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### Feb 22 session 3 hand 23

Posted: Fri Feb 28, 2014 9:30 pm
Code: Select all
`Vorhand            Mittelhand         Hinterhand         SkatJ:                 J: C D             J: S H             J:     C: A 9 8           C: 10 Q            C: 7               C: K   S: 7               S: 10 9            S: K Q 8           S: A   H: A 7             H: Q 9             H: 10 K 8          H:     D: A 10 9 7        D: Q 8             D: K               D:    `

I was Vorhand and neither of the opponents bid, and I decided to throw the hand in. The others in my seat both wanted to play the hand, one of them bidding to 22. The results were very different: Grand against 4 making for +120 and Null going off for -46.

Do you believe the Grand was sound?

Patrick

### Re: Feb 22 session 3 hand 23

Posted: Fri Feb 28, 2014 10:59 pm
Two questions here: whether you should play at all and what you should play.
After two passes it seems as though this hand has a lot of chances to be improved by the skat. If you don't find a jack or the missing ace, you still have the option of trying the null. I'm not sure whether I would have played it, but it seems a reasonable chance to take if you are feeling lucky. Holding a bid of more than 18 looks very risky, though.
Having picked up that skat I would definitely play grand. I throw the D10 and CK and if none of my aces is ruffed I have at least 64 points (14 in the skat, 44 for aces, and the club and heart aces must each catch at least a queen for the other 6 points). The chances of a void are I think significantly reduced by the fact that neither opponent managed to bid, even though they had four jacks between them.

### Re: Feb 22 session 3 hand 23

Posted: Sun Mar 02, 2014 12:02 am
Thinking about this some more, if we do the calculation naively, we score +170 if the Grand makes and -290 if it loses, so we need a 63% success rate to break even on these.
If the other 20 cards are dealt randomly, in each of our two-card suits there is a 97% chance that both opponents will follow to our ace, and in our four-card suits the chance is 79%.
So the chance of winning is at least .97 × .97 × .79 × .79 which is nearly 59%. This is a slight underestimate because:
a) there are other ways to win - for example by dropping a 10;
b) the distributions of the other suits are not independent;
c) the lack of bidding rules out some extreme distributions.
Overall, after we have taken the skat, I think the Grand is sound enough. Bear in mind also that if the Grand is losing, that increases the chance that any other contract you might try will also lose.

### Re: Feb 22 session 3 hand 23

Posted: Sun Mar 02, 2014 1:46 pm
I decided against bidding because I didn't like the thought of playing on after picking up something like SK, HK.

Assuming I am happy to play in diamonds if I pick up any trump, the hand becomes playable with a skat containing any jack or diamond, or the ace of spades or seven of clubs. That is nine cards, so 78 out of 231 possible skats won't give me any of them. The probability of a good card is just below 2/3, and it goes above 2/3 when you add in the three skats containing two higher clubs.

As for saying 'yes' to an opponent's bid, there are two hazards:
(a) the opponent's bid is based on diamonds, meaning I don't want to play in that suit and the break is more likely to be bad in Grand;
(b) the opponent's bid is based on hearts or spades, I hold a bid of 20 and a black jack in the skat stops me playing in diamonds.
Neither seems particularly likely, and in both cases there is still the chance of bailing out in Null.

Patrick

### Re: Feb 22 session 3 hand 23

Posted: Sun Mar 02, 2014 1:52 pm
I would have picked the Skat up, for exactly the reasons John stated, and played Grand, also for John's reasons.

### Re: Feb 22 session 3 hand 23

Posted: Sun Mar 02, 2014 9:45 pm
There are other skats that make this hand playable, apart from those that Patrick listed. For example, any two of H10, H9, H8 give you a playable null - that's three more. Moreover skats like H9+S8 or S10+S8 give you a Null with chances of winning, so the odds of a playable hand are comfortably over 2/3. That's without factoring in the fact that two passes increase the probability of finding a jack or ace in the skat.