03-25-2016, 12:32 PM

In reviewing this post from Mick, it struck me as I looked at the image with color-coded cards that a full 75% (15 of 20) of the tricks in this hand were worth 2 points. This seemed to be at odds with the notion that tricks should be counted as the average point value of 2.4 (sometimes rounded to 2.5) points each. Granted, the more tricks you take, the more they will tend towards the average - but I wondered if using the average as an estimate is a good idea. I decided to do a little more analysis.

I have 34 hand histories from various games I've played saved on my computer. So I entered all the data into Excel and did some analysis of the point values for each trick. For purposes of this analysis, I decided to ignore the extra 2 points awarded for the last trick - in my opinion, this is a different discussion - so the point values for the last trick were based only on the number of "pointers" (aces, tens, and kings) in the trick.

I should also note that some of the hand histories were abbreviated due to one player TRAM-ing. In these instances, I went to the point at which TRAM was declared and virtually played out the last few tricks to determine the point values for each of these tricks. To my recollection, there was only one hand where there was any question as to how the cards would have been played out. In this hand, there wasn't really a big difference in terms of the points for each trick, and it wouldn't have affected the overall numbers (i.e., it would have been something like 3 points on trick 18 and 2 on trick 19 or 2 points on trick 18 and 3 on trick 19 - the overall number of tricks worth 2 and 3 points would have been the same).

So, here are the results of my analysis:

Total tricks evaluated = 680

Number of tricks with 0 points = 3 (0.4% of total)

Number of tricks with 1 point = 49 (7.2% of total)

Number of tricks with 2 points = 351 (51.6% of total)

Number of tricks with 3 points = 227 (33.4% of total)

Number of tricks with 4 points = 50 (7.4% of total)

Based on this analysis, it seems that assigning a value of 2.4 points per trick would overestimate the value of almost 60% of the tricks (0.4% + 7.2% + 51.6% = 59.2%), while underestimating the value of 40.8% of the tricks. To me, this is a noteworthy observation - perhaps there needs to be a better way to determine overall point-taking ability of a given hand. (I don't have the answer, but would love to explore this further.)

I further analyzed the point value of tricks based on the trick sequence. Here is what I discovered (based again on analysis of 34 hands):

Trick 01 - average value = 2.09 points (< 2.4)

Trick 02 - average value = 2.21 points (< 2.4)

Trick 03 - average value = 2.38 points (< 2.4)

Trick 04 - average value = 2.35 points (< 2.4)

Trick 05 - average value = 2.38 points (< 2.4)

Trick 06 - average value = 2.12 points (< 2.4)

Trick 07 - average value = 2.21 points (< 2.4)

Trick 08 - average value = 2.29 points (< 2.4)

Trick 09 - average value = 2.47 points (> 2.4)

Trick 10 - average value = 2.47 points (> 2.4)

Trick 11 - average value = 2.00 points (< 2.4)

Trick 12 - average value = 2.41 points (> 2.4)

Trick 13 - average value = 2.44 points (> 2.4)

Trick 14 - average value = 2.29 points (< 2.4)

Trick 15 - average value = 2.47 points (> 2.4)

Trick 16 - average value = 2.24 points (< 2.4)

Trick 17 - average value = 2.29 points (< 2.4)

Trick 18 - average value = 2.74 points (> 2.4)

Trick 19 - average value = 3.06 points (> 2.4)

Trick 20 - average value = 3.09 points (> 2.4) (*not including 2 points for last trick)

Based on this analysis, later tricks are generally worth more than earlier tricks. Therefore, it may not be a good strategy for the Declarer to play all his aces in the beginning of the hand, unless he has reason to do so (long side suit without good ability to control trump, mid-length side suit where aces may be forced out and trumped, or short side suit where aces may get caught "hanging").

What other observations do you have from this analysis?

(If you're interested in the Excel data - which includes just the point values for each trick and none of the other game or hand information - send me a private message with your e-mail address.)

I have 34 hand histories from various games I've played saved on my computer. So I entered all the data into Excel and did some analysis of the point values for each trick. For purposes of this analysis, I decided to ignore the extra 2 points awarded for the last trick - in my opinion, this is a different discussion - so the point values for the last trick were based only on the number of "pointers" (aces, tens, and kings) in the trick.

I should also note that some of the hand histories were abbreviated due to one player TRAM-ing. In these instances, I went to the point at which TRAM was declared and virtually played out the last few tricks to determine the point values for each of these tricks. To my recollection, there was only one hand where there was any question as to how the cards would have been played out. In this hand, there wasn't really a big difference in terms of the points for each trick, and it wouldn't have affected the overall numbers (i.e., it would have been something like 3 points on trick 18 and 2 on trick 19 or 2 points on trick 18 and 3 on trick 19 - the overall number of tricks worth 2 and 3 points would have been the same).

So, here are the results of my analysis:

Total tricks evaluated = 680

Number of tricks with 0 points = 3 (0.4% of total)

Number of tricks with 1 point = 49 (7.2% of total)

Number of tricks with 2 points = 351 (51.6% of total)

Number of tricks with 3 points = 227 (33.4% of total)

Number of tricks with 4 points = 50 (7.4% of total)

Based on this analysis, it seems that assigning a value of 2.4 points per trick would overestimate the value of almost 60% of the tricks (0.4% + 7.2% + 51.6% = 59.2%), while underestimating the value of 40.8% of the tricks. To me, this is a noteworthy observation - perhaps there needs to be a better way to determine overall point-taking ability of a given hand. (I don't have the answer, but would love to explore this further.)

I further analyzed the point value of tricks based on the trick sequence. Here is what I discovered (based again on analysis of 34 hands):

Trick 01 - average value = 2.09 points (< 2.4)

Trick 02 - average value = 2.21 points (< 2.4)

Trick 03 - average value = 2.38 points (< 2.4)

Trick 04 - average value = 2.35 points (< 2.4)

Trick 05 - average value = 2.38 points (< 2.4)

Trick 06 - average value = 2.12 points (< 2.4)

Trick 07 - average value = 2.21 points (< 2.4)

Trick 08 - average value = 2.29 points (< 2.4)

Trick 09 - average value = 2.47 points (> 2.4)

Trick 10 - average value = 2.47 points (> 2.4)

Trick 11 - average value = 2.00 points (< 2.4)

Trick 12 - average value = 2.41 points (> 2.4)

Trick 13 - average value = 2.44 points (> 2.4)

Trick 14 - average value = 2.29 points (< 2.4)

Trick 15 - average value = 2.47 points (> 2.4)

Trick 16 - average value = 2.24 points (< 2.4)

Trick 17 - average value = 2.29 points (< 2.4)

Trick 18 - average value = 2.74 points (> 2.4)

Trick 19 - average value = 3.06 points (> 2.4)

Trick 20 - average value = 3.09 points (> 2.4) (*not including 2 points for last trick)

Based on this analysis, later tricks are generally worth more than earlier tricks. Therefore, it may not be a good strategy for the Declarer to play all his aces in the beginning of the hand, unless he has reason to do so (long side suit without good ability to control trump, mid-length side suit where aces may be forced out and trumped, or short side suit where aces may get caught "hanging").

What other observations do you have from this analysis?

(If you're interested in the Excel data - which includes just the point values for each trick and none of the other game or hand information - send me a private message with your e-mail address.)