Buy in requirements
 

For this post , i'll come up with different buy ins according to your win rate and the chance that you'll go bust .

If you win y % of your games , then the chance you lose is (1-y)% . The probability with N buy ins that you'll go broke at some point is [(1-y)%/y%]^N . So here is the breakdown .

Here is the probability you'll go bust with 5 buy ins
as a
a)55 % player .
b)60% player
c) 65% player

sol.
a)[.45/.55]^5= 36% which is too high .
b)[0.4/0.6]^5=13 % which is still too high
c) [0.35/0.65]^5 = 4.5% which is not bad but still high

The probability you go bust with 10 buy ins as a
a) 55% player
b) 60% player
c) 65% player .

sol.
a) [0.45/0.55]^10 = 13%
b) [0.4/0.6]^10 = 1.7% which is fairly low
c) [0.35/0.65]^10 = 0.2% This is extremely conservative .

The probability you go bust with 15 buy ins
a) 55% player
b) 60 % player
c) 65% player

sol.
a) [0.45/0.55]^15=4.9%
b) [0.4/0.6]^15 = 0.228% very conservative
c) [0.35/0.65]^15=0.00927% You'll never go broke

So if you're only working with 5 buy ins , then there is a significant risk of going broke even if you win 65 % of your games .On the other hand , with 10 buy ins you're pretty much playing comfortably if you can win 65 % of your games .If you're working with 15 buy ins as a 55 % player , then there is still a significant risk at 4.9% of going broke .

Make sure you think along these lines when you determine how many buy ins you need to play comfortably according to your desired ror .

Re: Buy in requirements
 

To be even more specific , your RoR depends on your s.d since it is possible that two players may have the same win rate at 60% but one player plays with more volatility .This same player would need more buy ins to account for this .

Re: Buy in requirements
 

Interesting post...This calculation is a "lifetime" calculation I suppose no?

Re: Buy in requirements
 

Oh yes , this is the probability that if you play the game for ever that you'll go broke at some point . It uses the fact that there will always be a game waiting for you no matter what . Your opponents' bankroll is infinite .

Re: Buy in requirements
 

Your missing the variability of variability though [img]/images/graemlins/smile.gif[/img]

You are assuming you always play your average opponent. In order to have an average opponent, you must play vs some opponents where your winrate is higher than normal, and vs some opponents where it is lower than normal. Sometimes, in a given sample, you will end up playing more tough opponents, and your sample winrate has a good chance at being lower than normal. During this sample, your chance at going bust due to variance is much higher than your normal chance. Since you only need to go bust once, this is what you have to plan for.

Re: Buy in requirements
 

good post jay, nice work.

Re: Buy in requirements
 

Well to be precise the correct formula to use is the following :

r0r= e^(-2ub/sigma^2)

ror= risk of ruin or the probability you go broke
u= hourly rate which is $/h over time
B=bankroll
sigma=standard deviation


Every player has a different standard deviation and you should be able to work it out yourself easily . Using 30 sessions , you should be able to determine your standard deviation which gives you all the information you need to determine your ror given various bankrolls .

Re: Buy in requirements
 

Is the rake included in your calculation?

Re: Buy in requirements
 

Cool calculations but I think kind of unnecesarry, I have a great bankroll strategy that has 0% ROR.

Re: Buy in requirements
 

It is very necessary as it doesn't get talked about in this kind of detail .

No matter what bankroll strategy you use , there is always a risk in going broke . Also ,it is perfectly acceptable to accept a 1 % risk in busting .

Re: Buy in requirements
 

[ QUOTE ]
c) [0.35/0.65]^15=0.00927% You'll never go broke


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The reason I find calculations like this fairly unnecessary is that in a real life situation someone with a mathematical ROR of 5% could in reality have a much lower ROR than someone with a mathematically figured ROR of .1% even assuming that winrate was constant and both players never tiled. If you have a 30 buy in roll and move down whenever you reach 20 buy ins (this is approximately what I do) assuming a constant winrate of 55% your ROR should be lower than the lowest ROR you provided with the 65% winrate.

Re: Buy in requirements
 

Cwar , everytime you step down in limits , you're compromising the growth rate of your bankroll . Sure , you may lessen the chance of going bust but it comes at a cost in earning less money over all .

What you really want to accomplish is to increase your bankroll at a maximum rate which stepping down in limits fails to accomplish .

Re: Buy in requirements
 

If your bankroll management plan doesnt include stepping down you are probably going to go bust eventually OR you have way too many buy ins for the level your are currently playing at and arent aggressively moving up in levels.

If your willing to move down you can attack the upper levels aggressively maximizing your growth potential when winning and playing well and moving down when you hit a losing streak or are tilting and playing badly. Im sure you have heard many pros recite the cliche that you need to protect your bankroll, its true. If your going to be playing for any serious amount of money for more than a couple years your going to experience changes in the games, your level of play and serious serious downswings. Playing carefully with your bankroll at these times is important. No player regardless of how well they handle these kind of issues should be playing as high as possible through these issues.

Moving down is an essential part of bankroll management because the poker world is not stagnant. To maximize your earn you should be able to use your bankroll aggressively and conservatively. If you dont include it you probably either dont move up as aggressively as you could, have ego problems or will eventually go bust regardless of how good you are.

Re: Buy in requirements
 

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Your missing the variability of variability though

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This inspired me to expand upon jay_shark's work and remove the implicit assumption that the player has the same chane of winning against each individual player. I simulated a player whose win rate is distirbuted uniformly between 50 and 70 percent (and therefore is a 60 percent winner on average). I also included rake.

P(busto given by ins)
5 buy ins: 15.0%
10 buy ins: 2.3%
15 buy ins: 0.4%

Re: Buy in requirements
 

the biggest problem with this analysis is that no one ever plays their best 100% of the time, if that was true this could be applicable but its not. You have to take into account that you will play bad sometimes and that makes 15 buyins way way too low especially for the turbos. For turbos u should have 35 buyins. For just regular HUs 25 is fine.

Re: Buy in requirements
 

I made the assumption that the probability you win every individual game is constant at x% , for x=55%,60%,65% .

If you want to be precise , you should use the formula that includes your standard deviation and win rates to calculate your ror . It's usually the case that you may win x % of your games on average but you don't necessarily win each game x % of the time . There is a subtle difference but one that should be pointed out .

Nycballer , the number of buy ins depends on how comfortable you are with a certain risk of busting . Some players may want a 1% risk while others wouldn't mind a 5% risk .Every player is different , so there isn't one correct number of buy ins for every single player .

Re: Buy in requirements
 

[ QUOTE ]

I made the assumption that the probability you win every individual game is constant at x% , for x=55%,60%,65% .

If you want to be precise , you should use the formula that includes your standard deviation and win rates to calculate your ror . It's usually the case that you may win x % of your games on average but you don't necessarily win each game x % of the time . There is a subtle difference but one that should be pointed out .

Nycballer , the number of buy ins depends on how comfortable you are with a certain risk of busting . Some players may want a 1% risk while others wouldn't mind a 5% risk .Every player is different , so there isn't one correct number of buy ins for every single player .

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I addressed this issue in my other post in this topic. If you'd like to see the results for other hypothetical players, let me know.

Re: Buy in requirements
 

Good post Ortom .

You may use the formula that I gave earlier about calculating your ror depending on your s.d and win rate .


r0r= e^(-2uB/sigma^2)

ror= risk of ruin or the probability you go broke
u= hourly rate which is $/h over time
B=bankroll
sigma=standard deviation

This is a better formula to use because it tells you your ror for various win rates and s.d's .This formula has been posted extensively in the probability forum which is very neat .

Re: Buy in requirements
 

One other thing Ortom .

I'd like to clarify is that your answer may still vary depending on your variance or s.d . For instance , take two players with a mean of 60 % but one player has a higher variance and plays more aggressively . His variance is higher and consequently his risk of going broke is higher . If you really want to be precise then you should use the formula I gave in the preceding post .

Re: Buy in requirements
 

[ QUOTE ]
For this post , i'll come up with different buy ins according to your win rate and the chance that you'll go bust .

Here is the probability you'll go bust with 5 buy ins
as a
a)55 % player .
b)60% player
c) 65% player


[/ QUOTE ]

The "flaw" here is that players will conclude they have a true winrate of x% long before their sample is large enough to draw such a conclusion (I realize this isn't really a "flaw" in your post; it is an error in how posters may apply it.)

A follow up for you Jay: How many games must a HU SNG plyer have under his/her belt before he can call him/her self a 60% winner.

Re: Buy in requirements
 

[ QUOTE ]
One other thing Ortom .

I'd like to clarify is that your answer may still vary depending on your variance or s.d . For instance , take two players with a mean of 60 % but one player has a higher variance and plays more aggressively . His variance is higher and consequently his risk of going broke is higher . If you really want to be precise then you should use the formula I gave in the preceding post .

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this is not true imo, if u assume 60% wins for each player their variance/sd is exactly the same, the ultra aggro player does not have higher variance with the same winrate, because in this case the variance is a function of the winrate (and number of games).
variance for binomial distribution is =n*winrate*(1-winrate) n is number of games.

off topic: variance ist highest for breakeven players.
doesnt make much of a difference though: var is n*0.25 for breakeven players n*0.24 for 60% winners.
so for 100 games the variance is approximately 25.
more interesting is sd which is var^1/2=5 because u can create confidence intervalls with sd.
a breakeven player should be within 40 and 60 wins of 100 for about 95%. 60% winner same within 50 and 70.
assuming 1000 games, var is 250 sd is around 16 so 50% winner should be within 500+- 2*sd=468,532 for 95% and 60% winner between 568,632 for 95%.
u can also see that your real winrate should be within +-3% of your observed winrate at 1000 games, and +-10% at 100 assuming 0,95 confidence level. u need 4x more games for double precision (half as big intervall), u would need 10k games to get under +-1, which sucks cause conditions will likely change or u might get better in that time.

Re: Buy in requirements
 

Donkeykong , it is true .

Your variance is NOT equal if you have the same win rate . You're assuming that the probability you win each individual game is the same when it's not . If this were the case , that is , the probability you win each individual game is always y% , then two players with the same win rate have the same s.d . Two players can have different styles and still end up with the same win rate over time , or close enough . Every players s.d is different and it's not a function of your win rate . They are two completely different things .

The variance of a binomial distribution is n*P*(1-p)
s.d = sqrt[n*P*(1-p)] but this assumes p is constant for each game .

Re: Buy in requirements
 

ah i get your point, but does it real make a big difference?
the variance for 1 game only reduces drastically if u win with over 80% oder lose with over 80% probability 0.16 vs 0.25 for breakeven players i just dont think u get over these values often enough to make that a big factor especially at higher stakes with few complete retards.
if u assume the ultra aggro player has almost always the same chance to win regardless of his opponent and the other player often wins or loses almost for sure than it does of course make a difference.

Re: Buy in requirements
 

i have a question, lets say your playing a heads up cash game. if you feel your a 65% favorite vs that player..would that make you a 65% winner? and would those calulations work here?

Re: Buy in requirements
 

[ QUOTE ]
The variance of a binomial distribution is n*P*(1-p)
s.d = sqrt[n*P*(1-p)] but this assumes p is constant for each game .

[/ QUOTE ]

I didnt' assume that p was constant for each game. It varied between 50 and 70 percent. In my simulation, I first picked what the winrate would be, then, based on that, decided if the player won.

Re: Buy in requirements
 

[ QUOTE ]
i have a question, lets say your playing a heads up cash game. if you feel your a 65% favorite vs that player..would that make you a 65% winner? and would those calulations work here?

[/ QUOTE ]

In other words
1. Probability of winning is .65 aka
2. In the long run, you win 65 out of every 100 games.

Re: Buy in requirements
 

[ QUOTE ]
[ QUOTE ]
The variance of a binomial distribution is n*P*(1-p)
s.d = sqrt[n*P*(1-p)] but this assumes p is constant for each game .

[/ QUOTE ]

I didnt' assume that p was constant for each game. It varied between 50 and 70 percent. In my simulation, I first picked what the winrate would be, then, based on that, decided if the player won.

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but assuming u sit down first in a sng, u should calculate with p=0.6 as u dont know anything about your random opponent, dont u? sitting there with a good or bad opponent is part of luck, so your variance shouldnt be reduced if u do well vs certain opps and do bad vs others. pls correct me if i m wrong.

Re: Buy in requirements
 

[ QUOTE ]
[ QUOTE ]
[ QUOTE ]
The variance of a binomial distribution is n*P*(1-p)
s.d = sqrt[n*P*(1-p)] but this assumes p is constant for each game .

[/ QUOTE ]

I didnt' assume that p was constant for each game. It varied between 50 and 70 percent. In my simulation, I first picked what the winrate would be, then, based on that, decided if the player won.

[/ QUOTE ]

but assuming u sit down first in a sng, u should calculate with p=0.6 as u dont know anything about your random opponent, dont u? sitting there with a good or bad opponent is part of luck, so your variance shouldnt be reduced if u do well vs certain opps and do bad vs others. pls correct me if i m wrong.

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Taking the average of your winrate does seems like it would reduce variance IMO but much much easier.

Re: Buy in requirements
 

[ QUOTE ]
i have a question, lets say your playing a heads up cash game. if you feel your a 65% favorite vs that player..would that make you a 65% winner? and would those calulations work here?

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I would say not. The whole point of winning $ at poker is not winning the higher percentage of pots you possibly can, its winning big pots when you win, and losing small pots when you lose.

Re: Buy in requirements
 

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I would say not. The whole point of winning $ at poker is not winning the higher percentage of pots you possibly can, its winning big pots when you win, and losing small pots when you lose.

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We're talking about sit and gos. Also, the entire point of poker is to force your opponent to make mistakes.

Re: Buy in requirements
 

[ QUOTE ]
Quote:

Quote:
The variance of a binomial distribution is n*P*(1-p)
s.d = sqrt[n*P*(1-p)] but this assumes p is constant for each game .



I didnt' assume that p was constant for each game. It varied between 50 and 70 percent. In my simulation, I first picked what the winrate would be, then, based on that, decided if the player won.



but assuming u sit down first in a sng, u should calculate with p=0.6 as u dont know anything about your random opponent, dont u? sitting there with a good or bad opponent is part of luck, so your variance shouldnt be reduced if u do well vs certain opps and do bad vs others. pls correct me if i m wrong.

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Who you opponent is is a random event, just like what cards you get. But that doesn't meen it can't be incorporated into a model for formula.

Re: Buy in requirements
 

yeah but isnt it useless to do this?