A visual on the effect of the luck factor on bankroll

[eastbay]

Lots of posts about streakiness, how bad is this run, etc.

I thought I'd put up a visual on how much of this poker business is luck.

Just to work with concrete numbers let's say you're taking $1k into the $55s with expectations of modest success. You're winning 1st, 2nd, 3rd place 13% of the time each, for an ITM of 39% and an ROI of 18%. Not great numbers, but realistic for a lot of players, especially if they are new to a level.

After 50, 100, 200, and 300 games, the probability curves of ending up with a given bankroll look like this:

http://rwa.homelinux.net/bankroll.pdf

To me, this is sobering. After 100 games, you "should" be up to $2k, but it's not all that unlikely that you'll have gone nowhere; it's equally likely that you could shoot up to $3k.

After 300 games, you could reasonably be up to anywhere between $2k and $6k. The flip side to this is that it's a little presumptuous, even after 300 games, to really make any hard and fast statements about your long-term ROI given just the current state of your bankroll.

Hope you find this interesting and useful for gauging your own success.

eastbay

[parappa]

What is the y-axis on this chart, eastbay?

[eastbay]

Literally speaking, it is the probability of your bankroll being in a bin $100 wide at each of the points after N games.

eastbay

[LinusKS]

I agree with you about how many games you need to get a decent estimate of your long-term results (and thanks for posting the chart, btw), but I have to nit-pick over what you call "not great" numbers.

Look at it this way (and my math skills are terrible, so please correct me if I miss something here) -

If you assume the distribution is roughly normal, and the average player is a loser (because of the 10% fee on every game), the fraction of players with a better than 10% ROI has to be a minority - and the fraction with with nearly double that must be even smaller.

Actually, my math is so bad, I can't even put decent numbers on it. But I'm guessing it must be in the 5% -15% range.

I think that's pretty good.

[zephyr]

good point,

too often we think that an ROI of 10%-20% means we're not that good of a players, when in reality even breaking even means we're doing better than most.

I don't think that player's roi's are distributed normally though, not even roughly normal.

Best regards,

Zephyr

ps. thanks for the good post eastbay, its for the reasons that are so well visualized in your graphs that the game exists with so many people losing money.

[stupidsucker]

I have begun to see on my own that 100 300 or even 500 SnGs cant give you a solid accurate read on your exact roi at all.

Perhaps its just my own shoty play, but after 500 SnGs one bad run of 100 can change your roi considerably. Lets say you have a nice roi of 35% over 500 SnGs at one level. Then you have an even streak of 100 SnGs. It drops your roi by 6%.

Bad runs of 100 SnGs are a painful reality of the game. Am I far off to say that you need well over 1000 SnGS to feel confident about your roi? Most of us want to change our game after a bad run of 100 or so, and this can negativly affect roi in itself (If you start doubting the right play). I start getting frustrated after a bad run of 30, and I shouldnt.

[LinusKS]

You know I've thought about this, and I could be completely off track here, but I think it depends partly on where you play.

If you play at Party, you're bound to have some sharp variance, because of the blind structure, the short stacks, and the high proportion of loose-aggressive players.

If you play at other sites, you may need fewer games to get a rough idea of where you're at.

At Party, though, 1000 may not be too far off.

[KJ o]

[ QUOTE ]
too often we think that an ROI of 10%-20% means we're not that good of a players, when in reality even breaking even means we're doing better than most.

[/ QUOTE ]

Do we know that for sure? Couldn't it be the case that some players are lose a lot and loads of players win a little? Isn't that the case for high-limit ring games (where a bunch of pros beat up on a few rich people)?

[Irieguy]

Actually, variance doesn't have anything to do with the site or blind structure. In the SNG setting, the only thing that affects variance is your ITM%. That's why Eastbay's graph is such a nice demonstration. If you change the ITM% to a higher number, the graph would be broader (representing less variance) at any given N.

But unlike in ring games, where a different structure will affect your variance, in a SNG setting that has finite, incremental outcomes, the only thing that affects variance is the measure of your finite increments (ie ITM%). That probably won't make sense to anybody, but it's true. Perhaps somebody else can state it more clearly.

Irieguy

[dethgrind]

[ QUOTE ]
Actually, variance doesn't have anything to do with the site or blind structure. In the SNG setting, the only thing that affects variance is your ITM%.

[/ QUOTE ]

This is misleading and only partially true. Misleading: the structure and nature of Party Poker (compared to other sites) results in a relatively lesser ITM%. This will in turn affect your variance.

Partially true: It isn't strictly your ITM% that determines your variance, but the specific breakdown of 1st, 2nd, and 3rd finish percentages. This is an important point because increasing your 3rd place finishes may decrease your variance, while increasing your 1st place finishes may increase your variance. But in both cases your ITM% has increased. Also, your ITM% can change without your variance changing.

[Irieguy]

Good points. I should have put the phrase "for a given ROI" after each time I used ITM%.

I find it more helpful to discuss things assuming that your ROI is constant because it takes so very many trials to really know what your ROI is, whereas you can be reasonably confident in your ITM% after around 500 SNGs.

But you're exactly right: on sites with longer SNGs (more chips, slower blind increases), you can acheive a higher ITM and ROI% than on PP... which will decrease your variance. I guess it's a chicken/egg argument- is it the site or the change in ITM/ROI that affects variance? I was just arguing the later- but both are true depending on how you look at it.

Irieguy