[jcm4ccc]

You are absolutely correct. As far as credentials (since it was brought up in other posts), I have a Ph.D. in psychology and am employed as a psychometrician for the American Board of Anesthesiology. Here is a post I made a few weeks back, in regard to a similar post about standard deviations of SnGs.



I don’t think you should use standard deviations for SINGLE SNGs. You should combine multiple SNGs to use standard deviation. A standard deviation is only useful when you have a normal distribution of data. For example, let’s assume that:

• The mean height of the American male is 70 inches.
• The standard deviation is 5 inches.
• The data is normally distributed.

The last statement is crucial. It allows you to use z-tables calculate all sorts of things, such as:

68% of American males are between 65 and 75 inches
99% of American males are taller than 55 inches.

Etc etc etc.

SNGs do not have a normal distribution of data (there are only 4 possible outcomes), so you can’t make similar calculations. For example, here is the data that you described:

• Lose $11 60% of the time
• Win $9 13% of the time
• Win $19 13% of the time
• Win $39 14% of the time

• The mean profit is $2.50
• The standard deviation is $16.36

If you had a normal distribution of data, then the following would be true:

• 34% of the time your profit would be between -$13.86 and $2.50 (the difference between the mean and one standard deviation below the mean).

However, in reality, you are making between -$13.86 and $2.50 around 60% of the time (the times you are out of the money).
One way to use standard deviations for SNGs is to combine multiple results until you approximate a normal curve. Twenty-five SNGs seems to be large enough to do that. I used Excel to simulate 30,000 different sets of 25 SNGs, using the following parameters:

• Lose $11 60% of the time
• Win $9 13% of the time
• Win $19 13% of the time
• Win $39 14% of the time
• All results are independent of each other (in other words, the fact that you just won an SNG has no bearing on whether or not you win the next SNG).

The results were:

Mean: $63.14
Standard Deviation: $92.19



Here is a frequency chart of the 30,000 sets. The first column is the amount of winnings over 25 SNGs. The second column is how frequently this occurred. As you can see, the data centers around 65 and spreads out in a nice distribution. I have a graph that shows the normal distribution of this data, but I couldn’t figure out how to paste it:


$ winnings # occurrences
-235 2
-225 3
-215 2
-205 6
-195 13
-185 23
-175 19
-165 41
-155 71
-145 79
-135 111
-125 142
-115 191
-105 251
-95 295
-85 356
-75 494
-65 500
-55 598
-45 755
-35 823
-25 894
-15 944
-5 1022
5 1170
15 1144
25 1242
35 1265
45 1267
55 1264
65 1203
75 1254
85 1236
95 1187
105 1182
115 972
125 1035
135 855
145 844
155 747
165 703
175 593
185 534
195 452
205 388
215 316
225 302
235 258
245 208
255 160
265 119
275 86
285 86
295 78
305 47
315 41
325 46
335 21
345 14
355 8
365 12
375 8
385 4
395 9
405 2
425 2
465 1
Total 30000




You can use this data and z-tables to ascertain a number of useful facts about playing a set of 25 SNGs:


• You will lose money 25% of the time
• 38% of the time, you will gain between $17 and $109 (one-half standard deviation above and below the mean)
• 16% of the time, you will gain more than $155 (one standard deviation above the mean)