96 > 99 > 87 > 97

I think. Not completely sure the decision is correct, but I'm pretty sure I dump the 96.

A very quick analysis makes me think that 87>96>>99>>97.

We have 4 hands to make 51 points. If we get average scoring in the next three, we need a bunch right now. My first thought was keep 7899. 10 points (-2 for opp). 3 cards give us 16, 4 give us 12, 6 give us 18, 1 gives 14, and 32 leave it at ten.

Keeping 6999 gives us 12 (-2) 42 times, and 4 cards give us 20.
I believe it gives us the better average and the best maximum.

Keeping 6789 is a distant third, and lol 6889.

87 is more dangerous in the crib? I’d toss 96 and not think twice.

I have 3 of the 6 cards that can singly improve 96. It takes and 87 combo to setup a run (dealer tosses 87 or x7/x8 and gets the other in a cut.

If my opponent improves by a 6,7,8, or 9 cut then I also improve to at least 12 and more likely 16+

If throw 87, opponent can hit another 8 or 7 (or both) and I don’t improve.

It is more dangerous, but I think we need to be agressive and not worry overmuch about defense. We need to put up some big numbers here and next hand. If the opponent gets really lucky too, we were going to lose anyway. If the opponent gets a bit above average for a hand or two, we still have a chance if we are aggressive, and try to maximize our own scores.

I threw some numbers in a spreadsheet with a bunch of assumptions. You have a gross for your hand about 12.7 vs 12 with your 6999. Most of that is due to bricks worth 12 vs only 10 for my 7899.

However I got a net that was about 0.5 points better with 7899. (More bad cards, especially 7s and 8s that are bricks for 6999 but big danger in crib)

Also by your big hand theory, I have 4 outs for 16 (6x3, 9x1) and 6 outs for 20 (7x3, 8x3) for 7899.... however you only have 4 outs for 20 (6x3, 9x1) for 6999.

So the net is better (less danger) and frequency of the big score is >twice as frequent. I will stick with 7899 and discard 69.

Also the frequency of disaster (big crib) will be more by tossing 78.

Whoops, I forgot to count the extra 15s. Good catch.

started when I was 6 years old. Rarely have to count- most of the time the total comes to me by simple recognition.

I agree with dan and didn't think it was too close tbh. Lots of folks were saying toss the 78, never break up 12, etc which I vehemently disagree with.

Let me see if I have this right.

7899
3 sixes (16 points)
3 sevens (20)
3 eights (20)
1 nine (17)
4 tens (12)
32 others (10)
------------------------------
553 points from 46 cards


6999
3 sixes (20)
1 nine (20)
42 others (12)
-----------------------------
584 points from 46 cards


6999 has about a 0.67 point advantage. Is this meaningful? For a gambler, this kind
of edge would be everything. For me, this would be the decider in this case. However, there is the fact that 7899 will give you two more maximums, which could be significant here. It raises the general question of when do you choose the higher EV, and when do you need to play for the longshot.

The final issue is a personal one. How important is minimizing the opponent's scoring? Throwing 78 does have more risk than 96, but how much does it matter? For me, I am not worried about the opponent; I am interested in getting the most out of my hands, because I will lose if I don't.

Yes. But the net is worse with 78. Much more dangerous in the crib (I ballparked 1.5 points more, for a net of about -0.7).

My other argument is that the frequency of the “big”
Hand is also much higher. 6 20s plus 1 17 and 3 16s vs only 4 20s

(And frequency of big opponent cribs goes up).

Gotta look at the whole picture-getting 0.7 closer on average does not help nearly enough compared to more than twice the chance to get 4-8 closer. Also you run the risk of opponent getting a big score and going out before you get to count your deal.

Put another way, that 0.7 is unlikely to be the difference - how often do you go out on the number?

I guess my point is that the net, in this case, has low relevance. If the opponent gets 51 in her dealer hand, crib, and pone hand requires two very good hands and a good crib with our discard. Our addition is not going to significantly affect the probability of her winning before we get to our crib. That's why I say that we need to maximize our own hands, rather than worrying about the opponent.

The point of including the 16s and 17s is a good one. I am left, then to weigh the expected value against the potential bigger hands. At what point do we ignore EV and go for the more likely longshot.

In the end, I suspect both plays give us about the same chance of winning. As I said at the start, 7899 was the initial attraction, and probably what I play in the moment.

I look that we are far enough out that we get 4 counts while our opponent gets 3. I need to get out in my 4 hands and 3 pegs and minimize his chance of going out in 3 counts and 3 pegs. I’d rank avoiding crib disaster a little above my hand.

Precisely. I don't understand how this isn't obvious. The 78 are two of the worst cards you could toss as pone.

Strategically, I agree wholeheartedly.

My choice here is purely tactical.

I think the whole issue is whether we can win in four counts with normal play. Or, perhaps, whether she can win in three. I don't think that we will inflate a so-so crib into a great one by tossing 78.

We need a few extra points per count; she needs a lot of extra points each count.

I would love to see a Monte Carlo simulation done for this situation. I think it is close, either way.

IME the bolded is absolutely false. Try throwing connectors (esp these) to the dealers crib often and see what happens.

Great discussion, all!

And here I am stressing the two sentences before your bolded one, lol. I won't go on because we are all entrenched in reasonable camps, but I will suggest that a crib helped by 78 will usually be helped by 69 as well. 78 might give a bit more, I will admit, but the difference between them should not decide the game.

This has been a fun discussion.

I like the point that if we toss 96 and a 8 or 7 cuts then no harm (absent dealers crib cards, but only the gutshot card is that dangerous). If I toss 87, and 6-7-8-9 cuts then any 6-7-8-9 dealer crib card makes 12. It’s not even close in danger 87>>>>96. For a gross gain of less than 1 it’s not worth it.

Apologies and don’t mean to offend, but can’t agree with two reasonable camps.

I don’t think the small gross gain Is worth the trade-off vs 1. net small loss, 2. frequency of our big hand, and 3. frequency of a crib big hand.

I also like that any good cut cards for 69 in the grub give us at least 16. Not true for 78. If I keep 6999 and 7 or 8 cuts I get nothing.

^ Once again dan, BINGO. Nice post.

Does no one else play regularly? Please, post hands, play me on CribbagePro, etc.

Just had an interesting hand come up....

Losing 98-82, pone with 78910JJ

WWYD?

Flip the table over and quit?

You need a big hand to get in range to even hope to get out next hand so you have to throw caution out the window???

JJ and 87 are the only options.

789T is 6 outs for 14 and 6 for 12
9TJJ is 6 outs for 16 and 1 for 15. Plus you can assume knobs half the time. You have to get close to 100 to have a chance so I would reluctantly toss the 78. Making 12 just isn’t enough.

More thought but even tho I hate it tossing 7J is prolly best. We have to survive their 3 counts.

Losing 105-102, you're pone with A23355

WWYD?

Realistically, we need to win with this count. Needing 19 points, we need quadruple runs, or a triple with a good bit of peggjng.

Throwing 55: A or 2 gives us 16 points, needing to peg 3. 3 gives us 15, needing to peg 4.
Throwing A2: 4 gives us 18 points, needing to peg 1.

The first gives 6 or 8 cards to get us close. The second gives us 4 cards to almost certainly win.

If we can estimate (can we?) that pegging 3 is about the same as 4, and that either is about half as likely as pegging 1 or 2: both plays give us the same chance of winning. Otoh, keeping the smaller cards gives you a slightly larger chance of 3/4; but keeping the larger cards, you need only 1, which is almost a sure thing.

Quick thought- keeping the low double run gives us lots of pegging opportunity. Lead the 2. Opponent is not going to pair us we want to save the 33 in case we can pair ourselves if oppo has to GO??

Agree we have to try and go out and not worry about the crib. Twice the chance to get close and peg out. Toss 55.