Risk of ruin--what am I missing?

I commonly hear that even for a substantially winning player that a minimum reasonable bankroll amounts to a two or three hundred big bets. However, Statking seems to suggest something very different.


For example, suppose that you have a $40/hr win rate a $340/hr standard deviation in a $20/$40 game. While most people would say that you need an $8,000-$12,000 bankroll to be safe, Statking says that with only a $4,000 bankroll you have less than a 1% chance of going broke.


What is going on here?


-Dan


P.S. If Statking is assuming a normal distribuation of results and results are for some reason not normally distributed, I would be curious to hear why that is the case.

I think the problem is the assumption that the long run expected value is to win $40 per hour. It would be rare to find a player who can win $80,000 per year playing $20-$40 hold'em (this would be $40 per hour x 2000 hours of full time play each year). Suppose the true expectation is $20 per hour?

Jim,


First of all, there are definitely some 20/40 games in this country that some players can beat for 40/hr. I agree that it takes a very good game and a very good player, but it happens.


Anyway, look at a 10/20 example if you like. Suppose a wine rate of 20/hr and a SD of 170/hr. There are plenty of games in the country where a very good player could achieve these numbers. A player with those numbers has less than a 7% chance of ruin with a bankroll of only $2,000.


I agree with the general point that most players need a large BR b/c they don't beat their respective games for even close to 1 BB/hr. However, for those who do, I think that common BR requirements estimates are overly conservative. Of course these are highly personal decisions that depend on individual risk tolerance, but the general point is that the risk of ruin is not as high as I think many would guess.


-Dan

I associate "ruin with "worst case", so if that is correct, then the larger B/R may also be correct??????

I think the reason the bankroll requirement is assumed to be higher than what you think is because the standard deviation is larger than what you list. In Poker Essays, Mason says that if you are a fairly tight 10-20 player, you should have a standard deviation around $200/hr, and that that number will go up if you play at higher limits or if you push more small edges. Your figure of 8.5 bb/hr standard deviation seems quite a bit lower than most of the numbers I've seen.

Maybe the problem is that many of these players spend their bankroll and at some point they hit an unusually long losing streak where they lose their bankroll. In your example, I am almost positive that a $10-$20 player, if he plays long enough, will encounter a period where he loses $2,000. I am certain that there are many excellent $20-$40 players who have gone through periods where they have lost $4,000.


Daniel, I cannot reconcile the math calculations with what I have observed and learned about this game over the past three years. A friend of mine won over $39,000 playing $20-$40 over a 1000 hour period. Over the next 800 hours he lost $13,000 playing $20-$40. I have seen Cissy Bottoms, one of the top $20-$40 players in the country, lose over $2,000 in a single session of $20-$40 and I have seen this happen to her on more than one occasion.


I know of winning players who play $15-$30, $20-$40,and $30-$60 regularly at the Bellagio and the Mirage here in Las Vegas. Many of these players have encountered losing streaks where they have lost $10,000 to $20,000 over a two or three month period.


I believe the bankroll estimates that I see posted and that I read about are severely understated. I also believe that the win rates in middle limit games that are posted are grossly overstated. This overstatement is usually due to the player not having played enough hours.

Jim,


I completely agree with you. As much as I want to believe the statistics, it just runs so counter to my own experience and intuition. That's exactly why I made the post.


Thanks for your response.


-Dan

"I believe the bankroll estimates that I see posted and that I read about are severely understated. I also believe that the win rates in middle limit games that are posted are grossly overstated."


I think the estimates that S. and M. give you are right on the money. That is a good player will win about 1sb and a great player or close to a great player will win 1bb. I think the difference between a good player and great player is just as huge as that half a bet that separates the two.


P.S. I never liked the S. and M. estimate and hoped it was not true. Unfortunately unless you are a great player poker is a ........ fill in whatever you want.

Even with more modest estimates of 20/hr and 400/hr s.d., the risk of going broke is less than 8%. i find this surprising and still think it goes against common wisdom.

Perhaps, but the whole point of the bankroll estimates is to give a figure which, if you are a good player and don't remove any money from your bankroll, will make it all but certain that you will survive. If you are playing 5-10 with a $3000 bankroll, and you play with a reasonable win rate and std. dev., you can feel confident that your bankroll will survive. Of course, if you want to take money out of your bankroll for living expenses you need a much larger amount. Basically, the idea is to have enough of a bankroll to allow you to make the appropriate bets without fear of losing. You can get away with a smaller bankroll if you are going to drop down to a smaller limit when you lose a bunch of money, and especially if you have a job which allows you to replentish your bankroll from time to time.