Party 15/30 BR - How much is enough?

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This post and much of this thread contains a common misconception. The 300 BB rule refers to a starting bankroll. That is you start with 300 BB and let your BR grow, never withdrawl. If you do this you are probably pretty safe starting with 300 BB. That is because when you hit the eventual 300 BB losing streak, you likely will have much more than 300 BB.

On the other hand if you continuously draw down your BR to 300 BB, then you do not have nearly enough. As GOT said 1000BB is more like it.

The chance of at some time having a 300 BB losing streak is much greater than the chance of going broke starting with 300 BB and letting the BR grow.

Paul

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No.

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Which statement do you disagree with?

Paul

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If you do this you are probably pretty safe starting with 300 BB. That is because when you hit the eventual 300 BB losing streak, you likely will have much more than 300 BB.

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The PP 15 game is way too volatile for a 300 BB roll to be adequate even for starting out. If you’re starting out with 300 BB, you’re taking a shot and hoping not to run bad, because there’s a substantial chance that you’re going to run bad and reach a point where you’re going to have a very good chance of going broke if you keep playing.

Let's take a hypothetical guy who'd like to play the Party 15 as a pro.

Let's say our pro has a SD/100 of 16 BB. This is right in the range of SD/100 numbers that I see reported and, incidentally, it's my SD over my last 10,000 hands.

While some players make more than 1.5 BB/100 and some players make less, it seems to be a number that comes up a lot on the Mid/High board, so let's say it's our pro's WR.

I don't personally know any 15 pros who get more than 40,000 hands per month—I’m sure some do, but I don’t and I couldn’t imagine wanting to.

I’m going to make up some monthly expenses
Rent: $500 (This is too low where I live)
Food/entertainment: $500 (This is also probably low for most people)
Health Insurance: $400 (I've been told this is high for most people, but it's close to what I'm currently paying)
Utilities/phone/internet: $100 (more if you have cable)
Car Insurance/gas: $250
Other random stuff that comes up: $250
Car payment: $500 (this is probably high but it makes the numbers prettier)

Let's call it $2500 in monthly expenses. Some people probably spend more, some people probably spend less. Actually, my guess is that most people probably spend a lot more, but let’s leave it at that for now.

Last year was the first year I've had substantial income that wasn't withheld from a paycheck and I haven't filed for this year yet, but let's say the tax rate ends up being something like 25%. I'm sure this is low. This is further complicated by the fact that our pro won’t owe as much in taxes if he goes broke. Someone who knows better should feel free to jump in and suggest a better way of figuring this out.

So, our pro’s monthly income is an expected $18,000. The government gets $4500 right off the bat (he should be paying estimated taxes every quarter), and he spends $2500. So now our player’s monthly income that we count in his win-rate for BruceZ’s formula is $11,000. His adjusted win-rate is 0.73 BB/100 hands.

So BruceZ’s formula would indicate that our player needed a 525 big bet roll to have a 5% risk of ruin.

I don’t know about you, but I’ve lost to a few two outers in my time, and the idea of having 5% risk of ruin would keep me up nights. If I was really dead set against stepping down in limits, I’d want a 1% risk of ruin at the maximum, which would require an 807 big bet roll.

To feel really safe, I’d probably want a .1% risk of ruin, which would require a 1211 big bet roll.

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[img]/images/graemlins/confused.gif[/img]

I'm losing this. I don't understand how the equation ends up with so few variables. I understand how if I know my winrate and my standard deviation and my bankroll at any given instant, I can calculate the probability of hitting zero in X number of hands. So I'd always assumed the 300BB applied from 'right this moment'.

But now I'm confused as to where X comes from? Do we make some lifetime estimate of how many hands we'll play? Do we have to add age into the equation? Won't the vast number of hands now played by pro poker players increase their chances of going bust? Am I completely on the wrong track?

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Take a look at the thread that a few posters linked to--it has a lot of information about how these formulas were calculated posted by people who are much more familiar with them than I am.

Discussion of Mason's method is available in Gambling Theory and Other Topics, and BruceZ mentions another book that contains discussion of these formulas in the thread.

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[MaxPower]

The number of hands you play doesn't enter into it. The formula is telling you the chance that you will go bust between now and the end of time assuming you don't take any money out (and nothing else changes).

When your bankroll grows, your risk of ruin drops sharply.

If my win rate is 1.5BB/100 and my SD is 16BB/100 and I want a 5% risk of ruin, I need 255BB.

Now, if I grow my bankroll to 500BB, what is my risk of ruin now? 0.3%

If I grow it to 750BB, my risk of ruin is 0.02%

You are right that the 5% chance of going broke starts from this moment. Let's say I have a 255BB bankroll and everytime I win 100BB I cash out and go back to 255BB. If I do this 20 times, what is the probability of never going broke? (.95^20) = 36%.

So if I stick to my 255BB bankroll it is almost a certainty that I will go broke.

I hope I didn't mess up the math.

[pokerjo22]

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The number of hands you play doesn't enter into it.

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Nope, still don't get it [img]/images/graemlins/frown.gif[/img]

Surely my risk of ruin is much lower over my next 100 hands of play than the next 1000000? I mean, in the extreme, my risk of ruin at limit poker in the next hand is zero, right?

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The number of hands you play doesn't enter into it.

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Nope, still don't get it [img]/images/graemlins/frown.gif[/img]

Surely my risk of ruin is much lower over my next 100 hands of play than the next 1000000? I mean, in the extreme, my risk of ruin at limit poker in the next hand is zero, right?

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Your risk of ruin in the extreme short term obviously very low.

Your risk of ruin in the near future is determined by your winrate, standard deviation, bankroll, and expenses.

Your risk of ruin in the extreme long run--assuming that you didn't go broke in the near term and were saving a substantial portion of your winnings after expenses--is very low. This is because at a given moment in the extreme long run, you will have a much larger bankroll and thus a lower chance of going broke from that point forward.

In a situation where you always spent every dime over the size of a given bankroll, you never replenished your bankroll, and you planned to play X hands over your lifetime, your risk of ruin would approach 1 as your hands approached infinity.

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[pokerjo22]

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Your risk of ruin in the extreme long run--assuming that you didn't go broke in the near term and were saving a substantial portion of your winnings after expenses--is very low. This is because at a given moment in the extreme long run, you will have a much larger bankroll and thus a lower chance of going broke from that point forward.

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Thanks, that's made it a lot clearer [img]/images/graemlins/smile.gif[/img]

[2ndGoat]

<<So, our pro’s monthly income is an expected $18,000. The government gets $4500 right off the bat (he should be paying estimated taxes every quarter)>>

1) Way low for a US player, unless that player has got a ton of deductions, considering the "pro" should be paying a 15% self-employment tax up to ~90k income, before even considering fed/state income tax. But I think you knew that.

2) I'm not sure if this is completely mathematically valid, but I actually consider taxes as lowering the stakes you're playing for, once you're solidly in the win column for the year. If you are definitely going to owe the government 35% of your winnings, then when you win 100 BB, you actually won 65 and the government won 35... when you lost 100 BB you lost 65 and the government lost 35. This is further complicated by the discrete nature of quarterly estimated payments rather than continuous adjustment.

Whatever the appropriate mathematical abstraction, I'm pretty sure that taxes do not count as bankroll expenses the same way a car payment does, since they do cost less in bad times than in good times.

2ndGoat

[2ndGoat]

<<Surely my risk of ruin is much lower over my next 100 hands of play than the next 1000000?>>

The RoR formulae break when the normal distribution of results break. If you're considering a time period so short that your results are not normally distributed (1 or 10 hands, for instance), you're right.. forget the formula, you have 0 chance of ruin.

Other posts have expanded on the RoR-for-x-hands vs RoR-for-infinity concept, so I'll leave my post at that.

2ndGoat

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<<So, our pro’s monthly income is an expected $18,000. The government gets $4500 right off the bat (he should be paying estimated taxes every quarter)>>

1) Way low for a US player, unless that player has got a ton of deductions, considering the "pro" should be paying a 15% self-employment tax up to ~90k income, before even considering fed/state income tax. But I think you knew that.

2) I'm not sure if this is completely mathematically valid, but I actually consider taxes as lowering the stakes you're playing for, once you're solidly in the win column for the year. If you are definitely going to owe the government 35% of your winnings, then when you win 100 BB, you actually won 65 and the government won 35... when you lost 100 BB you lost 65 and the government lost 35. This is further complicated by the discrete nature of quarterly estimated payments rather than continuous adjustment.

Whatever the appropriate mathematical abstraction, I'm pretty sure that taxes do not count as bankroll expenses the same way a car payment does, since they do cost less in bad times than in good times.

2ndGoat

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Yeah--I was sure that the way I was adding in taxes was wrong and would have a tendency to overestimate their impact on your RoR which was one of the reasons I chose such a low marginal rate. I figured if I was sure I was making two mistakes, I might as well try to make them in opposite directions. Since my purpose was to warn people about the volatility of the 15 game and the high bankrolls playing in it requires, I thought leaving the impact of taxes out of the analysis was worse than having an unreliable adjustment for them.

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[Paul2432]

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That is you start with 300 BB and let your BR grow, never withdrawl. If you do this you are probably pretty safe starting with 300 BB. That is because when you hit the eventual 300 BB losing streak, you likely will have much more than 300 BB.

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<---snip discussion of effect of expenses on bankroll--->

I don' think we really disagree about anything. Obviously if expenses are considered, BR requirements go up. That was the point of the sentence that you snipped from my OP, that I have added back in bold.

Perhaps I could have been more clear that "never withdrawl" meant that all expenses such as taxes and living expenses would be paid from another source. In fact, later in the OP, I suggested a 1000 BB BR for the Party 15/30.

Paul