ROI Confidence
I know we need a ton of tourneys to get a reasonable confidence of an ROI, but there are several factors that need to be considered.
Off the Top of my Head:
a) Field Size
b) Blind Structure (Deepstack/Turbos etc)
c) Payout Structures
Been playing a bunch of $6.60 Turbos that get around 60 players each. I have 346 Tourneys with an ROI = 34%.
That's probably enough to confirm some level of an edge, but how many more do I need to estimate the true ROI?
4 Replies
Good question and small field turbos are actually one of the better spots to get meaningful data faster because variance is way lower than large field MTTs. With 60-player fields and 346 samples at 34% ROI, your confidence interval is probably tighter than you think. I ran similar volume in $7.50 turbos on Stars a few years back and around 500 games my ROI stabilized within a few percent of where it ended up at 2,000. The blind structure in turbos does inflate variance somewhat compared to deepstacks, so I'd say get to 600-700 before trusting the number as truly representative, but you're already in the range where 34% ROI is almost certainly real edge and not pure heater.
Thanks Data Guy!!
In an attempt to come up with a analysis based rationale, I did the following:
1. Organized the data I already have into a distribution of cash rates vs prize sizes and set it = to my current ROI
2. Ran simulations based on samples ranging from 200 up to 5,000.
3. Estimate a confidence interval based on the min - max of the simulation results.
Here's what I came up with for my current sample size = 346
Average ROI from all simulations = 32.9% (pretty close to target of 34)
Max = 55.5% Min = 10.6% Range = +22.5%
So our true ROI is most likely no lower than 32.9-22.5 = 10.4% (edge confirmed)
The results of the same process for other sample sizes
200 Samples = +28%
300 Samples = +26%
400 Samples = +22%
500 Samples = +20%
750 Samples = +15%
1000 Samples = +12%
2000 Samples = +9%
3000 Samples = +8%
4000 Samples = +7%
5000 Samples = +6%
And here's my attempt at a rough estimate: Confidence interval = 420/(samples)^0.5
Well would you look at that!
Somebody already has a calculator for that.
After pecking in my results, it returned the following:
70% confidence ROI range = 18.4% to 48.7%
95% confidence ROI range = 4.6% to 66.3%
I'm going to guess my real edge is somewhere between ROI = 20% & 30%
