Doing the math on SNG bankroll management

[WutRUTryin2Hit]

For cash games, I know how to find and use the standard deviation stuff in Pokertracker and pop it into a risk of ruin calculator in order to figure out what kind of bankroll is good, however I haven't ever seen this applied to SNGs at all. Does anyone know the actual mathematical way to determine this stuff or calculate your standard deviation (per hour or whatever) in SNGs? 100 buyins is a nice neat number but I'd like to really get more exact.

[ymu]

http://forumserver.twoplustwo.com/showfl...part=1&vc=1

This should do the job. If it's an updated version of the one I use, it has variance and risk of ruin calcs in it. If not, repost and I'll work out where I got mine from, or post the calcs for you.

[cougar62]

Try this:

http://www.aleomagus.freeservers.com/Spreadsheet/

Some great spreadsheets to calculate that and many other things.

Couldn't open the spreadsheet in ymu's link...

[ymu]

^^Yep - that's the one I use. 'Tis fab.

[Aleo]

The actual calculations to determine a specific bankroll requirement or a specific ROR are:

B=-(SD^2/2W)LN(R)

r=EXP(-2WB/SD^2)

where,
W is your average profit per tourney ($)
SD is your standard deviation per tournament ($)
R is your desired risk of ruin
B is your bankroll ($)

These calculations assume that a player will continue to play at a certain level, and will not cash out profits. This is, of course, a foolish assumption. In reality, we will sometimes cash out profits, and we will sometimes move up or down in stakes.

What this means:

Buy-in Chart
ROR (percentages along the top)
ROI 50% 25% 10% 5.0% 2.5% 1.0% 0.5% 0.1% 0.01%
5% 20.0 40.1 66.5 86.6 106.6 133.1 153.1 199.6 266.2
10% 10.0 20.0 33.3 43.3 53.3 66.5 76.6 99.8 133.1
15% 6.7 13.4 22.2 28.9 35.5 44.4 51.0 66.5 88.7
20% 5.0 10.0 16.6 21.6 26.7 33.3 38.3 49.9 66.5
25% 4.0 8.0 13.3 17.3 21.3 26.6 30.6 39.9 53.2
30% 3.3 6.7 11.1 14.4 17.8 22.2 25.5 33.3 44.4

Note: These figures assume a SD of 1.7 Buy-ins. This is of course, an approximation, albeit a useful one that will roughly approximate most players actual SD.

[WutRUTryin2Hit]

Wow, that's a handy chart, just what I need. I wish I could calculate my true standard deviation though, or at least know for sure that 1.7 is sort of industry standard. But great, thanks!

And the spreadsheet sounds cool, I'll try that soon, I'm kind of Excel-impaired though and only have it on my other computer. But will check that, thanks all.

[Aleo]

Standard deviation in SNG poker is equal to

SQRT((F1)(p1^2)+(F2)(p2^2)+(F3)(p3^2)+(Fn)(pn^2)+( W^2))

where,
F1 = probability of finishing 1st
F2 = probability of finishing 2nd
F3 = probability of finishing 3rd
Fn = probability of finishing nth
(Note: all ‘out of the money’ finishes may be combined as one probability for ease of calculation)
p1 = Net profit for 1st
p2 = Net profit for 2nd
p3 = Net profit for 3rd
pn = Net profit (loss) for nth
W = win (loss) rate in net $/tourney

just for interest sake and cause I'm really just cutting and pasting from stuff I've written some essays about in the past:

Standard Deviation and long term expectation

When we are projecting our expectation over a long term, like the next 50, 100, or 1000 SNGs that we will play, it is not as simple as just multiplying out profit per tourney by that future sample. Yes, we will expect to earn as we have done in the past but in practice, there is a great deal of fluctuation that can and usually will occur. Standard deviation is a useful tool in evaluating the kinds of fluctuations we can expect to encounter.

Total SD after n tourneys equals
(SD*SQRT(n))

This means that in any sample (n) we expect to make our usual profit, but approximately 66% of the time (1 standard deviation), this will vary as much as our total SD above or below this expectation. 95% of the time (2 standard deviations), this will vary as much as double our total SD.

Confidence Calculations

As the # of SNGs played increases, a player's confidence in the statistical accuracy of their results will increase. As such, it is possible to derive a confidence interval based upon the accuracy of results desired. For example, if a player finds that fter a given number of tourneys, they are making a profit of $1.70/tourney with all tourneys having a $11 buy-in, they can say with a derivable degree of confidence that this is accurate to +/- $1 per tourney, +/- $.25 per tourney, or any other value for which they want to calculate confidence.

This is done as follows:

Z = (x (SQRT(n))/SD

Where,
x = +/- $x degree of confidence desired
SD = Standard deviation per tourney
N = total number of tourneys in the sample

This Z value is then converted on a normal distribution table to find an associated A value.

(just google 'normal distribution table')

Once we have converted our Z value to this A value, we can determine confidence.

% Confidence = 100(2A-1)

Winning Confidence

Winning confidence is slightly different, as it not only calculates your confidence in your profit per tourney +/- profit per tourney ($0 to 2x your usual profit), but also every other positive profit value possible.

This means that winning confidence is calculated by doing the usual confidence calculation on +/- W per tourney, where W=your actual win rate, THEN we take that confidence (C) and add (1-C/2). This factors in all the other positive profit possibilities

These confidence calculations assume that SNG tourney results obey a normal distribution. Some have speculated that this might not be true but it has been demonstrated using exact combinatoric calculations of confidence that after even a very small sample of SNGs, the normal distribution model is correct.

Also:

An important thing to remember about money management, bankroll and ROR considerations is that often, they are meaningless. There is no correct bankroll and there is no correct risk of ruin preference. All players will have personal opinions about how much risk they can accept and it is personal factors that should shape money management decisions. The important thing is that we are playing poker with a positive expectation, and as long as we do so, we will ultimately profit, no matter what our bankroll.
For most players, bankroll itself will be a very vague concept as most players are not professionals, and do not need to ‘live’ from their bankroll. For these players, who derive an income from regular employment, the most important aspect of bankroll may simply be that it will last until the next paycheck and can be replaced. If, for some reason, we were inclined to play only 5-10 SNGs each month, we would really only need 5-10 buy-ins to do so, as we can replace those buy-ins by depositing more money online if we have to. Assuming that we are winning players, our expectation will eventually be realized and we will no longer need to make any deposits. Similarly, we might choose to cash out all but 5-10 buy-ins each month. It would again make no difference to our overall profits so long as we can simply deposit more money online to replenish our bankroll if we should fall into a bad steak.
When our bankroll is not easily replaceable, proper bankroll management becomes a concern. College students on a limited budget, low-income earners, and high stakes players may not so easily be able to replace a bankroll and for these types of individuals, it will make sense to have a low risk preference so as to avoid ever having no money from which to play poker.

...

Wow, haven't looked at those old spreadsheets in a long time. Who knew that site of mine was even still going.

Download the file 'confidence calculator.xls'. it has ALL these calculations automated.

My old spreadsheets

[pineapple888]

[ QUOTE ]
The actual calculations to determine a specific bankroll requirement or a specific ROR are:

B=-(SD^2/2W)LN(R)

r=EXP(-2WB/SD^2)

where,
W is your average profit per tourney ($)
SD is your standard deviation per tournament ($)
R is your desired risk of ruin
B is your bankroll ($)

These calculations assume that a player will continue to play at a certain level, and will not cash out profits. This is, of course, a foolish assumption. In reality, we will sometimes cash out profits, and we will sometimes move up or down in stakes.

What this means:

Buy-in Chart
ROR (percentages along the top)
ROI 50% 25% 10% 5.0% 2.5% 1.0% 0.5% 0.1% 0.01%
5% 20.0 40.1 66.5 86.6 106.6 133.1 153.1 199.6 266.2
10% 10.0 20.0 33.3 43.3 53.3 66.5 76.6 99.8 133.1
15% 6.7 13.4 22.2 28.9 35.5 44.4 51.0 66.5 88.7
20% 5.0 10.0 16.6 21.6 26.7 33.3 38.3 49.9 66.5
25% 4.0 8.0 13.3 17.3 21.3 26.6 30.6 39.9 53.2
30% 3.3 6.7 11.1 14.4 17.8 22.2 25.5 33.3 44.4

Note: These figures assume a SD of 1.7 Buy-ins. This is of course, an approximation, albeit a useful one that will roughly approximate most players actual SD.

[/ QUOTE ]

Yes!!! I hit a 1-1000 shot! [img]/images/graemlins/tongue.gif[/img]

[Aleo]

[ QUOTE ]
Yes!!! I hit a 1-1000 shot!

[/ QUOTE ]

Actually, this post brings up another very important point

So lets say pineapple here hit his 1-1000 shot with a 100 unit bankroll and a 10% ROI. (sorry to use you in my example. I'll just be making things up about you for the rest of this post)

We can never be certain what has really happened, and I suspect that his ROI was not a constant 10% near the end of that nightmare. Your past stats just probably will not be accurate after you have lost 50 buy-ins.

In fact, the math probably isn't accurate anymore after you have lost 20 buy-ins. That kind of thing sucks, and tends to tilt players. Even if they say they are zen master poker robot warriors, it affects us all.

So, I think after you have lost (say) the first half of your bankroll, you have a very good chance of losing the last half. Even if you have a 5000 SNG past with a solid 15% ROI, you just can't reasonably expect that you are playing the same kind of game.

Or, maybe after a streak like that you cannot reasonably expect that your opponents are playing the same kind of game. Maybe you are playing at a different time of day? I don't know.

The point is, these psychological considerations mean that most players will go bust more often than these numbers indicate. For some players, much more often.

[pineapple888]

[ QUOTE ]
[ QUOTE ]
Yes!!! I hit a 1-1000 shot!

[/ QUOTE ]

Actually, this post brings up another very important point

So lets say pineapple here hit his 1-1000 shot with a 100 unit bankroll and a 10% ROI. (sorry to use you in my example. I'll just be making things up about you for the rest of this post)

We can never be certain what has really happened, and I suspect that his ROI was not a constant 10% near the end of that nightmare. Your past stats just probably will not be accurate after you have lost 50 buy-ins.

In fact, the math probably isn't accurate anymore after you have lost 20 buy-ins. That kind of thing sucks, and tends to tilt players. Even if they say they are zen master poker robot warriors, it affects us all.

So, I think after you have lost (say) the first half of your bankroll, you have a very good chance of losing the last half. Even if you have a 5000 SNG past with a solid 15% ROI, you just can't reasonably expect that you are playing the same kind of game.

Or, maybe after a streak like that you cannot reasonably expect that your opponents are playing the same kind of game. Maybe you are playing at a different time of day? I don't know.

The point is, these psychological considerations mean that most players will go bust more often than these numbers indicate. For some players, much more often.

[/ QUOTE ]

Good points.

Although it's also possible that you lose 80% of your preflop-favorite and post-flop-favorite showdowns for weeks on end, making all that psychological stuff irrelevant. I've seen it happen, unfortunately.