Tournament buy ins required, do they differ with field sizes

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Tournament buy ins required, do they differ with field sizes

Postby mattywein » Wed Jun 02, 2010 9:07 pm

OK here is a question for you all, but sun in particular.

Can you reduce the buy ins needed for correct bankroll management if you play smaller field sizes. For example should you still have 50 buy ins if you play heads up sng's? Does playing large field MTT's mean you should have a much bigger bankroll?

If so how many buy ins do you need to play heads up with? I personally think that 50 buy ins for heads up is on the safe side if you are a winning payer.

Hope you can help

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Re: Tournament buy ins required, do they differ with field sizes

Postby gp00052 » Wed Jun 02, 2010 9:39 pm

From everything I've read the number for S&G's varies from 25 buyins to 50 buyins per table. I'm probably wrong, but I would think the shorter the field the bigger # of buyins you need. The more skill, the less buyins. One reason for having behind having a proper bankroll for whatever game you're playing is to carry you through the ups and downs The bigger the field the greater number of payouts. I would think you wouldn't need as many buyins for a game that pays 3 spots as one that only pays 1.
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Re: Tournament buy ins required, do they differ with field sizes

Postby mattywein » Wed Jun 02, 2010 11:54 pm

Thanks for the input but I'd disagree. Its not about how many buy ins are available, but what percentage of the field gets paid. In heads up its 50% and in a 9 player sng its 33%. Therefore your would cash alot less often in a FR sng than in heads up.

For MTT's I've noticed that Coop has been without a cash for over 30 games in a row. So it strikes me that you would need more buy ins the lower the % of the field that gets paid.
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Re: Tournament buy ins required, do they differ with field sizes

Postby Quimp » Thu Jun 03, 2010 1:05 pm

Your assumptions are correct Matty. The swings are much greater in MTTs than it is in SNGs for example because variance (from a macro perspective) it is determined by the field size.

Heads-up SNGs have the lowest variance. If you are a winning player with a good win rate, you can have as little as 20 BIs. Now this is not true for HU cash because there is no payout structure and the number of hands you play per hour is far bigger than in any tournament.

In a nutshell, your ROI is probably different in 180's than it is in fields of 500-1500 and 10,000+. For the same buy-in amount ($), you could play with fewer BIs if the field is smaller.

For MTT's I've noticed that Coop has been without a cash for over 30 games in a row

15% ITM means no cash in 30 games happens 0.85^30 = 0.007 or under 1% of the time. If you play 1000 tournament per year, it will happen 7 times.
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Re: Tournament buy ins required, do they differ with field sizes

Postby gp00052 » Thu Jun 03, 2010 2:49 pm

mattywein wrote: Therefore your would cash alot less often in a FR sng than in heads up.


Quimp wrote:Your assumptions are correct Matty..


Sorry. :oops: Perfect example of why you should never open your mouth before you’re sure of what you’re talking about. After researching like I said in my post I was probably wrong and I was right; I’m wrong and you guys are right.
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Re: Tournament buy ins required, do they differ with field sizes

Postby mattywein » Thu Jun 03, 2010 5:29 pm

Not to worry GP. Its nice that there is a discussion on this and all contributions are welcome.

Quimp thanks for the input. 20 buy ins seems reasonable. I'll stick to that heads up and go up to 60 for the 180's. :)
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Re: Tournament buy ins required, do they differ with field sizes

Postby sun137 » Sun Jun 06, 2010 9:02 pm

Only catching up on this thread now.

The short answer is - the buyin ratio does NOT change for field size (HU, SNG, MTT), even if you are playing up to 6 SNG/MTT at the same time (though I would NOT recommend 6 x HU games at once :) ).

MTT.................................50 x Buyin + Fee
10 minute Turbo...................Double Bankroll
5 minute Turbo....................Treble Bankroll
Rebuy..............................Treble Bankroll
Turbo Rebuy.......................Multiply the Bankroll factors together (eg 10 minute Turbo Rebuy = 6 x BR)


The following link (part 7 of the BR series may help explain why):

viewtopic.php?f=10&t=1652

It is important to play a mix of SNG and MTT with your BR, but the critical elements are SKILL, TIME EFFICIENCY and the CORRECT GOAL. You are paying to achieve a positive return over a long period and irrespective of the game type (HU/SNG/MTT) it requires more skill to finish ITM on a more regular basis. I have lifted the key summary points from the thread:

The additional reward for playing SNG games with more players is ONLY beneficial if you achieve a TOP 2 place finish, due to the extra time required to finish the game. This is the reason why, earlier in the series, I suggested larger games should only be played as the bankroll grows (because a growing bankroll indicates an increasing skill level).

The additional reward for playing MTT instead of SNG (small, medium or large) is ONLY beneficial if you achieve a TOP 1% finish due to the extra time required to reach this point, as the prizes for the remaining 2% - 10% of the field are only equal to a normal SNG prize fund. This rule applies even if you are choosing a TURBO MTT.

I must restate, however, the point made earlier in the series - we keep MTT in the mix of games because statistically a good player will, in time, with the volume of games played, hit a top 1%/FT finish and the reward will be equal to almost a year normal cash/SNG profit for an equivalent buyin level. It is also for this reason we do not rely on MTT solely for Bankroll Building.


and

If you examine the potential prize v the time taken however, for SNG (non MTT games), an interesting pattern emerges. Positions 1/2/3 in a single table (9 player game) equate to 2/3/4 in an 18 player game, 3/4/5 in a 27 player game and 5/6/7 in a 45 player game and 8/9/(10-18) in a 180 player game - basically the first 3 places in the single player game become the last 3 places in the multi player games.Therefore you MUST play for a higher place than this is the bigger games, otherwise it is NOT worthwhile.


and

There is increasing reward in achieving an 'additional place' finish to match the extra risk involved due to the larger field (1st in an 18 player game, 1st/2nd in a 27 player game, 1st/2nd/3rd in a 45 player game, 1st - 7th in a 180 player game).

THere is absolutely NO BENEFIT in playing multi table games if an 'additional place' finish is NOT your aim. You may as well stick with single table SNG because your bottom line profit, in relation to the time you actually play dictates this to be the case.


and finally,

The most cost effective table?

The answer goes back to the earlier guideline - as the bankroll improves, the skill level will have improved, so play against a larger number of players - because the additional reward FAR OUTWEIGHS the time taken and the 180 player standard blinds game is the best option for the skilled player. The less skilled player should stick to the smaller games as they will produce more consistent reward. The simple logic is the more hands you play, the more chance of a less skilled player making a mistake.

I do not like turbos, but am persuaded by the logic and time factor that they are THE BEST OPTION for a very skilled player, as the reward/time ratio is considerably greater than for a standard game. However, the bankroll guidelines MUST be adhered to for turbo events (a 5 minute turbo requires TREBLE the bankroll) as the additional variance can, in the short term, cause problems for a player who does not have sufficient funds to manage short term fluctuations.


The BR Series is 2 years old now, but the sequence remains - play SNG to build up the BR initially, moving to bigger games but chasing the additional places for extra profit, playing the 180s as the most cost effective AND Time efficient game and with an increasing skill level building a high volume of MTT to allow the maths to force you to a FT.

The HU games have the same principle, the higher your HU skill level, the more HU games you should play as a % of your overall number of HU/SNG/MTT games. You need an edge in a 50% payout game and limited skill = no edge and eventually no Bankroll. The 50% v 33% payout for 2 v 9 players is a trade off between the number of tables you can play at one time for the best overall WR/hour (assuming equal solid skill levels).

It should be noted solid HU play is critical for long term SNG success and solid SNG play is critical for long term MTT success - but the SNG/MTT games should be used to build a BR at the start before playing any HU games once a good skill level has been developed.

You stick to the same 50 x buyin ratios all the way through and variance will not be an issue.

Coop began with the $0.10 MTTs and played a large volume of them, hitting a final table and moving up to the $0.50 and then $1 events, before making his mark on the $3, $5, and $11 MTTs. He would play more MTTs in a day than most of us would enter in a month - multi tabling to make maximum effective use of available time.

It is possible to go for long periods (15+ games) without cashing and a 50 x BR will cover this occasional variance - you should regard the ITM events as 'stops at a petrol station to refuel' on your journey towards the big petrol depot at the end of the road, because unless you play enough volume and have enough skill to go deep ITM/FT/Top 3/Win, you will be on the road stopping at petrol stations for a long time.

If you would like to see a table showing the comparison in prizes for SNG/MTT $10 buyin events, expressed in $ value and number of buyins, the table below should be helpful in working out the best use of your time (based on your skill):

Image

Image

The SNG 1,2,3 % for a 10% ROI shows the % places (of 1st, 2nd and 3rd combined) required over the long term for 10 and 9 player tables - the same 1st place should be used except in the last row.

The Right Hand Section shows prizes as the number of buyins and the top right section shows the number of levels to be played to reach ITM, FT, Top 3 and Win events. All SNG/MTT have an average Green M Zone for the first 3 levels, Yellow for levels 4 - 6, but it changes from level 7 when the antes kick in - SNG move into the Red M Zone and MTT move into the Orange M Zone for average chip stacks. The MTT average moves back into Yellow M Zone with around 50 - 100 players left.

The middle section (just below the top) shows the average cost per hour for each event as well as the ITM prize value per hour and win value per hour. The average ITM profit per hour (prize - cost) falls as the number of players in the event increases, but the average Win profit per hour increases dramatically. This is the key reason why SNG should be the main focus as a % share of games played at the start of the BR building process, but the MTT % of games played should increase as the skill level rises with more experience.

The BR ratio never changes.

I know it is a longer post than you possibly expected, but I hope it answers your question.
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Re: Tournament buy ins required, do they differ with field sizes

Postby mattywein » Sun Jun 06, 2010 10:21 pm

Thanks Richard. I have one question that I don't think you have covered and its quite specific to what I want to achieve.

I am rebuilding a bankroll on Pokerstars. I am playing heads up sng's. I have a fairly high skill level at HU and am confident of a 60%+ itm rate playing 1 table at a time. Can I play with a smaller number of buy ins say 20-30 without the risk of going bust increasing? My gut feel is that I can, but I'm not capable of working the maths out.

sun137 wrote:STEP 1 - Review the Bankroll Guidelines for each type of game

FL Cash...........................300BB
NL Cash...........................15 x Max Buy in
SNG.................................40 x Buyin + Fee
MTT.................................50 x Buyin + Fee
10 minute Turbo...............Double Bankroll
5 minute Turbo.................Treble Bankroll
Rebuy..............................Treble Bankroll
Turbo Rebuy.....................Multiply the Bankroll factors together (eg 10 minute Turbo Rebuy = 6 x BR)


I note in this post that you only need 40 buy ins for SNG's. I would take this to mean that because the field size is smaller and itm is easier to obtain then you should need even less for heads up.

Thanks in advance.
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Re: Tournament buy ins required, do they differ with field sizes

Postby Quimp » Sun Jun 06, 2010 10:58 pm

This leaves me surprised. I was thinking that since we have a different ROI/win rate in each format, then by definition the number of buy-ins required should be different.

Digging in my database, I get the following results (since September 2009). I don't have 6/9-man STTs resuts on this computer (except for a few satellites which are wrongly marked as -100% ROI).

HU SNGs at 2$
games: 807
variance: 3.9
ROI: 9.1%
bankroll required: 53.65$ for a 1% risk of ruin
buy-ins required: ~25

MTTs below the 5$ level
games: 257
variance: 122.4
ROI: 57.5%
bankroll required: 354.32$ for a 1% RoR
buy-ins required: ~160 for the 2$
With a RoR of 5%, I can play with around 70 buy-ins.


My MTT results are very skewed because of a deep cash that is not included in the above numbers. With it, it marks my required bankroll as an astronomical figure (more than I've ever won despite a positive ROI, due to the high variance in my results). So, I know my samples are small and I know the above numbers are not revealing everything, but I thought the trends were interesting:
1) increase in variance as the field increases;
2) consequentially, increase in buy-ins required as the field increases.

It has always been in my mentality to treat each level and game structure differently but perhaps these even out in long-term if you are a consistent player? I can see myself play HU with 30 buy-ins but I wouldn't dare playing large field MTTs with so few buy-ins. It might be that my MTT skills differs from my STT skills? But isn't that to be expected?

My gut feel is that I can, but I'm not capable of working the maths out.

If you use HEM and you have a big enough sample size of HU SNGs, hit me up and I can show you how to run the numbers like I did above. For what it's worth though, you can probably achieve a 12% ROI if you are very skilled, 1-tabling and playing on Stars (the blind levels last longer than on FTP I believe). 60% ITM is possible (I run at 58%).
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Re: Tournament buy ins required, do they differ with field sizes

Postby sun137 » Mon Jun 07, 2010 3:27 pm

This leaves me surprised. I was thinking that since we have a different ROI/win rate in each format, then by definition the number of buy-ins required should be different.


I understand the logic of the argument Quimp, but the reason for 2 approaches is a bit more complex.

The standard 'one fits all' 40 or 50 x BR ratios are designed for new or less experienced players who should not be thinking about more aggressive BR strategies or changing their BR ratios every month to reflect performance. They are quite comfortable ratios when starting out and allow the player to focus on decisions at the table. The modest increase from 40 buyins to 50 buyins (SNG to MTT) reflects the increased chance of poor decisions for an unskilled player during the BR building phase.

I don't recommend players altering their BR buyin ratios to reflect actual ROI% until they are experienced with a long term WR (1500+ games in any type of SNG or MTT). The accuaracy of past WR is not credible until reaching this number of games (about 20% accurate after 200 games, 40% after 500, 60% after 1000 and 80% after 1500) and it is safer to use the standard 40 or 50 x buyin figures.

It also allows a player to look at the most efficient use of playing time, find a game they are good (and profitable) at and develop key skills in that area - playing around with BR ratios is for the experienced players.

If you look at the initial ITM prize for a 9 player $10 SNG in the table, it is $18. However you earn the same amount in a 3000 player $10 MTT event when you reach ITM at position 432 on level 13. The SNG is usually HU by level 14 ($27 for 2nd place in the SNG is equal to 288th in the MTT) and over by level 15 ($45 for 1st place in the SNG is equal to 90th in the MTT), but $45 is the most you can earn in the SNG - you can go up to $4425 for a win in the MTT.

Therefore you need to look at your effective profit per hour for SNG v MTT to establish which event is more worthwhile and make a decision:

Do you focus on your current 'best' event or try harder to improve in the other events to obtain a better all round game (and how many tables you can play at once).

It is not possible for a less experienced player to make these decisions profitably.

I am rebuilding a bankroll on Pokerstars. I am playing heads up sng's. I have a fairly high skill level at HU and am confident of a 60%+ itm rate playing 1 table at a time. Can I play with a smaller number of buy ins say 20-30 without the risk of going bust increasing? My gut feel is that I can, but I'm not capable of working the maths out.


I will cover your 60%+ ITM and BR for different ROI below but suggest reading the following thread first viewtopic.php?f=9&t=7809 and I would also recommend bookmarking the Web 2.0 Scientific calculator at web2calc (it is .com but I didn't want to provide a direct link from TI as per site guidelines).

OK, we now know our Bankroll reflects different levels of Comfort, Win Rate, Standard Deviation and the level of Risk of Ruin we find acceptable. This 'comfort' approach is a more accurate way to establish the level of BR needed based on past performance but is no guarantee of accuaracy for future performance (unless our future WR and SD match our historical data).

The key information:

BR = Comfort Level x SD^2 / Win Rate, so CL = BR x WR / SD^2 OR BR = -(SD^2 / 2 x Hourly Win Rate) x the Inverse of the Risk of Ruin

The Risk of Ruin is e ^(-2WR*BR / SD^2) or e to the power of -2WR*BR / SD^2 OR e^-2*CL (e to the power of -2*CL) and we normally use a ROR of 5%, 1% or 0.1%

e = the constant 2.718281828

The inverse of 5% or 0.05 = -3.0
The inverse of 1% or 0.01 = -4.6
The inverse of 0.1% or 0.001 = -6.9

The Range of expected future Win Rates = WR + or - Level of Confidence x SD / SQRT of hands played

68% Level of Confidence = 1
95% Level of Confidence = 2
99.7% Level of Confidence = 3

p = probability of winning
q = probability of losing OR 1-p
x = winning value
y = losing value

Variance (V) = SD^2 [Standard Deviation Squared] OR px^2 + qy^2 - WR^2

The standard SD for SNG is approx 1.7 buyins
The SNG ROI = WR for the ROR formula

Example with 60% ITM in HU SNG

It is possible you could use a lower BR ratio Matty, but I need your ROI and SD to work out exact BR and ROR figures. I will give you a wide selection to work from to show you the expected BR ratios for ROI between 10% and 60% (you can use your own figures in the formula below):

If we assume an average Comfort Level of 3 and the standard SNG SD of 1.7:

60% ROI.................BR = 3 x 1.7^2 / 0.6 = 3 x 2.89 / 0.6 = 8.67 / 0.60 = 14.45 buyins AND ROR = e^(-2*0.6*14.45 / 1.7^2) = e^(-17.34 / 2.89) = e^(-6) = 0.25%
50% ROI.................BR = 3 X 1.7^2 / 0.5 = 3 x 2.89 / 0.5 = 8.67 / 0.50 = 17.34 buyins AND
40% ROI.................BR = 3 X 1.7^2 / 0.4 = 3 x 2.89 / 0.4 = 8.67 / 0.40 = 21.67 buyins AND
30% ROI.................BR = 3 X 1.7^2 / 0.3 = 3 x 2.89 / 0.3 = 8.67 / 0.30 = 28.90 buyins AND
20% ROI.................BR = 3 X 1.7^2 / 0.2 = 3 x 2.89 / 0.2 = 8.67 / 0.20 = 43.35 buyins AND
10% ROI.................BR = 3 X 1.7^2 / 0.1 = 3 x 2.89 / 0.1 = 8.67 / 0.10 = 86.70 buyins AND

All the above examples will give a ROR of 0.25% (the first ROR is worked out).

A 10% ROI with a SD of 1.7 would need approx 67 buyins for a 1% Risk of Ruin and approx 100 buyins for a 0.1% Risk of Ruin.

We can (using the other BR formula) show the detail to prove this:

BR = -(1.7^2 / 2*0.1) * Inverse of 0.01 = -(2.89 / 0.2) * -4.6 = -14.45*-4.6 = 66.47 buyins (for a 1% ROR)

BR = -(1.7^2 / 2*0.1)* Inverse of 0.001 = -(2.89 / 0.2) * -6.9 = -14.45*-6.9 = 99.71 buyins (for a 0.1% ROR)

The current expected ROI for low to high SNG buyins is as follows:

$11s - 20% ROI
$20s - 15% ROI
$33s - 10% ROI
$55s - 8% ROI
$109s - 7% ROI
$215s - 6% ROI

Therefore the 40 - 50 buyin figure is a reasonable general guide for bankroll builders at the low levels but it is important to work out your true BR figure based on performance as you move up to the $11 events and beyond.

You may also adapt the standard Kelly formula to obtain a more aggressive BR strategy based on positive past performance:

f = ROI * ITM / (ROI + (100 - ITM)) where f is equal to the % of overall BR to use to buy into an event.

If you have a 10% ROI and 60% ITM:

f = 10*60 / (10 + 40) = 600 / 50 = 12%

If total BR = 100%, the 1.2% figure for f allows you to play with 100/12 = 8.33 buyins

An increase to 20% ROI but a fall to 30% ITM produces a figure of 6.66% for 15 buyins (20*30 / 20+70)

You can work out the increased ROR in the normal way described above for the reduced BR ratio.

The Kelly principle relies on strict discipline to move down after losses, so it is important to produce a total BR table for buyin levels above and below your initial entry level AND to move down if you reach half way between the BR figures for 2 levels.

If the Kelly formula is too aggressive, apply the half Kelly and double your buyin ratio to obtain a new BR requirement.

SUMMARY

There are a number of methods for working out BR requirements for SNG/MTT, but the key point is to establish a ratio you are comfortable with, a ratio that allows you to focus on decisions at the table and not worry about the cost of entry AND have the mental discipline to move down if BR falls to a minimum ratio for the current level.
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Re: Tournament buy ins required, do they differ with field sizes

Postby mattywein » Thu Jun 10, 2010 8:03 am

So in summary. My specific BR requirements vary according to how aggresive I want it to be, my ROI and my SD. They don't vary at all with the number of players or payout structure as this is covered in the ROI figure.

As I've just started playing at this level I don't have many games to go on. I'm at a 68% ITM over 100 games. My ROI is about 20%. I don't mind a more aggresive ROR figure of 5%. I don't know how to work out my SD so any info on that would be helpful.

I've grown my BR from $50 to $137 so its all going well so far. I'm going to move up to the $5 HU games soon. What sort of figure would you think I would need?
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Re: Tournament buy ins required, do they differ with field sizes

Postby Quimp » Thu Jun 10, 2010 9:03 am

Thanks sun, very detailed analysis.

This topic should be useful Matty: viewtopic.php?f=9&t=7809 and specifically it states that "when you are taking a shot at a level, you can use a much lower comfort level than normal because you should be planning to move down quickly if you hit a bad streak."

Plan when you are going to move down i.e. if you have less than 20 BIs at a level, move down.

Your sample is very small and unless you play NBI (no blind increase), deep stacked or a very slow format, you will not be able to sustain a 20% ROI. But then your WR ($/hr) will be much lower. 15-16% is probably the max for regular speed HUSNGs but please prove me wrong!
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Re: Tournament buy ins required, do they differ with field sizes

Postby sun137 » Thu Jun 10, 2010 1:30 pm

Matty, HEM has a SD stat - can you let me know if you use HEM and can find the stat before I give you the suggested buyin ratio for the figures you gave in your last post?

Thanks.
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Re: Tournament buy ins required, do they differ with field sizes

Postby mattywein » Thu Jun 10, 2010 4:35 pm

under what sub title should I look? I'm playing tournaments not cash. I'm looking under the I can only see a sd/bb button. This don't look right buts its 30.22.

At the moment I'm looking under the tournaments tab and reports
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Re: Tournament buy ins required, do they differ with field sizes

Postby sun137 » Thu Jun 10, 2010 6:57 pm

The final answer you want is at the bottom of the post, but it is not a bad idea to follow me through the workings............

You pick the stats you want in your reports with the green + button and this will apply to that type of report for all games (for example if you add SD big blind in the default stats section of stat selection for your position report, this report will be the same for cash, SNG and MTT).

There are only 2 SD stats - for Big Bets and big blinds. You want the SD big blind stat (the other one is only used for limit holdem games). You appear to have found the correct stat and 30.22 is your current figure (6 is normal for MTT and 1.7 for SNG but you have a small sample - I assume you have entered all the position finish, entry fees and prize data).

OK, let's proceed to a suggested BR.

Actual data:

ITM................68%
ROI................20%
SD bb.............30.22
ROR accepted....5%

We will assume an average Comfort Level of 3

The normal BR with a 20% ROI is 43.35 buyins where the SNG SD is a normal 1.7 and this has an ROR of 0.25% (for e^-6) - see the example in my previous post.

If we use the 30.22 figure for SD.............

BR = Comfort Level x SD^2 / Win Rate

BR = 3 x 30.22^2 / 0.20
BR = 3 x 913.25 / 0.20
BR = 2739.75 / 0.20
BR = 13698.75 buyins (I think you are right........30.22 is a ridiculous figure, small sample or incomplete data perhaps)

The MTT normal SD of 6 would produce a required BR of 3 x 36 / 0.2 = 540 buyins

However the ROR is still 0.25%.......

The Risk of Ruin is e ^(-2WR*BR / SD^2) or e to the power of -2WR*BR / SD^2 = (-2*0.2*13698.75 / 913.25) = -6 and e^-6 = 0.25%

If you wish to run with a more aggressive ROR, a figure in the formula must change. The actual numbers for WR and SD cannot change, therefore the size of your BR changes. If you change the size of you BR, this affects the result of the Comfort Level (CL) formula by giving you a lower level of comfort. This is how they are all related depending on the level of risk (and comfort) you wish to take.

So, we work backwards in the formula.

You require a ROR of 5% and the inverse of 5% (or 0.05) = -3.0 (see the inverse figures for ROR in my previous post)

Therefore e^-3 = 5% (e to the power of -3 = 5%)

Image

This calculator is very useful - play around with it for different levels of risk.

and as e^(-2WR*BR / SD^2) is also = 5%, (-2WR*BR / SD^2) must be = -3

Therefore (-2*0.2*BR / SD^2 = -3

If we use a SNG SD of 1.7.................

(-0.4*BR / 2.89) = -3

-0.4BR = -3 x 2.89 = -8.67

0.4BR = 8.67

BR = 8.67 / 0.4

BR = 21.7 buyins

Therefore you need 21.7 buyins for 5% ROR with a normal SNG SD. The level of BR increases by the SQUARE of the increase in SD (remember SD squared = Variance). A SD of 2 moves your BR up to 30 buyins for the same 5% level of Risk and the normal MTT SD of 6 increases required BR to 270 buyins. I would suggest putting in some SD numbers into the formula to see the BR impact (30.22 SD = 6849 buyins btw).

The Comfort Level for 5% ROR = BR x WR / SD^2 = 21.7 x 0.2 / 2.89 = 1.50, a bit less comfortable that the average figure of 3.0

You could use the alternative ROR formula shown in my previous post:

BR = -(SD^2 / 2 x Hourly Win Rate) x the Inverse of the Risk of Ruin

BR = -(1.7*1.7 / 2*0.2)*-3

BR = -(2.89 / 0.4)*-3

BR = -7.22*-3

BR = 21.66 = 21.7 buyins

It doesn't matter what formula you use, the result will be the same.

SUMMARY

The size of your game sample is critical for accurate measurement (see my last post) and anything under 1000 games is suspect - use standard SD figures as a BR guide up to 1000 games.

The Field Size argument is a red herring, the relationship between long term risk and reward is the key driver for BR requirements in all events and the number of opponents you pass on the way to ITM/FT is only a different (and useless) way to measure time efficiency v reward.

The actual WR or ROI and SD are based on performance, but the level of risk or comfort is a personal decision. The combination of all these factors determine the basic BR you need at any level. The most important element is your SD, because BR increases by the square of the SD and the SD figure only falls with consistent results. If your skill improves, the level of consistency will improve, SD will fall and BR requirements will reduce - but the opposite is true as well.

This is why a poor player will always need a much bigger BR for long term profit, because of inconsistent performance - assuming he is a winning long term player of course.

A losing long term player doesn't have a Bankroll, just a giant toilet with a fast action handle. :)

If you are starting out, a 40 to 50 buyin BR is enough to find out where your skill level is at. You should be playing SNG will a much smaller proportion of MTT until experience grows and skill increases.

I am rebuilding a bankroll on Pokerstars. I am playing heads up sng's. I have a fairly high skill level at HU and am confident of a 60%+ itm rate playing 1 table at a time. Can I play with a smaller number of buy ins say 20-30 without the risk of going bust increasing? My gut feel is that I can, but I'm not capable of working the maths out.


The answer to your question is yes if your SD is 2 or below, 25 - 30 is fine. I would suspect your SD for SNG is closer to 2 than 30.22

(I know I went through a lot of information in my 3 posts, but I am trying to explain in detail why you should focus on certain factors and not others).
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