Buy in requirements

[cwar]

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


[/ QUOTE ]

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.

[jay_shark]

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 .

[cwar]

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.

[ORTOM]

[ QUOTE ]

Your missing the variability of variability though

[/ QUOTE ]

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%

[nycballer]

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.

[jay_shark]

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 .

[ORTOM]

[ 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 .

[/ QUOTE ]

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.

[jay_shark]

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 .

[jay_shark]

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 .

[tipperdog]

[ 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.