ITH Poker Forum

[toronexti]

If I run 10 guys in the million ($2,150) what are the chances that I'll end up on any given week?

Assuming that they cash 15% of the time, and have a 50% ROI. I'm not sure if you need more info.

[mchilger]

Actually, I think you would need the actual distributions of their payouts to know their standard deviations. If the ROI is achieved by hitting a big payday very rarely, then you would likely lose money every week. If the ROI is achieved by consistent regular paydays, then you might arrive at something different.

Without doing a lot of math, you would expect that 1.5 players would cash on average. Most of the time their cashes would come below $2,000 total, so you'll often be losing money. You lose, you lose, you lose, and then you hit a nice payday every now and then. That nice pay day with eilther 1/ cover your losses or 2/ when it is really good give you your profits. But you could wait a good amount of time before seeing those profits.

From my own personal experience, I play about 10 tourneys on Sundays. I usually lose, and then every now and then I hit a nice 5-digit payday. And then once I hit a 6-digit payday. I don't know how to do the math you requested, but I think the percent you are looking for will be quite low.

Another example, I've played the last two Wednesday night and cashed in 5 of 14 tourneys. This includes a 10th and 14th. I broke even. So a 36% cash rate but not enough to show a profit. It takes top 5 finishes to make money.

I know now what you are looking for, but maybe some intuitive perspective.

Matthew

[the_hawk]

For starters, in a field as big as the Mil you can probably ignore any "interference" effects between your runners - that is, the calculation should be more or less identical to that for a single runner playing the Mil ten times. Building on Matthew's point, IMO a ROI as high as 50% is simply not achievable over any reasonable sample by way of "consistent regular paydays"; it implies deep runs and final table finishes.

The following is a guess - but partly based on looking-up an unnamed ITHer on OPR who happens to have ROI and ITM figures in that ballpark. Running some numbers to give the "right" ROI gives:

1 of 20 cashes is a deep run (defined as a prize of 60 buyins on average)
7 of 20 cashes are a moderate run (15 buyin prize on average)
12 of 20 cashes squeak into the money (3 buyin prize on average)

This distribution, allied to 15% ITM, gives a 50% ROI.

From this, in a sample of 10 tourneys you expect 0.07 deep cashes, 0.52 moderate cashes and 0.9 "squeaks".

I could probably do some more calcs to work out standard deviations etc. but these numbers tell us:

1. You'd expect to get something back just about every week.

2. You'd expect to at least get your money back one week in two. One moderate cash from your field is enough to show a profit on the week, and you'd expect one every other week on average.

3. You'd expect a proper return - in terms of a deep cash - about once every four months (14 weeks)

[toronexti]

What kind of bankroll would that require assuming that your #s are right?

[the_hawk]

What would one advise a MTT regular? You should know better than me. 100 buyins perhaps? That would look about right.

[toronexti]

I guess that makes sense the standard bankroll requirements for someone who plays for themselves would apply when you're staking 10 players into 1 event.

Yeah 100+ buyins. Hopefully someone wins the mil soon

[toronexti]

I posted the same question on 2+2 and got these replies:

Wargawd wrote:

Unless I miss my guess what you really want to know is whether this would be profitable for you.

And moving ahead with that assumption and with the further assumption that 50% is their true ROI over a large (i.e. ideally infinite) sample of comparable tourneys, then of course it would be profitable OVER THE LONG TERM.

If you had a stakeback + 50% of profits type deal then your long term expectation would be 50% of (322.5-215) *10 = $537.50 per week. The only thing then to worry about would be the variance being greater than your backing roll could withstand.

Obviously with 10 identically performing horses the collective variance would be smaller than for any one individual (one will go really deep when the others all bust, and all those scenarios)

The key is that your horses are profitable long term and so you would be as well, sharing in half their profits.

I suspect you're partly after what kind of variance you could expect so you can decide how deep your roll needs to be to avoid going broke. If you like I can point you to some sources and references that could answer that question better than I will here, but we can come up with a crude estimate (again always hinging upon whether that ROI is close to real).

For a single player recommended rolls would be in the vicinity of 200 BI to have something like a 95% confidence of not going broke. With variance reduced by mutiple players the total roll should be therefore somewhat less than 10 times the 200 BI. Just taking a WAG here, I'd guesstimate the number might come out to be somewhere in the vicinity of 1200-1400 BI or in this case $250 - $300k. I might be off a bit but prob not by more than a factor of 2.

MDGordon responded:

If I can remember correctly from my statistics class, to find the required bankroll to back those ten players each week with almost zero risk of ruin, you would take the square root of the sample (10).

So, 200 BI x (sqrt 10) x $215 = 136k

I would look into your actual question OP, I believe you would need to know the standard deviation of profits each week (which would be very high, due to high variance obviously). Long term you would expect to make $2,150 x .5 = $1,075/week, but the standard deviation could be like (let's contrive numbers here) $4,350.

To find the probability that your horses are >$0 on any given week, you'd find a z-score by subtracting the mean ($1075) from the experimental value ($0), and dividing by the standard deviation.

So, in this example, ($0 - $1075)/($4,350) = -.25. You would then check a z-score table to see that the probability of your horses being below the experimental value on any given week is about .4013, and therefore your chances of profiting on any given week is about 60%.

Followed by Wargawd who wrote:

I may be wrong but I think that's off by a factor of 2. I think the error is $2150 translates to 100% ROI (Ie @ 50% ROI, the profit portion is 1/2 the buyin total of $2150, or $1075, and backer gets 1/2 of that = $537.50)

Lemme know if u think I somehow fkd up on ROI calcs

Thx

Thoughts?

[the_hawk]

Thoughts?

These guys are nuts. Specifically, they're blithely searching for the "right" statistical formula without using their heads. 600-1200BI is ridiculous. They are not taking into account the size of the field. For a sensible recommendation to be anything other than that for a single player playing repeatedly (200BI, if you like) then the following must be true:

1. Your runners must meet at some stage

2. Their (distribution of) results must be materially affected by the fact they're playing one another as opposed to a random in the field.

(1) will happen from time to time I guess, but at any given time it's pretty unlikely given the size of the field.

But (2) is the deal-breaker here IMO. This would be really hard to quantify but instinct tells me that even if two of your runners were to meet at the final table - which seems very unlikely as any given runner has something like a 1 in 400 chance of FTing in any given week - the effect of this is going to be very small.

Remember that we are talking about the long-term distribution of finishing positions in a massively multi-field tourney, and if two of your runners meet we're talking about "changing" one player on a 9-handed table. You have to accept that this event will happen often (it won't) AND that if it does happen, it will have a substantive effect on their results distribution (it won't).