Friday 3:04 AM

Covers for a possible six or nine to add. Ace,seven or eight cuts do well also. Ten-Ace to crib might add more also. Ace lead do not want to engage in middle card opening pegging. dec

   

Friday 3:08 AM

2 cut could bode well for my crib and I need it. Defense

   

Friday 3:13 AM

Way to go james500! Another hand for discussion.
Stayed with 6 pts in the hand and 2 pts in the crib. This arrangement has a slightly higher expected average than tossing A-T. If my calculations are correct, 31 cuts keeps this hand at 8 points.
My choice has 22 cuts for improvement at a lower maximum while tossing A-% has 15 cuts at a higher maximum. But we still have 2 points in the crib.

   

Friday 3:17 AM

This morning I went for the Hail Mary because I am losing this game and feel I need it.

   

Friday 5:37 AM

I’m in pretty good shape if I can limited my opponent from forward movement on this deal. I like little pairs to my crib.

   

Friday 6:07 AM

I'll toss myself the Aces. The alternative is A-10 or 8-10, neither of which is promising.

In this position, I gotta weigh my chances of getting to hole 96 versus trying to stifle my opponent from doing the same. I need to travel 25 pegs, and my opponent just 11. The 2 starter makes that decision easier, play defense.

   

Friday 6:17 AM

I'll try keeping a known eight points in my hand, with close cards in my box.

   

Friday 8:14 AM

Not sure whether to play offense or defense here. But I will play it this way no matter my stance. I like having that escape card in my hand. (A-10) is surprisingly not much worse than (8-10). This choice has the higher average hand by almost a full point over A-A-7-7, and two full points over 7-7-8-10. I’m in the minority today. Using S’s theory I may learn something today. I know I did yesterday. Thanks James for two excellent puzzles. May the hits keep on coming.

   

Friday 8:18 AM

A-10 throw for me. I want that lucrative double run.

   

Friday 12:00 PM

Based on my scant empirical data, holding A-7-7-8 or 7-7-8-10 are less than .1 point variance with the former having the nudge. That's true if considering offense or optimal pegging strategy. Would not play it so safe as to choose defense with opponent at hole 84. Offense seems a bit reckless since non-dealer needs only 11 points to reach 4th street CPZ 95-99. Holding A-7-7-8 better fits the optimal choice than does the 7-7-8-10 as it allows an escape card wit the Ace. There is no escape with 7-7-8-10 if non-dealer decides to play on dealer responses. So potential hand value, an edge on optimal pegging score is enough to overcome the larger crib value of the A-A discard. Will play off the lead and attempt to close the count a couple of times. If opponent has middle cards, playing this hand becomes very difficult. Hope for X-pointers or small cards or a combination thereof so that pegging damage remains minimal. Another good puzzle James 500! The quality of the puzzles has become so high that I have been deleting a couple of mine each month to make room for other contributors. Great to see the improvement in puzzle quality and many added contributors. You deserve a standing ovation though most folks in the age group that frequents this site can't clap and stand at the same time.

   

Friday 1:49 PM

I don't think its worth keeping A-A-7-7 to throw the gapper 8-10 as there are so few cuts that improve A-A-7-7 but let's look at the three possibilities:

A-A-7-7: 8pts + 4¾pts (Schell: 5.10) = 12¾pts

A-7-7-8: 8pts + 3½pts (Schell: 3.65) = 11½pts

7-7-8-10: 6pts + 5¼pts (Schell: 5.38) = 11¼pts

Potential:

A-A-7-7: Improves with AA, 6666, 77, 888 = 11 cuts = 11/46 = 23.9% up to 12/14/20pts with all cuts.

A-7-7-8: Improves with AA, 6666, 77, 888, 9999 = 15 cuts = 32.6% up to 12/14/16/18pts with all cuts.

7-7-8-10: Improves with AA, 5555, 6666, 77, 888, 9999, 101010 = 22 cuts = 22/46 = 47.8% up to 12pts with 6666, 77, 888, 9999 = 13 cuts.

Pegging:

I think A-A-7-7 may peg best with perhaps A-7-7-8 next best.

Position:

We're at par-hole but Pone is only 12pts from 96pts so I will try to score points with the pegging but reasonably safely.

Summary:

A-A-7-7 has the least number of cuts for improvement but it has the best maximum and also should peg best. It also starts with 1¼pts more than the other two so I don't think the better potential of the other two will catch up. I'll throw the 8-10 which as a small bonus is suited.

   

Friday 2:35 PM

At 70*-84 playing a Defense strategy for the pegging the dynamic expected averages and Win/Loss %s are:

__________________Pone's
Defense____Hand___Pegs___Crib_Total____W3 %___W4 %
A-7-7-8____10.22+(-2.07)+3.29=11.44____11.5___26.7
7-7-8-10____8.26+(-2.11)+5.25=11.40____10.8___25.2
A-A-7-7_____9.39+(-2.07)+3.67=10.99____10.3___24.3

Defense________L3 %____L4 %
A-7-7-8________39.6____64.1
7-7-8-10_______41.6____66.3
A-A-7-7________41.9____67.4

A-7-7-8 is 0.04pt better than 7-7-8-10 and 0.45pt better than A-A-7-7. It is also best for Win %s and Loss %s which take account of the board position at this critical stage. So I'll select A-10 to discard.

After the 2 cut I'll play Optimally (cautious offense) to the lead.

   

Friday 2:44 PM

Pulling my hair out today!

I've always said that Toss (A A) is under-rated, but with the two other choices of either Keep (A A 7 7) or Keep (A 7 7 8), note that we hold an interesting form of "Sweet Sixteen," which pegs very well against a Dealer who holds 5-X-X-X.

So, james, you've apparently stumped me, as I like each choice better than the one before it!

In mathematics, today's puzzle is reminiscent of what's called a "Non-Transitive Probabilistic Comparison" which you can learn a bit about at: https://www.youtube.com/watch?v=zzKGnuvX6IQ

   

Friday 5:36 PM

I will put the pair of aces in my crib. The cut is nice, and just maybe the pone will discard a 3.