Risk of Ruin over 7 events

[New2This]

Hello!

A friend will be staking me for several smaller WSOP events, specifically three $1,500 events, two $2,000 events and two $1,000 rebuy events.

I'm trying to help him determine his Risk of Ruin (how likely he is to make exactly $0) over this very small sample. We both understand that the accuracy of this figure will be quite low considering the absurd sample size, but we want to figure it out anyway.

Online my average buyin is ~$70, i regularly place very high in the $75FTP and the $22rebuy on PStars. My online ROI is roughly 80% over 2000+ tournaments, my live ROI is ~350% over 50 games including 4 final tables with significant ($5k+) cashes.

I don't know my ROI in these very large, slow events. I expect i'll be one of the best players in each of the events i play in, perhaps with the exception of the $1k rebuys.

Sooooo, how do i calculate my RoR over this small sample? My friend understands that my average result and the expected actual result will be quite different. I'd presume i'll make it to the $$$ in 2-3 events with a decent shot of getting 1 Final Table over the course of 7 events.

Any ideas?

[SubGreen]

" I expect i'll be one of the best players in each of the events i play in, perhaps with the exception of the $1k rebuys."

how do you figure? that is a bold statement, i don't know anything about you but this seems pretty unlikely

[Yeti]

heh yeah man what are you talking about. 3 cashes and 1 ft? one of the best players there? large slow events? they are pretty much crapshoots!

[sketchy1]

obv a guy named New2This has to be one of the best in the field. they all play like party poker $1 rebuys New2This, you'll own them.

[Greg (FossilMan)]

Even if you are the #1 best player in the field, your chances of making 1 final table out of only 7 tries isn't very good. The field size in the events you mention, if they are all NLH, is going to be over 1,000. Even a great player will make the final table here only about 1 time in 20-30, if that. So, you might be about 5:1 against making a final table in your run, but you've probably got less of a chance than that.

The field size has little impact on your chances of cashing, but they do only pay about 10% of the field. Again, even a great player can't expect to cash more than 1, maybe 2, times out of 7. So, for you to expect 2-3 times is unreasonable.

Have fun, whatever happens.

Later, Greg Raymer (FossilMan)

[SGspecial]

[ QUOTE ]
Even if you are the #1 best player in the field, your chances of making 1 final table out of only 7 tries isn't very good. The field size in the events you mention, if they are all NLH, is going to be over 1,000. Even a great player will make the final table here only about 1 time in 20-30, if that. So, you might be about 5:1 against making a final table in your run, but you've probably got less of a chance than that.

The field size has little impact on your chances of cashing, but they do only pay about 10% of the field. Again, even a great player can't expect to cash more than 1, maybe 2, times out of 7. So, for you to expect 2-3 times is unreasonable.

Have fun, whatever happens.

Later, Greg Raymer (FossilMan)

[/ QUOTE ]

Greg, what events are you planning on playing this year?

[Bonified]

With 10% of the field being paid, the chance of going 0/7 for an average player is (0.9^7) = 47.8%.

Your chance depends on where you stand against the average player. I'm sorry but with this :

[ QUOTE ]
I expect i'll be one of the best players in each of the events i play in

[/ QUOTE ]

you're kidding yourself. If that was the case you wouldn't need to be staked. The best online MTT players are making 20-30K a month and more (see www.officialpokerrankings.com).

Try to have more realistic expectations.

[New2This]

[ QUOTE ]
" I expect i'll be one of the best players in each of the events i play in, perhaps with the exception of the $1k rebuys."

how do you figure? that is a bold statement, i don't know anything about you but this seems pretty unlikely

[/ QUOTE ]

Thanks for all the responses.

I agree my statement is bold and perhaps optimistic. I use this assumption since it would seem to simplify the "problem". We can easiest make presumptions about 3 types of players, awful ones with almost no chance, average ones with a chance reflected based on commonly known statistics, and phenomenal players with figures that exceed currently available benchmarks and may outperform most reasonable guesses.

Since i know i'm waaaay better than average, it seems most useful to presume i'm the absolute best and adjust my guesstimates accordingly, rather than starting with the presumption of average.

I really want to simplify this analysis as much as possible, let's just assume i'm as good as any of the top known players.

[ZBTHorton]

Sure. While we're at it, we should just assume you can see the other players hole cards too.

[Bonified]

OK, I'll leave the assumptions to you, but here's how you work it out. Your probability of cashing in any one event is C. For an average player, C = 0.1 .

Probability of (cashing 0/7) = (1-C)^7 = 47.8% for average player
P(cashing 1/7) = 7 x C x (1-C)^6 = 37.2% for average player
P(cashing 2/7) = 21 x C^2 x (1-C)^5 = 12.5% for average player
P(cashing 3/7 or more) = 1 - (sum of the above) = 2.5% for average player

If you want to know where these numbers come from, google "Binomial Theorem".

Even if you plug in C = 0.15 then P(cashing 3/7 or more) is only 7%, and personally I think anyone who is cashing much more than that is probably losing equity by not "going for the win".