Sacrificing at IMPs (White on Red)

Yesterday I went over the potential outcomes when your table is in a 6 hearts that you think could/should make and you could bid 6 spades doubled which you're sure is going down at least 2 and possibly 4 (or even 5!) We were red and the opponents were white and sacrificing was right but only if we were sure partner had spades or diamonds or both to cover our non-Ace losers. Today we'll look at the same information but with the vulnerabilities switched.

IMP result if I pass 6 hearts.

tricks in S/H	4 or 5 hearts	5 spades doubled	6 hearts	6 spades doubled
10/12	-13	-16	0	-15
10/11	13	5	0	9
9/12	-13	-15	0	-14
9/11	13	9	0	12
8/12	-13	-14	0	-12
8/11	13	12	0	14

IMP result if I bid 6 spades (doubled).

tricks in S/H	4 or 5 hearts	5 spades doubled	6 hearts	6 spades doubled
10/12	9	-5	15	0
10/11	8	-5	-9	0
9/12	5	-5	14	0
9/11	4	-5	-12	0
8/12	-3	-7	12	0
8/11	-4	-7	-14	0

IMP gain by bidding 6 spades (doubled) compared to passing 6 hearts.

tricks in S/H	4 or 5 hearts	5 spades doubled	6 hearts	6 spades doubled
10/12	22	11	15	15
10/11	-5	-10	-9	-9
9/12	18	10	14	14
9/11	-9	-14	-12	-12
8/12	10	7	12	12
8/11	-17	-19	-14	-14

Our gain is better in every single cell of this table as opposed to the one from yesterday. We didn't include the down 5 option (possible if you can't take a single diamond trick) in either chart but it would have been an insane loser yesterday. Very bad if they were making and abysmal if they were going down in 6 hearts. On the flip side, today it would still be a positive move when they're making. (Pretty darn bad if they're going down, but at least if you're very sure they're making it's a good sac even at down 5.)

Perhaps the biggest difference comes when the other table stops in 4 or 5 hearts. Yesterday your loss when 6 didn't make was more than your gain when it did at all numbers of spade tricks. If you were going down 3 and the other table stopped short 6 hearts had to be making 19 of 22 times (86%) just to break even. On the other hand, the same situation with today's table only has to see 6 hearts make 9 of 27 times (33%) for the sac to be right.

A similar difference shows up when the other table stops in 5 spades doubled. Assuming down 3 again, bidding on yesterday was right if they had more than a 86% chance of making. Today it's right to bid on if they have more than a 58% chance of making.

This is something you can actually try to figure out. Are your teammates apt to miss their 26 point distributional slams? If so then saccing red on white is almost certainly going to be wrong. You need to be sure partner has the spades/diamonds you need to make it reasonable. Saccing white on red, on the other hand, has a lot of value. You need to be _really_ sure you're going to set them to let them sit in this 6 heart contract with wimpy/non-accurate teammates. There's no way with my hand that I can have any confidence of setting them more than 2/3rds chance of setting them, so if I doubt Andrew and Byung will find/get pushed into the slam, I need to sac this time.

Sacrificing at IMPs (Red on White)

Byung commented on Board 117 that he'd be worried about the opponents making 6 hearts holding my hand. Since partner never acted and I only have 1 ace with a very distributional hand he has good reason to be worried. It's possible that ace doesn't even cash what with there being only 6 outstanding spades between 3 hands. (Especially if partner refuses to bid with 4 of them. I asked Andrew what he would have done and he would have done everything Jack did on that hand, including the low spade lead. *sigh*) My only other chance at a trick is the diamond king, which is only a trick when West doesn't have AQ and when they don't have 11 tricks outside of diamonds. With me have stiffs in both hearts and clubs that isn't very unreasonable at all, especially with the amount of bidding they did.

Assume they make it to 6 hearts at my table. (I did consider bidding 5 spades off the hop to put them to one heck of a guess, after all, and partner saccing 5 spades over 5 hearts is often a bad idea but could happen anyway.) At IMPs, I need to compare my potential actions against what the other table is going to do. They could end up stopping in 4 (or 5). They could play 5 spades doubled. They could play 6 hearts. They could play 6 spades doubled. I can't imagine stopping in a part-score or in just 4 spades. As far as my potential result, I can either leave them in 6 hearts or I can play 6 spades doubled. Also I need to look at how many tricks are actually there in spades and in hearts, represented by X/Y. Realistic numbers are, I think, 10/12, 10/11, 9/12, 9/11, 8/12, and 8/11.

IMP result if I pass 6 hearts.

tricks in S/H	4 or 5 hearts	5 spades doubled	6 hearts	6 spades doubled
10/12	-11	-13	0	-10
10/11	11	6	0	11
9/12	-11	-10	0	-5
9/11	11	11	0	13
8/12	-11	-5	0	3
8/11	11	13	0	15

IMP result if I bid 6 spades (doubled).

tricks in S/H	4 or 5 hearts	5 spades doubled	6 hearts	6 spades doubled
10/12	-1	-7	10	0
10/11	-2	-7	-11	0
9/12	-8	-7	5	0
9/11	-8	-7	-13	0
8/12	-12	-7	-3	0
8/11	-12	-7	-15	0

IMP gain by bidding 6 spades (doubled) compared to passing 6 hearts.

tricks in S/H	4 or 5 hearts	5 spades doubled	6 hearts	6 spades doubled
10/12	10	6	10	10
10/11	-13	-13	-11	-11
9/12	3	3	5	5
9/11	-19	-18	-13	-13
8/12	-1	-2	-3	-3
8/11	-23	-20	-15	-15

Now, each of these cells will have different odds of actually occurring, so it's not as straightforward as simply summing all the potential results. Given the information we have let's try to come up with some reasonable odds for the different outcomes. The information we have is East has a maximum pass with clubs and hearts, longer clubs. West has a hand good enough to both takeout double 1 spade and penalty double 4 spades. He has longer hearts than clubs, likely significantly so, since he pulled 5 clubs to 5 hearts. He also has longer hearts than diamonds since he skipped 5 diamonds. Partner is broke. He has either very few points, or very few spades, or both.

How many tricks can I take in spades? Well, partner definitely doesn't have any aces, so 10 tricks is certainly the max. I only get to 10 tricks when I can set up or ruff my diamonds with no additional losers. Which requires Qx and 2 extra spades to ruff with, or Qxx and 1 extra spade, or xx with a correct diamond finesse and 2 extra spades, or xxx with two correct finesses and 1 extra spade. Or Qxx with diamonds 3-3 or Qxxx with diamonds 3-2, and so on. If partner has long diamonds then they're massively double fit in the round suits and must be making. If partner has the extra spades and the Q of diamonds they're again massively double fit. If partner has neither then my A of spades should cash, maybe the K of spades too, and partner may have a long trump trick.

Certainly I think their odds of making go way up when our odds of taking 10 tricks go up. 10/11 actually seems pretty unlikely, unless partner somehow has the A of diamonds. The other /11s could happen when partner has a round trick and I have no way of knowing if he does or not. If he does, we shouldn't bid on. If he doesn't, and has either spades or diamonds then we should bid. I have no way of knowing that, so I can't ever make the winning play.

There is a way I could gain that information, though. After an auction of P-P-1S-X partner actually gets a turn to bid. Even with the 4-3-3-3 3 count that he had, I want him to bid 3 spades. And I believe I can infer he doesn't have long spades when he doesn't do so, really making pass over 6 hearts the right play from my hand. I probably should have seen the problem coming in the first place and bid 3 diamonds and not 4 spades, trying to find out if we're actually double fit or not.

At any rate, saccing red on white at IMPs is pretty hard to justify. We really needed a perfect storm to set up to actually make it a super-winning play on the actual board (10/12 was the actual layout). And the opponent actually never found their slam at either table anyway, so it's really a moot point. Just interesting to look at, I thought.

IMP Point Strategy

Sky asked (and rightly so) why I accepted the invitation last board with a pretty mediocre hand. I did have a 5th diamond and a full 13 points so I don't think my hand was the worst it could have been for the bidding but it was still pretty bad. The reason is I've been told you should stretch to bid vulnerable games at IMPs. I want to math it all out though, to justify following that advice in the future. Maybe it's hocum.

At any rate, assume the same number of tricks will be made at each table. (Not a guarantee, look to board 106 for an example.) Assume you don't get doubled in any situation, since it should be at least close if you're talking about accepting an invitation. Then we have the following pay-out table, with 4 possible cases. (We bid 3 or 4, they bid 3 or 4.)

	3-3	3-4	4-3	4-4
Make 2	0	+3	-3	0
Make 3	0	+6	-6	0
Make 4	0	+10	-10	0
Make 5	0	+10	-10	0

So now to determine our expected IMP gain with each action (pass or accept) we need to work out the odds of the opponents going on and the odds of each result.

Assume they always wimp out and stay in 3. Then by passing we get 0 IMPs no matter the result. By going on we lose 3 IMPs when the board makes 2. We lose 6 IMPs when the board makes 3. We gain 10 IMPs whenever the board makes 4 or more. Let's abstract things even more and assume the board never makes 2 or 5. We make 3 p of the time and 4 1-p of the time. Then the equilibrium point is when -6*p + 10*(1-p) = 0, or when p = 62.5%. So if game is 37.5% or better and the opponents pass then we need to bid on.

Assume they always blast on to 4. Then by bidding on we get 0 IMPs no matter the result. By passing we gain the 6 IMPs when it fails and lose the 10 when it makes. Again, the equilibrium point is the same 62.5%.

So, the question then becomes, does game make 37.5% of the time or better when holding QJTx - xx - AKTxx - Kx and partner invites? Partner should have 10-12 points for an invite here I think, so can we build an optimal 10 count fitting his bidding to make? AKxx - xxxx - Qx - xxx makes on a club lead. AKxx - xxxx - Jx - Qxx makes whenever you can pick up the Q of diamonds, which is better than 37.5% for sure. 9xxx - AKxx - Jxx - Qx is pretty much the same, making whenever you can pick up the Q of diamonds. Or maybe you should be ruffing a diamond to try to set them up whenever they split 3-3 (36% itself, plus you make on the 4-2 splits with QJ doubleton). Hands where this is true are hands like Kxxx - AKxx - xx - xxx when you actually make 5 on a club lead when diamonds are 3-3 and can also ruff twice on any 4-2 diamond split when trumps are 3-2. Kxxx - AKxx - Qx - xxx is pretty much cold for 4, but that's probably not an invite at all but a blast to game.

But there are plenty of invites with no play. Kxxx - KQxx - Qx - xxx loses 4 tricks off the top whenever they don't lead a club and East has an entry.

Was this hand an accept? No, probably not, but I think it's pretty close. Turn the K of clubs into points in any other suit (even QJ tight in hearts) and I think it is an accept.

Really it comes down to partnership agreement. If partner is inviting with a bad 8 count and would blast on with the above 12 count then clearly passing is right. But if I can trust partner to not be a moron with his invites and if he's a little conservative with his 11-12 counts then accepting is going to be right.

But why is this important when vulnerable and not as much when non-vulnerable? Well, instead of the numbers being -3, -6, +10, and +10 they're -2, -5, +6, and +6. Then the equilibrium point is 54.5%, so you should only stretch to bid 45% games instead of 38% games. That doesn't seem like enough of a difference to really warrant a truism, but it is still a difference. Working to include the making 2s and making 5s should widen that gap as well, but not by a whole lot.