Jboling

I think playing Odwyrtka (found on Dan's WJ2005 webpage) is the best alternative: 2NT = 4+ support, 2♦ = diamonds or balanced less than 4 card support. Jassem suggest natural followups, but after 2NT you can for sure play your favorite Jacoby/Stenberg structure, and after 2♦ I think you can play something similar to Bubrotka: 2♥ = any minimum 2♠ = 11+, 4+M 2NT = 11+, 6+M, singlesuiter 3m = 9-11, 5+m, 4M I think that it is good that responder usually bid 2♥ or 2♠, after which opener can show a balanced hand with 2NT, and other bids are descriptive with 4+ diamonds (lowest rebid can be 4441). Furthermore it can noted that 1♣-1M-3♦ is also free for something. I think 5+♦-4+M is a good choice, as this means that 1C-1M-2D denies 4M.

I think it would be beneficial if 1♣ would deny clubs, as you then use the 2♣ rebid for various purposes with no additional cost, for example: 1♣-1M-2♣ = 10+ with diamonds (as I think Helene already implied). 1♣-1M-2♦ = 18+ Bubrotka or similar artificial. 1♣-1♦ = 0-6 1♣-1♦-2♣ = artificial GF 1♣-1NT = 7-11 no major 1♣-1NT-2♣ = 15+ with 5+♦, responders rebid 2♦ showing 7-8 1♣-1NT-2♦ = 10-14 with 5+♦ A problem with this is that 1♣-1M-2♣-2♦ must be as non-forcing, so no low-level relaying here.

I think the reasons for using 15-17 have been mentioned already, but I think 14-16 is optimal together with T-W. When I play like that I do not open 1♣ with 11 (unless it is an upgrade to 12). This means that the most common balanced range (12-13) is more accurately bid. The problem that Adam mentioned with getting too high with 17 can be reduced by splitting up 17-19 into two parts. And then you might as well combine it with 20-21 balanced. What I mean is that 1♣-1R-1M is either 12-13 or 19-21, and 1♣-1R-1NT is 17-18. 19 feels like a GF against a 1-over-1 response, while 17-18 is not it, so I like this a lot. Starting low with 20-21 balanced is also good. Typically you do 1-over-1 with 5 points anyway, and missing games with 21+4 is not too bad (21 balanced against any hand with 4hcp makes 3NT only about 45% of the time), so you can play like this without big changes (except you need to play 1♣-1R-1M as almost forcing, and agree on how to show 19-21 balanced later on in the bidding). And naturally you also win by freeing the 2NT opening for something else than 20-21 balanced.

I thought 1♣-1♦-3♦ is more narrowly defined, something like 21-23. With 18-20 you have to choose between 1♥, 1♠ and 1NT, in this case probably 1♥. Of course change one of the hearts to a minor card, and you have to bid a very non-ideal 1NT.

Yes this was the number I used as the standard deviation of VP round-off. This assumes that all results are possible and equally likely, which neither are true, but it is an ok approximation. The standard deviation for rounding off imps is then also about the same, but when you express that in VPs it is not a constant, it depends on the actual imp-difference. You can most conveniently observe it using the new imp-to-vp table for 12 deals matches, when you have a standard deviation of 1 expressed in IMPs. This means that we have a maximal standard deviation of 0.36 VPs at imp-difference 0, and below 0.3VPs at imp-differences greater than 8. So on average we should have about the same standard deviation.

Good point, I did some calculations regarding this too, I estimated that the standard deviations for the errors due to round off to whole numbers are about equal (~0.3VP per match) for the IMP and the VP conversion.

I did also try Henrys formula, and did niether get the same as USBF nor the same as woefuwabit. Below mine and USBF (in that order): 0 0 0 1 1039 1039 2 1077 1077 3 1114 1114 4 1150 1150 5 1185 1185 6 1218 1218 7 1251 1251 8 1283 1283 9 1314 1314 10 1343 1344 11 1372 1373 12 1400 1401 13 1428 1428 14 1454 1454 15 1480 1480 16 1505 1505 17 1529 1529 18 1552 1552 19 1575 1575 20 1597 1597 21 1618 1618 22 1639 1639 23 1659 1659 24 1678 1678 25 1697 1697 26 1716 1716 27 1734 1734 28 1751 1751 29 1768 1768 30 1784 1784 31 1800 1800 32 1815 1815 33 1830 1830 34 1844 1844 35 1858 1858 36 1871 1872 37 1884 1885 38 1897 1898 39 1910 1910 40 1922 1922 41 1933 1933 42 1944 1944 43 1955 1955 44 1966 1966 45 1976 1976 46 1986 1986 47 1996 1996 48 2000 2000 I think the difference compared with woefubit comes from that the type cast (int) does not round, I think it truncates. By the way I did the calculations using floating point, and first forgot that you then have to add a factor that takes into account the finite precision of floating point numbers in the comparison. For example ((V[i+1] - V) > (V - V[i-1]+0.005))

I have actually tried to reverse engineer it, I do not think that there is any simple underlying function, they have probably just constructed the tables by hand. The imp-limit for 20-0 seems to be 15 multplied by the square root of the number of deals. Using this (for normalization of the imp-ranges) and a third order polynomial I could get down to an maximal error of about 0.02, but no significant improvement if I used higher order polynomials. Which was an disappointment, an error below 0.005 would have resulted in a simple formula for perfect generation of the tables, which also could have been used for generation of conversion tables for any other number of deals as well.

Interesting, thanks for the tip. Here is another variation, transfer-Gazzilli, found under Note [5]: http://www.ecatsbridge.com/documents/files/cc/OpenTeams/Germany/Fritsche-rohowsky.pdf

If dbl was negative, 2D is just showing a hand without interest of game against a minimal negative double, with reasonable support for diamonds (and denying support for hearts)

When I played Wilkosz according Matulas scheme given above, I changed 3♣ to threesuited invite with short spades, because I thought it was missing from the scheme. With a weak hand with long clubs, we passed and corrected to 3♣ if it was doubled. The responses to 3♣ were pass/3♦/3♥ = to play (typically with spades as the other suit) 4m = m+♠, good hand, reinvite 4♥ = to play 4NT = both minors 5m = to play (typically m+♠ with weak spades).

I did the full table as well, but only with 1000 deals like Cascade: hcp west : 10+ tricks : average tricks 0 279.0000 8.9210 1.0000 302.0000 8.9730 2.0000 321.0000 9.0280 3.0000 310.0000 8.9660 4.0000 296.0000 8.9840 5.0000 269.0000 8.8920 6.0000 274.0000 8.9280 7.0000 312.0000 8.9450 8.0000 286.0000 8.9590 9.0000 294.0000 8.9190 10.0000 307.0000 8.9670 11.0000 294.0000 8.9210 12.0000 313.0000 9.0030 13.0000 332.0000 9.0330 14.0000 319.0000 9.0060 15.0000 334.0000 9.0410 16.0000 343.0000 9.0740 17.0000 334.0000 9.0350 18.0000 326.0000 9.0600 Looks quite similar to Cascades table, except that I limited it to a 4-4 fit in spades, so my numbers are lower. Having more than 8 cards in trumps increases the number of tricks, when I redid the 9hcp with west situation with a 4-4+ fit the number of 10+ deals increased from 294 to 391, and the average number of tricks increased from 8.9 to 9.2. So the effect of additional trumps is clearly bigger than the distribution of points with the opponents (in a DD setting, it is probably the other way around single dummy). Keeping everything else but hcp constant would be the ideal when you study the effect of hcp. By the way I got the same strange maximum at 2 points with west. The reason for that you get more tricks with the majority of points with east is probably that he is often endplayed when leading. Why this trend does not last to the end seems strange. But still I think the connection between these investigations and real play is rather weak, as in a single dummy setting you really gain a lot single dummy, if you know based on the bidding where the majority of the points are.

I tested a double dummy study, but realized that it probably was pointless. DD is DD, so you already know the location of every single card from the start, so nothing is gained from that you know that LHO has 14 points from the bidding. The average number of tricks, under the conditions Ken suggested, with opponents points 4-14 and 9-9 were 9.0 and 8.8 respectively. And the likelihood for making at least ten tricks (with a 4-4 spade fit, with spades as trumps) were 31% and 28% respectively. Or maybe this was what Ken actually was asking for? Most likely you gain much more in a single dummy setting from knowing more about the point distribution based on bidding.

No Name is one of the strong pass systems found in the book "Introduction to Weak Opening Systems" by Slawinski and Ruminski. Suspensor is a later developement of No Name by Balicki and Zmudzinski. All this according to http://www.bridgeguys.com/pdf/forcingpass.pdf, written by Jan-Erik Larsson and Ben Cowling.

I play these tranfers slightly different: 1. Transfer to a already bid suit is forced, because it might be sign-off. Super-accepting is ok, you then bid something else but completion of the transfer. 2. Transfer to a new suit asks for a four card fit, and is only completed with one, other bids are natural and denies a fit in the transfer suit. This makes it almost impossible to stop at the three-level in a new suit, but makes it easier to agree the trump suit, in case responder is interested in slam.