Math/Excel Help (re: a Poker League)

[digamma]

I am in a poker league.

We are coming down to the end of the season and I'm trying to figure out whether I've clinched a spot at the final table (top 8).

I currently sit in 5th place with 90.5 points.

The remainder of the top 11 (only ones who can possibly knock me out of the top 8) are as follows:

6. 72 points
7. 71 points
8. 69 points
9. 67 points
10. 65 points
11. 64 points

Points are awarded from 1st to 9th place in tournaments as follows:
20-16-12-9-7-5-4-3-2

Two tournaments remain.

Other than brute force and trial and error (I can do this), can anyone come up with an excel formula I can use to try to see what the magic number for clinching a top 8 spot is?

If it matters (and I don't think it does 4th place has 93 points).

[Suburban Rhythm]

Highest possible total 9th can reach is 107

Not knowing the tie breaker, you need to finish with 107.5

So you need 17 points over the next two tournaments

[Travis]

True, but if 9th does that, the current 8th place team can only finish with a high of 101 (16 points in each tourney), so they'd be the team to get passed so long as digamma can get to 102 points.

I think the answer here is a combination of what's the lowest rated person who could pass him and how the points then spill out above that and how many people would get leapfrogged before digamma would be eliminated.

Obviously 17.5 points gets him in, but a much lower number is probably the magic number.

[Suburban Rhythm]

Good point

Honestly, putting into Excel in my head...You might be better off with the brute force math.

You'd need to do an IF for every possible finish combination, 1st thru 9th (10th and 11th don't receive points if I'm reading correctly, so those don't need to be part of the IFs).

[NobodyHere]

Well by adding the highest amounts of points left to the lowest total scores below I get

72 +16+9=97
71+12+16=99
69+9+20=98
67+20+12=99

So it seems to me you need 7 points to clinch.

[Easy Mac]

If you get no points from the first game, then to still have a chance to jump you:

#10 and 11 need to finish no worse than 5th in the first game.
#9 needs to finish no worse worse than 7th in the first game.
#8 needs to finish no worse than 9th in the first game.

[cuervo72]

One scenario where 6-9 would pass you:

<table border="0" height="156" width="425" cellpadding="0" cellspacing="0"><colgroup><col style="width:48pt" span="5" width="64"> </colgroup><tbody><tr style="height:15.0pt" height="20"> <td style="height:15.0pt;width:48pt" height="20" width="64">Cur Points</td> <td style="width:48pt" align="center" width="64">T1</td> <td style="width:48pt" align="center" width="64">T2</td> <td style="width:48pt" align="center" width="64">Final</td> <td style="width:48pt" align="center" width="64">Cur Rank</td> </tr> <tr style="height:15.0pt" height="20"> <td style="height:15.0pt" align="right" height="20">72</td> <td align="right">12</td> <td align="right">7</td> <td align="right">91</td> <td align="right">6th</td> </tr> <tr style="height:15.0pt" height="20"> <td style="height:15.0pt" align="right" height="20">71</td> <td align="right">16</td> <td align="right">5</td> <td align="right">92</td> <td align="right">7th</td> </tr> <tr style="height:15.0pt" height="20"> <td style="height:15.0pt" align="right" height="20">69</td> <td align="right">5</td> <td align="right">20</td> <td align="right">94</td> <td align="right">8th</td> </tr> <tr style="height:15.0pt" height="20"> <td style="height:15.0pt" align="right" height="20">67</td> <td align="right">20</td> <td align="right">9</td> <td align="right">96</td> <td align="right">9th</td> </tr> <tr style="height:15.0pt" height="20"> <td style="height:15.0pt" align="right" height="20">65</td> <td align="right">9</td> <td align="right">16</td> <td align="right">90</td> <td align="right">10th</td> </tr> <tr style="height:15.0pt" height="20"> <td style="height:15.0pt" align="right" height="20">64</td> <td align="right">7</td> <td align="right">12</td> <td align="right">83</td> <td align="right">11th</td> </tr> </tbody></table>
I don't think it's possible for you to be passed by any more than that (there just aren't enough total points), so I *think* you can focus on four spots. With that in mind, it would be worse for you if those currently in 6-9 all finish in the top 4 in the next two tourneys:

<table border="0" height="156" width="444" cellpadding="0" cellspacing="0"><colgroup><col style="width:48pt" span="5" width="64"> </colgroup><tbody><tr style="height:15.0pt" height="20"> <td style="height:15.0pt;width:48pt" align="center" height="20" width="64">Cur Points</td> <td style="width:48pt" align="center" width="64">T1</td> <td style="width:48pt" align="center" width="64">T2</td> <td style="width:48pt" align="center" width="64">Final</td> <td style="width:48pt" align="center" width="64">Cur Rank</td> </tr> <tr style="height:15.0pt" height="20"> <td style="height:15.0pt" align="right" height="20">72</td> <td align="right">12</td> <td align="right">16</td> <td align="right">100</td> <td align="right">6th</td> </tr> <tr style="height:15.0pt" height="20"> <td style="height:15.0pt" align="right" height="20">71</td> <td align="right">16</td> <td align="right">12</td> <td align="right">99</td> <td align="right">7th</td> </tr> <tr style="height:15.0pt" height="20"> <td style="height:15.0pt" align="right" height="20">69</td> <td align="right">9</td> <td align="right">20</td> <td align="right">98</td> <td align="right">8th</td> </tr> <tr style="height:15.0pt" height="20"> <td style="height:15.0pt" align="right" height="20">67</td> <td align="right">20</td> <td align="right">9</td> <td align="right">96</td> <td align="right">9th</td> </tr> <tr style="height:15.0pt" height="20"> <td style="height:15.0pt" align="right" height="20">65</td> <td align="right">5</td> <td align="right">7</td> <td align="right">77</td> <td align="right">10th</td> </tr> <tr style="height:15.0pt" height="20"> <td style="height:15.0pt" align="right" height="20">64</td> <td align="right">7</td> <td align="right">5</td> <td align="right">76</td> <td align="right">11th</td> </tr> </tbody></table>
There might be some other way to pack these together more, but I'm not searching for it. I think you need to get to 97 to be absolutely sure. So one 5th place should do it.

ETA: what NobodyHere said, essentially. And I guess he did find a way to pack them together more. But yay for your half-point.

[NobodyHere]

ETA: what NobodyHere said, essentially. And I guess he did find a way to pack them together more. But yay for your half-point.

I ignored the people in 10th and 11th since it seems to me that digamma's worst-case scenario would have the 4 people right behind him grabbing all the top points.

[TCY Junkie]

With 28.5 being the average of the top four scores combined and their average being slightly less than 70, I'd say 98.5 should get you in.

Edit:I know it's a given to get in so I just averaged it, 97.5 is the number I came up with when I was trying to focus on something else.

[MIJB#19]

I agree with TCY Junkie.
The absolute most a non-qualifying 9th ranked person can have equals: the average of 6th through 9th plus average of the top4 scores plus average of the top4 scores.
= (72+71+69+67)/4+(20+16+12+9)/4+(20+16+12+9)/4
= 279/4+57/4+57/4
= 69.75+14.25+14.25
= 98.25
That means 98.5 (or even 98.26) should be sufficient.

[digamma]

Thanks all.

It will be interesting to see what the final 8th place number is. I'm not sure it will be 90 points (there are 28 people in the league and there have been 18 tournaments so far (half online, half in person)). If averages hold, 8th place ends up at 77 or so.

[digamma]

Second to last tournament was tonight. I finished on the points bubble, but had some things break my way.

Going into the last tournament we sit...

5. Me 90.5 points
6. 78 points
7. 77 points
8. 71 points
9. 69 points
10. 69 points

So, I'm in for the championship game. Bigger is there are some incentives (actually non-financial) for finishing in the top four. Those are in play for the final game as 4th place is at 93 points.