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View Full Version : How do ROI and ROR relate?


SuitedSixes
12-14-2004, 08:12 AM
Help me figure this out . . . I am using hypothetical numbers here. If someone is a 40% ROI $11 player, they make $4.40 per tournament. However, if that same player has a 5% ROI at $110, they make $5.50 per tournament. If someone has the normal goals of making as much as possible while not losing their bankroll, which is the best to play? Do you find the highest level in which you have a positive ROI? Does the lower ROI increase the ROR, or is this an incomplete problem without knowing the standard deviation?

AleoMagus
12-14-2004, 11:42 AM
Strictly speaking, this is an incomplete problem without knowing the SD, but we can still come to some definite conclusions with a few generally valid assumptions about SD.

While it is possible for all sorts of weird SD values to be associated with those ROI values, in practice this is just not how it works and we can make some very reasonable assumptions about SD for most SNG players, as most SNG players will have a pretty similar SD just based on the structure of SNG poker alone.

If we assume for example, that the 40% ROI gets that way with a finish ratio of:

1st 15.5%
2nd 15.5%
3rd 15.5%

and the 5% ROI gets that way with a finish ratio of:

1st ~11.5%
2nd ~11.5%
3rd ~11.5%

then the 40% ROI will have a SD of 1.65 buy-ins
and the 5% ROI will have a SD of 1.59 buy-ins

which brings us back to answering your question.

In these two cases, if a player wanted to secure a 1% ROR, the 5% ROI player would need a bankroll of 116 buy-ins, while the 40% ROI player would only need a bankroll of about 17 buy-ins.

So, it is pretty clear that your actual ROR has a lot to do with your ROI. I have actually mentioned this before when talking about the usual 20-30 recommendations. These recommendations are really only valid when speaking about our usual 25%ish ROI benchmark. For a player barely making a profit at all, more is needed. For a player crushing the game, less is needed (and I recommend never assuming that you are crushing a game if bankroll is an issue).

Regards
Brad S

AleoMagus
12-14-2004, 11:47 AM
Here is the actual ROR calculation if you want to mess around with the numbers (though this may be easier to just do with one of the many SD/ROR calculating spreadsheets)

B = -(SD^2/2W)LN(r)

r = EXP(-2WB/SD^2)

where,
W is your profit/tourney ($)
SD is your standard deviation ($)
r is your desired risk of ruin
B is your bankroll ($)

Regards
Brad S

Edit: This thread brings up a couple additional points which are important:

As multi-tabling players typically have a smaller ROI, bigger bankroll is needed. As high stakes players typically have a smaller ROI, bigger bankroll is needed

If players are willing to step down in stakes as they diminish their bankroll (so as to always stay at a certain number of buy-ins) they can significantly reduce their risk of ruin because they effectively are playing with multiple bankrolls. They would figure their ROR for half (or whatever) of their actual bankroll at the level they are playing, then multiply that by another ROR for half of that remaining bankroll at a lower stake, and so on. In this way, 20% ROR at $109 followed by 20% ROR at 50+5, followed by 20% ROR at 30+3 etc... will actually turn out to be a very very small ROR.

What this means is that you can actually maximize profit by playing at higher stakes, and still maintain a very small ROR as long as you are willing to step down when things run badly. It is worth noting that this is psychologically very difficult. you will experience big swings upward this way, which will often crash down again but become 'compressed' as you drop in stakes. Fun

Mr_J
12-14-2004, 12:00 PM
Well I'm a beginner but I'll give it a go.
First of all, obviously variance will be much higher playing the $100s with the much smaller edge.
I think that the $100s may take a little longer on average compared to the $10s because I think alot of players would be looser at lower limits (never played $100s, but it makes sense).

So, while ROI per sng might be higher for the $100, $/hr might be even after taking into account that you have a higher # of sngs per hour at the $11 table.

Also, w/ multi-tabling: I'd take a guess that if this affects your ROI, it has a larger affect the higher the level you play at. Ie, playing 8 at once at $100 will lower your ROI more than if you play 8 at once at a $10. I'm thinking this because opponents will make you think more at higher levels, and with 8 at once you probally don't get much time to think, so you may make more mistaktes??

"If someone has the normal goals of making as much as possible while not losing their bankroll,"

Depends on the size of the bankroll. However, you'd be able to use a much smaller BR (in terms of # of buy-ins) at the $10 sngs since variance is much lower there due to the much higher edge.

"Do you find the highest level in which you have a positive ROI?"

No. You'd find the level where you make the most $/hour.

"Does the lower ROI increase the ROR, or is this an incomplete problem without knowing the standard deviation?"

In this case yes, however a lower ROI doesn't always mean a higher ROR. You don't need to know the standard deviation, you can tell it's much higher at the $100s.