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| ==Against all odds?==
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| We shall show how defines his measure of skill and of chance for a game using the following data from five weeks of our low-key Monday night poker games.
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| <center>
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| <table width="90%" border="1">
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| <tr>
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| <td width="13%"><div align="center"></div></td>
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| <td width="13%"><div align="center">Sally</div></td>
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| <td width="12%"><div align="center">Laurie</div></td>
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| <td width="13%"><div align="center">John</div></td>
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| <td width="13%"><div align="center">Mary</div></td>
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| <td width="12%"><div align="center">Sarge</div></td>
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| <td width="12%"><div align="center">Dick</div></td>
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| <td width="12%"><div align="center">Glenn</div></td>
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| </tr>
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| <tr>
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| <td><div align="center">Game 1</div></td>
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| <td><div align="center">-6.75</div></td>
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| <td><div align="center">-10.10</div></td>
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| <td><div align="center">-5.75</div></td>
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| <td><div align="center">10.35</div></td>
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| <td><div align="center">9.7</div></td>
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| <td><div align="center">4.43</div></td>
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| <td><div align="center">-1.95</div></td>
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| </tr>
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| <tr>
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| <td><div align="center">Game 2</div></td>
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| <td><div align="center">4.35</div></td>
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| <td><div align="center">-4.25</div></td>
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| <td><div align="center">.40</div></td>
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| <td><div align="center">-.35</div></td>
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| <td><div align="center">-8.8</div></td>
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| <td><div align="center">-.15</div></td>
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| <td><div align="center">5.8</div></td>
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| </tr>
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| <tr>
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| <td><div align="center">Game 3</div></td>
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| <td><div align="center">6.95</div></td>
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| <td><div align="center">-4.35</div></td>
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| <td><div align="center">.18</div></td>
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| <td><div align="center">-7.75</div></td>
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| <td><div align="center">7.65</div></td>
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| <td><div align="center">-5.9</div></td>
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| <td><div align="center">3.9</div></td>
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| </tr>
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| <tr>
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| <td height="24"><div align="center">Game 4</div></td>
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| <td><div align="center">-1.23</div></td>
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| <td><div align="center">-11.55</div></td>
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| <td><div align="center">4.35</div></td>
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| <td><div align="center">2.9</div></td>
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| <td><div align="center">4.85</div></td>
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| <td><div align="center">-3.9</div></td>
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| <td><div align="center">3.25</div></td>
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| </tr>
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| <tr>
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| <td><div align="center">Game 5</div></td>
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| <td><div align="center">6.35</div></td>
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| <td><div align="center">-1.5</div></td>
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| <td><div align="center">-.45</div></td>
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| <td><div align="center">-.65</div></td>
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| <td><div align="center">-.25</div></td>
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| <td><div align="center">-4.9</div></td>
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| <td><div align="center">1.42</div></td>
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| </tr>
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| </table>
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| </center>
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| To compare the skill and chance in a game Sherman uses a statistical procedure called Analasis of verations (ANOV).
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| Sherman assumes that this variation is due primarily to skill. The within group sums of squares estimates the variation of the winnings within players and Sherman assumes that this is primarily due to luck. This leads him to define the skill factor as the ratio of the between group sums of squares to the total sums of squares and the luck factor as the ratio of the within group sums of squares to the total sums of squares. This gives us a skill % and a luck %. Using our poker data and the SAS ANOVA program we find that the total sums of squares is 1069.95, the between groups the sums of squares is 311.447and the within groups the sums of squares is 758.499. Thus from our poker data we would estimate the skill % to be 311.447/1069.95 = 29.1% and the luck % to be 758.499/1069.06 = 70.9%. Thus not surprisingly for our games luck is more important than skill.
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| In his second article, Sherman reports the skill % he obtained using data from a number of different types of games. For example, using data for Major League Batting hits the skill% was 39% and for home runs it was 68%. For NBA Basketball for points scored it was 75% and for poker stars in weekly tournaments it was 35%.
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| Sherman concludes his articles with the remarks:
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| <blockquote>If two persons play the same game, why don't both achieve the same results? The purpose of last month's article and this article was to address this question. This article suggests that there are two answers to this question: Skill (or systematic variance) or Luck (or random variance). Using both the correlation approach described last month and the ANOVA approach described in this article, one can estimate the amount of skill involved in any game. Last, and maybe most importantly, Table 4 demonstrated that the skill estimated involved in playing poker (or at least tournament poker) are not very different from other sport outcomes which are widely accepted as skillful.<\blockquote>
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| ===Discussion questions===
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| (1) Do you think that Sherman's measure of skill and luck in a game is reasonable? If not why not?
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| (2) There is a form of [http://www.duplicatepoker.com/WebSite/epokerusa.aspx?page=dpg_rules duplicate poker] modeled after duplicate bridge. Do you think that the congressional decision should not apply to this form of gambling?
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| This is not finished.
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