Originally posted by excelgeo
this thread is totally sickbut tell you what, every tuesday i go out with a group of people i dont meeth throughout the rest of the week. 2 of them are mathematicians, one of them is a university lecturer with a Phd dissertation of fractals and chaos.
need help?
Bring those guys here and you will win the thread!
I've found a couple more sites that are helping my understanding of Bernoulii Trials, so I will report back tommorrow to see if I can get an answer to the REAL question here, which is...
If hero has a p chance of finishing 1st, on average how many tournaments would he need to play (n) to expect to finish first 5 times?
Ok I think I have it !
source: http://probabilitytheory.info/topics/winning_losing_runs.htm
n=number of trials
p=probability of event in a single trial
r=the maximum run of successes expected given n
so if ln(n)/-ln(p) = r
then -ln(p).r = ln(n)
Results....
Hero 1st Place % - Ave SNG's to expect run of 5 wins
10% ----------------- 100,000
11% ----------------- 62,092
12% ----------------- 40,187
13% ----------------- 26,933
14% ----------------- 18,593
15% ----------------- 13,169
I hope that this is the right answer, though if the poster with Maths friends could ask them to offer their thoughts it would be great.
I've done another couple of things since posting this last night.
1. Cross-referenced the results with those from Bernouilli Trials formula
ie for p=0.1 I entered n = 100000
and for p=0.11 I set n = 62092
and the results came out all between 57.3-59.3% so it seems close but one method is perhaps slightly innacurate.
2. Calculated EV for each %1st place.
10% -$0.10
11% -$0.04
12% $0.05
13% $0.17
14% $0.34
15% $0.56
Hey, nibbana! Great work, man! Looks like we're really solving this.
So, an edge of 12% is enough to make it +EV! This even looks too good to be true.
I'll try to understand the logic behind these formulas and find possible objections at a later time, tried to do that for a while before posting but I got lost utterly. And I gotta go now.
Thanks for your huge work and interest in this topic!
Am I getting this wrong?
If you have a +ve ROI, it means you are making money? isn't it? no matter how much. The more game you play the more money you earn. If you have a chance to scoop the jackpot at the same time no matter your +ve, you are still winning. isn't it?
let 's say you have 10% ROI. SO with the equation I would need an average of 100 000 games to succeed yes I have spent . let's give it a go if the games are $3.00. yes you might have spent an extra 20.000 in rake but you have made a profit of $30000 so what is the problem. still worth it? and again you might be lucky and make it before the 50000 games.
Am I wrong?
yea you're wrong on two counts !
For a start the 10% in the results refers to 10% 1st place finishes, that is on average you finish first 1 in 10 SNGs, NOT 10% ROI.
Secondly, if your ROI is 10% in a normal SNG then this will naturally drop playing one with an extra rake/fees. So in your example you wouldn't have $30k profit after 100,000 games, you'd only have $10k because of the extra rake, this would go up to $20k if, as expected you got the jackpot. I've realised though that this $0.20 extra isn't totally accurate.
For example - you play 100,000 SNG's at PokerStars $3.00 + $0.40 (13.3% fee)
you make $34,000 so your ROI is 10%.
At PartyPoker you pay $2.40 + $0.60 (25.0% fee), so the equivalent at Pokerstars would be $3.00 + $0.75
so lets play the same 100,000 SNG at Pokerstars with a 0.75 rake
you make $34,000 (you're still contributing $3.00/game to the prizepool so you wouldn't expect this to change) and now your ROI is.... 9.1%.
So it follows that by choosing a PP SNG over a PS SNG you're losing 0.9% ROI. Also if we played a $2.40 tournament with PokerStars equivalent rake we'd have fees of $0.32, so the actual difference in fees is not $0.20 but infact $0.28 !!
so my inital EV calcs were wrong. The results in that table show the $EV of playing a PartyPoker tournament (with the jackpot up for grabs!) over a tournament with 20% fees.
The $EV of playing a $2.4 PP SNG over a PS $3 SNG is
10% -$0.18
11% -$0.12
12% -$0.03
13% $0.09
14% $0.26
15% $0.48
Where the % show how often you finish first in a PartyPoker SNG !
