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

[Michael Davis]

Does Slotboom's weak-tight advice promote a higher percentage of winning sessions? Does it help avoid the occasional complete disaster albeit at a steep long-term price?

If either of these is true, it is easy to see why someone could be convinced that playing his way is right if they do not read carefully.

-Michael

[pudley4]

It's possible that since Rolf plays much higher games than he writes about, he's not familiar with how poorly most 10/20 players really play.

It's also possible that since he plays a lot of PLO (Pot Limit Omaha), much of his thinking from that game still bleeds over into his Holdem advice (especially the "be wary when you don't have the nuts" advice)

[Nate tha' Great]

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.

[ QUOTE ]
Does Slotboom's weak-tight advice promote a higher percentage of winning sessions? Does it help avoid the occasional complete disaster albeit at a steep long-term price?

If either of these is true, it is easy to see why someone could be convinced that playing his way is right if they do not read carefully.

-Michael

[/ QUOTE ]

[thrillhouse7]

[ QUOTE ]
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

[/ QUOTE ]

Whats the math on that.

[Nate tha' Great]

[ QUOTE ]
[ QUOTE ]
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

[/ QUOTE ]

Whats the math on that.

[/ QUOTE ]

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.

[TimM]

[ QUOTE ]
[ QUOTE ]
[ QUOTE ]
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

[/ QUOTE ]

Whats the math on that.

[/ QUOTE ]

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.

[/ QUOTE ]

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 />

[Cazz]

Some math: (It is early so there may be an error or two in here)

If your standard deviation (sigma) is 10 BB for 1 hour, then for N hours the standard deviation is sqrt(N) * 10 BB.

Confidence intervals. Results should be around the expected value (win rate per hour * hours)
----------------------
+/- 1 std. deviation 66.7% of the time
+/- 2 std. deviations 95% of the time
+/- 3 std. deviations 99% of the time

So, over N hours you should expect to win
N * avg +/- sqrt(N) * sigma, 66.67% of the time.
16.7% of the time you will fare worse and 16.7% of the time you will fare better. You can alter this percentage by selecting a larger or smaller range
N * avg +/- X * sqrt(N) * sigma, where X is some scalar.

X = 1 -&gt; 16.7%
X = 2 -&gt; 2.5%
X = 3 -&gt; 0.5%

If your goal was to limit losing session to some percentage of the time, you can select the correct scalar, X. Using X you can then determine the relationship between the average and the sigma.

The lower value on the confidence interval is
N * avg - X * sqrt(N) * sigma
Set this to zero (or &gt;= zero) and solve:
avg &gt;= X*sigma/sqrt(N)

Example: You want limit losing sessions to 16.7% of the time, and a session is 8 hours. Your sigma is 10 BB.
avg &gt;= 1.0 * 10 BB /sqrt(8)
&gt;= 3.54 BB

Also, for every 1 BB your single hour sigma goes up (or down), your average must go up (down) by 0.35 BB (1/sqrt(8)) to keep the losing session percentage the same.
Or for every 1 BB per hour you give up, you have to reduce
the single hour sigma by 2.83 BB.

[ACW]

[ QUOTE ]
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.


[/ QUOTE ]

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.

[pzhon]

[ QUOTE ]
[ QUOTE ]
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.


[/ QUOTE ]

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.

[/ QUOTE ]
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.