Risk of Ruin

[Dan Mezick]

I'm curious how many players actually realize their risk of ruin expressed in percentage terms.

Please be honest in your answers to the poll.

Let's discuss the RoR concept.

[jason1990]

I voted for the fifth option, but it probably should have been worded differently. No one can know their RoR exactly because (1) the formulas for RoR are based on models that incorporate simplifying assumptions, and (2) no one can "exactly" know their true winrate and standard deviation (SD).

I've brought this up before, but it's been a while, so I'll bring it up again. We all are well-versed in sample size requirements for winrate. But what about SD? In Mason's essay, Computing Your Standard Deviation, he says

[ QUOTE ]
A good rule of thumb is to have at least 30 observations (playing sessions) for the estimate to be reasonably accurate.

[/ QUOTE ]
It's true that 30 observations are going to give you a pretty accurate confidence interval for your winrate. (I don't mean a small interval, just one whose size accurately corresponds to the given degree of confidence.) The confidence interval for your winrate should ideally be built using your true SD. But in practice, you must use your estimated SD, which is going to have an error. How different is the confidence interval which uses the estimated SD from the confidence interval which uses the true SD? Well, with 30 observations, it's not going to be much different. But it is not because your estimated SD is close to your true SD.

When I started in nano-limits, I did some analysis of my SD. After about 40 sessions, I had an estimated SD of 21 BB/100, but a 95%-confidence interval for my SD was [17,29].

So 30 sessions is plenty if all you want to do is build a confidence interval about your winrate. But it is not enough if you want to get close to your true SD. And accurately estimating your true SD is what you need to do to compute RoR. (Of course, it may be harder to get close to your true winrate, which you also need for RoR, but at least you can try to get one statistic nailed down.)

[jason1990]

[ QUOTE ]
How different is the confidence interval which uses the estimated SD from the confidence interval which uses the true SD? Well, with 30 observations, it's not going to be much different.

[/ QUOTE ]
Okay, this was said in a sloppy, hand-wavy, sweep-it-under-the-rug type way, and, as it stands, it's probably not even true. So I feel compelled to elaborate on where the 30 comes from.

Suppose I play n sessions which, for simplicity, are all the same length, say 100 hands. Let X_i be the number of BBs I won in the i-th session and I will assume each X_i is normal with (unknown) mean w and (unknown) variance s^2. So my true standard deviation is s. Let W and S be my estimated (or observed) winrate and standard deviation, respectively.

If I knew s, then I could build a confidence interval for w by using the fact that (W - w)/(s/sqrt{n}) is normal. But I don't know s, so I must use S. And the problem is that (W - w)/(S/sqrt{n}) is not normal. But when n is at least 30, then this quantity is close to normal, so in this sense we are justified in using S instead of s in our usual construction of the confidence interval. But that does not mean that the numerical values of s and S are necessarily close.

Which means we may not be justified in replacing s with S in other formulas, such as the RoR formula.

[fnord_too]

I selected 4, but none of the options are really correct for me. My risk of ruin is pretty near zero, since I will drop down if my bankroll drops, and I carry a large bankroll for what I play. You cannot know your RoR exactly. It is impossible to know your exact expectation or standard deviation in Poker. You cannot solve explicityly that like you can in craps, say. Maybe 5 was a more apropriate choice, because I am always looking at EV and bankroll and adjusting accordingly. Basically, what I am saying, is that trying to get an exact figure is futile and silly since estimation error is so high. (As the old saying goes: "Measure with a micrometer, mark with chalk, cut with an axe.")

[Dan Mezick]

This is what I am getting at: precisely calculating your (estimated) risk of ruin.

Why?

This is a hugely important calculation, because you must accept the risk to accept responsibility for your results.

I believe we may all reasonably agree that to be able to accept the risk, you must first know the risk. Specifically, you MUST know your risk of ruin. If accurately estimating your RoR is impossible in poker, then accepting responsibility for all your results in poker is also impossible. This risk-acceptance issue is actually a Psych Forum issue, and to address it, RoR must first be determined.

I'm calling on all probability experts on this Forum to help me solve this problem of defining a specific problem: tournament poker RoR. It’s a function of estimating the following player info:

per-session probability of winning,
the average win per session,
the average loss per session, and
the bankroll size.

Let’s say the game is a weekly rebuy tournament where it costs $40 to play and $20 to rebuy. You can rebuy during hour #1 if your chips fall below 50% of the starting chip count.

Let’s say you have a stop-loss rule of $80 per session: if you rebuy twice on top of the $40 ($40+$20+20) and you lose all your chips, you exit the event, EVEN IF it is during the 1st hour when you could rebuy again. Downside risk is thus precisely defined at a max of $80 per session.

Let’s say you have $2000 of bankroll to start with.

Further let’s say you have 30 observations of playing sessions, with wins and losses, as follows:

1 -$40.00
2 -$40.00
3 -$60.00
4 $60.00
5 -$60.00
6 -$80.00
7 -$100.00
8 $960.00
9 -$60.00
10 -$60.00
11 $300.00
12 -$40.00
13 -$60.00
14 -$80.00
15 $150.00
16 -$40.00
17 -$60.00
18 -$40.00
19 $200.00
20 -$40.00
21 $500.00
22 -$40.00
23 -$40.00
24 -$80.00
25 -$60.00
26 -$40.00
27 -$40.00
28 -$40.00
29 -$40.00
30 -$40.00

$890.00 (+)

What’s your estimated RoR? HOw does it change if you make the stop loss $60 or $100 instead of $80?

With these observations you can calculate risk of ruin for various bankroll sizes. And by sizing the bankroll, you can adjust RoR to a RoR-probability acceptable to you, if that probability is not currently acceptable.

Correct? Is 30 enough observations to construct a valid RoR estimate? Is using the last 30 ("rolling") observations the right approach, to incorporate subtle changes in the game and your play in it, over time?

Those interested in solving this problem may be interested in this paper, which discusses achieving these goals in another game of probabilities-- trading.

Position Sizing
http://www.traderscalm.com/psizinginterview.html

Thanks in advance for those who find this an interesting probability problem, and post some answers to this tournament RoR question.

If I have not provided enough info please post that. I believe 30 observations is enough to get it right in terms of a valid estimate of RoR.

[uphigh_downlow]

Based on your strategy of reducing the stakes that you ply at (which most people do)

I would like to ask a question that I hope will get answered sometime. Assuming that you play always play a game where your roR is a certain onstant.

Do you have any idea about at what RoR, you will be a break-even player over the long run(infinite time). Or do we need more variables to answer this more accurately.

idea is that you get stuck in the cycle of changing stakes, and never seem to make a profit. Since you win at lower stakes and lose at higher.

[dabluebery]

I wish there had been another option for me. I HAD calculated all this stuff a while back, but once I realized I have plenty of BB's in my bankroll for my risk levels, I stopped worrying about it.

Now I play 6-max and I'm broke. It's the darndest thing.

Rob

[Dan Mezick]

[ QUOTE ]
idea is that you get stuck in the cycle of changing stakes, and never seem to make a profit. Since you win at lower stakes and lose at higher.

[/ QUOTE ]

This is directly related to RoR and indirectly related to taking responsibility for all results.

If you know by moving up you are increasing your RoR by a factor of 3,4,5 or even 10, you will be much less likely to make the move until and unless all conditions (proper bankroll) are in place for an acceptable RoR at the new level.

Items that get measured tend to get managed, items managed tend to improve. Attention is essential to perception.

This is especially true of risk.

[Dan Mezick]

It's likely you increased your RoR dramatically when you moved to 6-max. Maybe it was a HUGE increase. Knowing your RoR and accepting the risk is essential to taking responsibility.

Taking responsibility is essential to eliminating denial. Eliminating denial is essential to playing well.

Therefore knowing your RoR for a given scenario is essential to playing well.

[pzhon]

Risk of ruin is a simple concept, but in practice you aren't sure of

[img]/images/graemlins/diamond.gif[/img] Your win rate.
Of course you may have an estimate, but small differences greatly affect the ROR. If you will change levels, you have to guess what your win rates will be at the other levels. You also have to guess whether games will get tougher or softer in the future, and what bonuses will be offered.

[img]/images/graemlins/diamond.gif[/img] Your standard deviation.
This is harder to figure out than you might expect. My SD estimates according to PokerTracker have oscillated wildly.

[img]/images/graemlins/diamond.gif[/img] What you will do if you hit a large upswing or downswing.
If you will step down, when will you move back up? What is your plan for taking shots at higher levels?

[img]/images/graemlins/diamond.gif[/img] How much is really in your bankroll (as opposed to your balance).
It's hard for me to imagine going on a huge downswing and losing my whole balance. If I did, I think I would put more money into poker. That extra money counts as part of my bankroll now.

With some simple estimates, I find my risk of ruin is under 0.01% (1/10^4), as long as I don't go crazy after I hit a hot streak. I'm not going to worry about calculating it more exactly until I hit a big downswing and it increases greatly.

So, are risk of ruin calculations useless? I don't think so. You can replace the bankroll with a session balance to get a session risk of ruin. You can use this when you are taking shots at a higher level or a different game. Your session balance can start at the amoutn you budget for trying the new level. You can use the session risk of ruin to determine how likely it is that you will have your balance cut in half, which might be the threshold you use for moving down in limits.