Many thanks, guys. 2k games is a tad more reasonable than 1 million. Hooray for cEV in this case!

This factors in the jackpot factor. You could figure out your win rate then use the simulator to account for the jackpot variance, right? How many games do you need to determine your win rate?

EDIT: Just saw ****'s post, thanks.

From what coon74 says above, 1k to 2k games should be enough to figure it out from cEV results. I'm not familiar with the formula linked and not sure to what certainty 1k or 2k games gives.

PT4 already calculates "c net adjusted" in dollars and "ROI adjusted" for example:




Is that accurate? For example if after 1-2k games i have 10% "adjusted ROI" can i be fairly certain that i will sustain 10% ROI after 1,25 million games too (given that opponents remain similar in skill level)?


BTW what i am trying to figure out here is the minimum accepted amount of games i need to play to be close to certain that my ROI is X number. If that number is too low i won't bother with this format, if it is high maybe it is worth the trouble to accept the variance issue. I have already calculated the ROI i need to make this worthwhile.

Assuming it is implemented correctly and the same as used for existing STTs, it will take much more than 2k games, but also a lot less than a million. I don't have an answer yet for what the proper sample size would be for C Net Adjusted and ROI % Adjusted to converge to your true ROI with reasonable accuracy in these games.

If the cEV previously posted is an accurate way to estimate true ROI, I would use that since it reportedly converges much more quickly.

On Monday, Spin & Gos were being detected as 4-max and the adjusted line was equal to the actual winnings line. But, after the tournament detection rules were auto-updated, they started being detected as 3-max, and the EV line became non-trivial.

However, it does take into account the size of the actual prize pool when it's known (i.e. when Hero has finished in the 1st or 2nd place); only if Hero has finished 3rd, and hence the actual prize pool is unknown, PT4 assumes it was average (3 BIs minus rake).

E.g. if you lose a 50/25/25 flip in a $750 Spin & Go for all the 1500 chips and finish 3rd, PT4 will tell that you've gone merely $43.2 below EV because there will be no way to tell from the recorded HH file that the tourney was for $750 and PT4 will deem the prize pool equal to its average, $86.4.

But if you win this flip, PT4 will tell that you've gone $375 above EV because the first place prize will be known from the HH. Likewise, if win a flip for the prize of $60, PT4 will say that you've gone $30 over EV. So this way of evaluation of the EV difference is unbiased because, even for 120+ BI prizepools, PT4 shouldn't take into account the prize pool info even if the player finishes 3rd*.

So the money EV line is still not the best approximation to the expected (ITM-based) winnings, and you should use the chip graph instead.

* While there's no dealmaking facility, the prize pool can be retrieved as 12x of the 3rd place prize if it's more than zero. However, when deals are enabled, there will be no reliable way to retrieve the prize pool if Hero finishes 3rd because, e.g., Hero can get $600 either as a prize in a 240x $30 tourney with no deal or as a prize in a 120x tourney as per a chop deal that was made when Hero had 250 chips.

Ok with the formula above if i use "chips" i have:



for 6000 "chips won": ((27*500+6000)/1500)/27=0,481
for 3000 "net expected chips won": ((27*500+3000)/1500)/27=0,407

so my ROI = ITM * 2.88 - 100%

ROI=0,481*2.88-100%=1,38 or 38% ROI pre rakeback
adjusted ROI = 0,407*2.88=1,17 or 17% adjusted ROI pre rakeback

Are the these calculations correct? My math skills are useless.

Yes, they're correct. Note that the calculated 38% ROI isn't equal to the actual 51% ROI because you ran better at $15s than at $7s.

But of course 27 tourneys are too few.

As a rule of thumb, the one-sided 10% confidence interval starts at roughly the observed ROI minus 1.3 / sqrt(2*#ofgames). (Sqrt is the square root.)

E.g. here, 1.3 / sqrt (54) ~ 17.7%. Hence if your real ROI was negative, then the probability of you running so hot would be less than 10%, which prompts the assumption that you're a pre-rakeback winner (congrats).

Of course the fact that you're a serious player (an a priori winner) makes my prediction of your expected ROI significantly bigger than zero, but that's already the realm of Bayesian analysis, which it would take long to discuss here.

Of course more games are needed to get a more accurate assumption on the ROI.

Thanks for the help!

When i first started playing HUSNGS i used this chart to figure out my true ROI and Win Rate after specific sample sizes:



Is there any way to do something similar for 3max SNGS?

For example you said before that 1-2k matches are enough for 3max. Whats the confidence interval at that sample size?

Surely, but not immediately.

To get a preciser table, I first need to merge my two main databases so that I get a better picture of the extent to which the chip EV is a preciser measure than actual chip winnings (I assumed that 3/4 of the variance noise is removed by accounting for all-ins, but it might be 2/3 or anything)...

I believe the "Effective rake" field gives slightly incorrect result.

The rake on PS.com (above $7) is not 4% but 4.17%, since the buyin is $28.80+$1.20 (1.20/28.80 = 0.041666666666...)

Same with the number of buyins: in 100000 games (300000 buyins) 288000 buyins are awarded. 300K / 288K = 1.04166666667, which means the rake is 4.17%.

Or am I wrong?

You're not wrong, it's just that there are two common ways to calculate rake -- as a percentage of the total buyin (as calculated by SwongSim) or as a percentage of the amount going into the prize pool (as you describe). Either method is fine as long as you understand the calculation. I simply chose the first method because that's how I typically think about it.

$1.20 / $30.00 = 4%

(300k - 288k) buyins / 300k buyins = 4%

Personally I've always found the other way described by sawwee a bit of a misnomer. Percentages should be a fraction of a whole - the whole amount being total money collected in tournament entries or in a cash game pot, the fraction being the amount of rake. So $1.20 from $30.

If you want to express $1.20 vs $28.80, then we have ratios to describe that relationship (1.2:28.8)

rake is 4% not 4,17% definetely.

1,20/30 in this case

It boils down to traditions. Poker rooms used to (and many still do) write tourney buy-ins as the pure BI plus rake, like $20+$2. They hence like to make the rake an integer percentage of the pure BI.

For those rooms that 'integrate' the rake into the buy-in, i.e. write the total BI in the main lobby and state the rake in the individual tourney lobby, like Pokerstars, Full Tilt or iPoker, expressing rake as a % of the full BI makes more sense.

The last but not the least, it's more convenient to calculate ROI with cashback by adding the rake % of the full BI, multiplied by the cashback ratio, to the pre-cashback ROI.

Nice program.

So if 1000 clones of a player with a an ITM% of 35.0% were to play 60000 games, 40% of them will end up losing money (negative ROI)?

For a player with an ITM% of 35.5%, only 10% of the clones will end up losing money?

And a player with an ITM% of 37% will at least have won about 1800 buy-ins (they experience a 3% ROI although their true ROI is 6.5%)?

Interesting.

www.dropbox.com/s/ukpadqy24se12th/SwongSim.exe?dl=0

• Added new lottery-payout schedules for PokerStars Spin&Go. (Effective Nov. 3rd, 2014.)
• Added legend identifiers for traces on the graphical output.

thanks, so there is more variance on new structure right?

I don't know. It looks like swing will be slightly smaller, ROI obviously lower, and it will take longer to have a reasonable shot at realizing full EV (whihc is lower anyway).

Shifting lottery payouts from higher tiers to lower tiers is good. Upping the rake while doing it is bad. Overall, I would call it worse than before, but I haven't studied it closely at all.

Thanks for the great tool and continued work to improve it! I've started grinding the Twister format on .fr (stuck in France for now) after a friend recommended it given the incredibly atrocious field, despite higher rake (7%). I've had a shockingly high success so far, which he predicted, and have to say it's reassuring to see how much confidence can be had in winnings given a high enough ITM% and good RB. Just wondered about one thing. I suppose the likeliness of an early 50+BI downswing accounts for how incredibly likely it is to hit a negative low point? I plan to exercise cautious BRM so it's not scary, just wondered why it's almost unavoidable to hit a negative career low over 6k-10k game samples.

I'm not sure I understand the question perfectly so please ask again if I don't address it properly.

The low point numbers indicate the lowest point reached during the simulation, starting from 0. Since it starts with a low point of 0, the number will never be greater than that (it's impossible to have a positive low point). Given the predominance of 2x payouts in the lottery structure it's likely you start off losing, even if you win some games. So most runs will have a negative low point unless the win rate is high enough to produce a very high expected RIO.

If you're asking about ending with a negative ROI a lot over 6k-10k samples, that's also a matter of it being a small sample for the lottery-payout structure which takes many thousands of games before the average run will reach EV. Even then, a large number of runs can end negatively when the win rate produces a small expected ROI.

I should have worded it better. I meant to say I was surprised by how likely it was to hit a significantly low point (40-50BI in the red) while having a <1% likeliness of being a loser or even less than a significant winner over 10k games given ITM% in the 38-39% range and heavy RB. It makes sense of course if you account for how likely it is to have 50+BI downswings and that you start at 0 winnings. Most of the significantly low points would occur within the first few hundred games, maybe up to first 1k games.

Let's say a simulation tells us that only 10% of our clones have had a low point < -50BI. If we're up 51BI from our original bankroll (B+51) at time T could we consider there's a <10% chance we'll ever fall to future bankroll B' < B? All this is of course assuming data entered into the simulation is accurate to reality. I'm shockingly bad at the math having to do with variance and have probably answered my own question, it's just a part of poker math I have a difficult time with (mostly due to my own laziness in the subject).

Yes, that's exactly correct.

OK thanks And thanks again for your work on this software!

Cheers and gl!