T1W x %T2W x %T3W x $T3W) + (SS1 x %T1C x $TIC) + (SS1 x %T1W x %T2C x $T2C) + (SS1 x %T1W x %T2W x %T3C x $T3C)
From there we can go ahead and calculate the following quite easily, remembering the formulas listed before:
$TC = SS1 x $EC (Total Cost)
$NP = $TP - $TC (Net Profit)
ROI = $NP / $TC (Return On Investment)
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Alright so that looks like a mess, but it's actually the easiest way to just figure out our Total Profit (and thus our Net Profit and ROI as well) with the least amount of inputs. Speaking of inputs, let's go ahead and create a hypothetical sample problem to see just what kind of returns we could potentially be talking about, and to put this beast of an equation to proper use finally.
We will set our initial sample size at 50 (SS1 = 50), meaning we're going to be playing 50 Tier One $6+.50 games, and we will set up our other constant values as follows:
| Tier Payouts: |
One ($6+.50 6P-T) |
Two ($24+2 18P) |
Three ($69+6 18P) |
| Top Finish: |
$26 Token |
$75 Token |
$205.20 |
| Partial Finish: |
$10 |
$57 |
$162 |
| No Finish: |
$0 |
$0 |
$0 |
| Tier Win Rates: |
One ($6+.50 6P-T) |
Two ($24+2 18P) |
Three ($69+6 18P) |
| Top Finish: |
.30 |
.38 |
.33 |
| Partial Finish: |
.18 |
.04 |
.04 |
Alright, so those win rates should be somewhat reasonable for an above average player. That's all the data we really need, now let's go ahead and calculate this bad boy:
SS1 = 50
$EC = 6.50
$TC = 50 x 6.50 = 325 (we invest $325, and are -$325 in the hole before calculating profits)
$TP = (SS1 x %T1W x %T2W x %T3W x $T3W) + (SS1 x %T1C x $TIC) + (SS1 x %T1W x %T2C x $T2C) + (SS1 x %T1W x %T2W x %T3C x $T3C)
Now sub everything in:
$TP = (50 x .30 x .38 x .33 x 205.20) + (50 x .18 x 10) + (50 x .30 x .04 x 57) + (50 x .30 x .38 x .04 x 162)
Simplify:
$TP = (385.98) + (90) + (34.2) + (36.94)
And finally add it all up:
$TP = 547.12
Let's finish our prediction with the remaining calculations:
$NP = $TP - $TC = (547.12 - 325) = +$222.12
ROI = $NP / $TC = (222.12 / 325) = .6834, or 68.3%
So to sum things up:
SS1 = 50;
$TC = $325;
$TP = $547.12;
$NP = $222.12;
ROI = 68.3%;
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This is a very solid return on investment, though keep in mind that this is using estimated win rate data, which may err on the optimistic side. Still, this ROI is about 3-4 times the standard ROI that we would expect an above-average player to experience with playing strictly standard SNG's at the same level, for instance the $5+.50 9-player SNG's. Even if the data used in this example is a little over-zealous, it's likely that the Tier SNG's would be at least as profitable as the standard SNG's. The issue of time invested is another thing to consider, and we will take a look at that in a later analysis.
One last thing to remember with this evaluation is the concept of variance. Our formula is based on long-term profits, and will become more accurate in reality as the sample size increases, particularly as we begin to collect data that we can then use to better estimate our average win rates. Variance is especially going to be an issue with step SNG's because sample size will decrease as we go up in levels, thus increasing variance with each level; in this situation we will be playing less Tier Three SNG's than Tier Two's, and less Tier Two's than Tier One's. We may do incredibly well at the Tier One level, accumulating 5 $26 Tokens out of 10 games. Then we could do incredibly well at the Tier Two level as well, turning 4 out of 5 of our $26 Tokens into $75 Tokens. We could then have a terrible run of bad luck and bust out in 4 straight Tier Three SNG's, returning almost no profit rather than a potentially very large ROI, even if we only cashed in one. This is the risk involved in the short-term window of opportunity, but over the long-run we should still find Step SNG's to present a very profitable alternative to the conventional SNG circuit.
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