[twcho]

Well, Ben's idea is absoultely workable but as our partnership will bar the double at the 1st round (which promises the other 2 unbid suits). Then let's working from here.

E's 1st pass and the 2nd round double (we play this double takeout) should surely indicate hands similar to 4H (with 5card more likely he will take action in the 1st round of bid 2H now), <4C, <3D(we won't double with length in D here) and by deduction, we must have length in S. And with vul as shown, E must have at least a decent hand to risk the double after pd's silence in both rounds.

The 3rd round pass by E indicates that he probably didn't have 5 card S (although he might). So the most probable handshape is 4423 exactly.

Let's turn our attention to North and South bid. North did not rebid his S in 2nd round so nearly for certain his S is a 5 card suit. Consider S's bids. The 1D then 2C should promise at least 9 cards in minors and with the final bid of 3D, he must hold at least 5 card D. So we can deduce the distribution for all hands (seldom you will have such informative bidding auction that you can deduce everyone's pattern before you see the dummy).

From West viewpoint, the most likely shape for South will be 1354 or 1255 and north will be 5233 or 5323. North should have honors in S suit so the most of the remaining HCPs must be with south.

Then now west has to decide whether he should pass or bid 3H. If partner has some C minor honor (such as K, Q or J), they rates to be useless and now you are almost dead because either they will make 3DX or caught you with 3HX. So we must hope that East to hold CAxx. And he rated to hold the HA as well. For S, any reasonable holding is OK, because we can easily finesse vs North. Again, DK in the west hand shd likely score.

From then, we can easily conclude if SA is with North, opp will make 3D and if partner holds at least KJxx is S, 3H will make as well, so pass will be a success. If East holds SA and he also possess SJ. Then, 3H will be a make and 3DX will be one down. If East has SA but not another honor, then 3H will be one down and 3D will be one down also and this is probably the only losing situation that if we continue with 3H rather than pass 3D.

So my conclusion is that 3H bid by west is the likely winning action.

Someone may doubt the last double by East but please bear in mind that partner does not promise to have such good H (may even have only 3 card H when he considered passing 2DX is fatal) and equally possible is that he holds Kxxx in H and KQx in D, then 3Dx will be a success. Of course, the final double by East is very risky but it may be equally rewarding.

One final note: the final result shown that if 3D undoubled just make, you will get an exactly avg score. If you make 3HX, you will get a top of course and even if you are not doubled, 3H just make will give you a share top in this board. And I don't think opp will sacrifice in 4D and even they do, 4DX -1 will give you a second top.