Slotboom's quiz vs Ed Miller and percent of winning sessions

[Andy B]

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Also when you are playing for a living, you have an interest in lower varince even if you are sacrificing some EV.

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Why would this be? If you are adequately bankrolled, you should be maximizing EV at every opportunity.

[GuyOnTilt]

Why would this be? If you are adequately bankrolled, you should be maximizing EV at every opportunity.

Not that this relates directly to what you're saying, but most people's definition of "adequately bankrolled", even on this site, is not big enough to handle high variance games and plays. For instance, at the 15 game at Party a very skilled player making 3BB/100 will go through a 300 or 400 BB downswing. Does he still have a proper bankroll after that drop? Most will not either because they didn't think ahead that far or they refused to believe it would happen to them, and they'll be forced to step down or foolishly (for the non-wealthy) continue to play on a short roll. For this reason I encourage most everybody I know to keep a working bankroll is excess of 500 BB's once they go beyond 5/10. For a pro online 15 player, 1000 is smart.

GoT

[Jaquen H'gar]

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Also when you are playing for a living, you have an interest in lower varince even if you are sacrificing some EV.

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Why would this be? If you are adequately bankrolled, you should be maximizing EV at every opportunity.

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If you play for a living, you should be maximizing your EV/variance, not necessarily your EV. Protecting your bankroll from negative variance is a positive EV move. Adequately bankrolled means not going broke, not necessarily not losing half your 'roll. If you lose half your roll due to variance, your stakes drop and your EV drops then it takes a whole lot longer to comeback since your win rate/hr drops.

Absurd example: what if making a certain play increases your EV by $0.01 per hour but increases your variance by $1000 an hour. Should you add this move to your repertoire? Of course not. Thus, maximizing EV is not always correct. What if the EV gain was $1.00/hr and the variance increase $100/hr? What if the EV gain was $10/hr and the variance was $10/hr? As the variance of the move in question drops and the EV rises, at some point it is advantangeous to make the move. This philosophy is usually referred to as risk averse.

[bygmesterf]

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Why would this be? If you are adequately bankrolled, you should be maximizing EV at every opportunity.

Not that this relates directly to what you're saying, but most people's definition of "adequately bankrolled", even on this site, is not big enough to handle high variance games and plays.

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To Andy B: GoT wrote what I was going to say, better than I could have.

[pzhon]

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A player with a +2 BB/hr winrate with a variance of 14 BB/hr will emerge as a winner in a 5-hr session about 63% of the time.

A player with a +1 BB/hr winrate with a variance of 7 bb/hr winrate will emerge as a winner in a 5-hr session about 59% of the time.


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I don't see how this can be correct. Consider playing 0.50/1 and winning 2BB/hr with 14BB/hr variance and compare with 1/2 winning 1BB/hr with 7BB/hr variance. They're both +$2/hr with $14/hr variance, so the probability of a winning session must be identical.

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Variance has units of square dollars (per hour), not dollars. The square root, standard deviation, has units of dollars (per sqrt(hour)). So, a 2.0 BB earn rate at 0.5-1 with a variance of 14 BB^2 has a standard deviation of 3.74 BB, $3.74. At 1-2, a 1.0 BB earn rate with a variance of 7 BB^2 has a standard deviation of 2.65 BB, $5.29, for the same earn rate in $.

Even so, I think there is something wrong with the figures. First, 10 is a reasonable figure for the standard deviation in an hour. The variance should be about 100. 7 and 14 are much too low. Second, the percentages don't quite work. With earn rate r and standard deviation sd, after 5 hours, breaking even is sqrt(5)(r/sd) standard deviations below average.

59% corresponds to at most .23 standard deviations below the mean, so r/sd ~ .10, standard deviation/earn ~ 10.
63% corresponds to at most .33 standard deviations below the mean, so r/sd ~ .15, standard deviation/ean ~ 7.

The 63% agrees with interpreting the 14 as a standard deviation, not a variance. Perhaps the 59% was supposed to come from a standard deviation of 10 BB and an earn rate of 1 BB. That would indeed have about half of the variance, but the variances would be about 200 and 100.

[Andy B]

It is my opinion that people who are risk-averse should not be playing poker for a living.

[TimM]

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A player with a +2 BB/hr winrate with a variance of 14 BB/hr will emerge as a winner in a 5-hr session about 63% of the time.

A player with a +1 BB/hr winrate with a variance of 7 bb/hr winrate will emerge as a winner in a 5-hr session about 59% of the time

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Whats the math on that.

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I simulated it using some EXCEL programming. The numbers should be accurate within half a percentage point or so. There are more mathematically elegant ways to make the caclulation, but this is easier for me.

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It's actually 62.5% in both cases. I use the NORMDIST excel function.

A more interesting result:
1 BB/hr, 7 SD/hr, P(30BB or more loss in 5 hr) = 1.3%
2 BB/hr, 14 SD/hr, P(30BB or more loss in 5 hr) = 10.1%

Of course, this works both ways:

1 BB/hr, 7 SD/hr, P(30BB or more win in 5 hr) = 5.5%
2 BB/hr, 14 SD/hr, P(30BB or more win in 5 hr) = 26.1%

[TimM]

Calculation example:

<font class="small">Code:</font><hr /><pre>
A1: $/X or BB/X (X can be per hour, per 100 hands, doesnt matter)
A2: Standard Deviation in $/X or BB/X (Same X as above - use your SD/hr or SD/100)
A3: Session size (in multiples of X. Use 5 for 5 hours or 500 hands)
A4: Session result (in $ or BB as above)
A5: =NORMDIST(A4, A1*A3, A2*SQRT(A3), TRUE) (Computes chance of this session result or worse)
A6: =1-A5 (Computes chance of this session result or better)
</pre><hr />

[Mason Malmuth]

Hi Everyone:

I'm going to give Slotboom the benefit of the doubt here. There's no question that some of his advice in the past has been at best highly confused. But he has stated elsewhere on these forums that this quiz is flawed and that it is several years old.

He probably should be judged, criticized, praised, etc, based on what he's doing now.

Best wishes,
Mason

[Jaquen H'gar]

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It is my opinion that people who are risk-averse should not be playing poker for a living.

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Actually, professional gamblers who use risk-aversion, i.e. always considering EV/var rather than simply EV usually perform better over the long term than those who don't.