benlessard Posted April 10, 2008 Report Share Posted April 10, 2008 Ive already post this 2-3 years ago on BBO forum but nobody did understand or nobody was interested. 1C ! strong----??? you have a GF balanced hand and decided that 2D to 3S is reserved for balanced hand with GF values. 1-33342-33433-33434-4333 5-23446-24347-2443 8-32449-424310-4234 11-342412-432413-4423 14-344215-434216-4432 17-233518-323519-3325 20-235321-325322-3352 The order you want to put it is your choice. But youll need to memorize it. Now 2D=A2H=B2S=C2Nt=D3C=E3D=F3H=G A=(+1) the + is very importantB=(+2) the + is very importantC=(+3) the + is very important D=1 (there is no+)E=4F=9G=14H=19 Lets says you have 3253 wich is hand number 21.By looking at the letter we see that the way to make 21 = (+2)+19 So we start by B (+2) 1C-----2H (B or +2)2S©----3S(H or 19) The 2S by partner is only a relay but still take the letter "C" If you have hand 13 /4432/the way to make 13 is (+1)(+3)(+9) 1C-----2D (A == +1)2H(B)----2S(C == +3)2Nt(E)-----3C(F == 9) For a 2suiter its the same thing 1H------------1S (relay)1Nt (clubs)----2D (art GF)??? 1S-------------1Nt (relay)2C (diamonds)--2H(art Gf) 1S-------------1Nt (relay)2D (hearts)-----2Nt (art GF) the hands are 5422 ==15431 ==25413 ==35440*==45521 ==55512 ==65530 ==75503 ==86421 ==96412 ==106430 ==116403 ==126511 ==136520 ==146502 ==157411 ==167420 ==177402 ==186601 ==196610 ==207501 ==217510 ==22 You have a 6430 wich is hand number 10. partner just Gf at 2D so...2H=A2S=B2Nt=C3C=D3D=E3H=F3S=G 2D (GF)------2H (A==+1)2S (B)-------3H (F==9) Lets say you have a 7402 and are lucky enough that opps dont interfere. 7402= 18 to make 18 its (+1) (+3) and 14so its A=C=G 2D (GF)------2H (A==+1)2S (B)-------2Nt (C==+3)3C (D)------ 3S (G == 14) and voila youve just showned a 7402 under 3Nt. The chart for one suiter can be something like 6322 ==16232 ==26223 ==36331 ==46313 ==56133 ==67321 ==77312 ==8 7231 ==9721373307303703382218212812283118313813380??8?0?8??0 If you are not able to Gf early you can play a simpler variant. Wich is probably more practical. A=+1B=+2 C=1D=3E=6F=9G=12H=15 So if you you have hand number 11 its B (+2) and F(9) Partner bid X (GF) -----you bid X+2 (B)he bid X+3( relay C)------you bid X+6 (F) Feel free for any questions or comments. Quote Link to comment Share on other sites More sharing options...
Echognome Posted April 10, 2008 Report Share Posted April 10, 2008 Not that I followed all that (symmetric seems much easier in terms of rules to memorize), but where are your 3-suiters? 4441s and 5440s. Quote Link to comment Share on other sites More sharing options...
matmat Posted April 10, 2008 Report Share Posted April 10, 2008 Not that I followed all that (symmetric seems much easier in terms of rules to memorize), but where are your 3-suiters? 4441s and 5440s. that distribution is not allowed when playing this system. Quote Link to comment Share on other sites More sharing options...
Free Posted April 10, 2008 Report Share Posted April 10, 2008 Interesting concept, but you're reinventing the wheel imo. Symmetric relay is extremely efficient and easy to memorize... Quote Link to comment Share on other sites More sharing options...
benlessard Posted April 10, 2008 Author Report Share Posted April 10, 2008 Symmetric relay is extremely efficient and easy to memorizeEasy to memorize ok but extremely efficient no.In term of effiency there is no comparaison between symmetric relay and what ive post. Pick 8 random hand (without or after the reverser) and you will see . As for the 5440 ive put an * because sometimes there is none and sometimes there should be 2 of them. For simplicty we always carry 1 and only 1(the void is 1 under the 4 card suit) 5S+4H = only 5404 is possible.5S+4D = only 5440 is possible5S+4C = only 5044 is possible 5H+4S = 45045H+4D = 45405H+4C = 0544 As for the 4441 we are responding 1D or opening 1D with them. But we could treat them like 2 suiters. Just that with a structure like mine exception are a pain. Quote Link to comment Share on other sites More sharing options...
Free Posted April 10, 2008 Report Share Posted April 10, 2008 Symmetric relay is extremely efficient and easy to memorizeEasy to memorize ok but extremely efficient no.In term of effiency there is no comparaison between symmetric relay and what ive post. Pick 8 random hand (without or after the reverser) and you will see . ~snip~ The way you can compare relay systems is the sum of frequency * level for all possible distributions. For example, if you start of showing 5+♠-4+♦, at what step do you have the right distribution. The normal start of a 2-suiter is 54+ with the longest suit known. In symmetric relay it goes:A = 55+ (now B = relay ; C = high shortage, D = 6511, E = 5521,...)B = high shortnessC = 5422D = 5431 low shortness (+ 6511)E = 6421 low shortness (+ 5521, 5512)F = 6430 low shortness (+ 5530, 5503)G = 7420 low shortness(...) Your method goes:ABC = +1, +2, +3D = 5422E = 5431 low shortness (+ 5521, 5512, 5530, 5503)F = 5431 high shortness (+ 6421, 6412, 6430, 6403, 6511)... Where do you see the better efficiency? Only the 5530's are bid lower in your method. In function of frequency, symmetric wins huge on the frequent hands:5422 = +1 step5431 = +1.5 steps (1 or 2 depending on the shortness - so 50%)6421 = +1 step5521 = equal5530 = -1 step6511 = +2 stepsYour method can probably catch up one or several steps for wild hands, but that's negligible compared to the frequency of these hands (not to mention the chance you'll get to just relay out when you have such a freak B) ). So I'd say your 2-suited scheme is not as great as you might think. Comparing the singlesuiters will probably result in a similar conclusion. This doesn't mean your system can't be more efficient than another system. If you can start this scheme at 2♦ while another system would have to start at 2♠, you gain bigtime. But using symmetric relays at 2♦ would be even more efficient ofcourse. B) One important thing I noticed: your 'simpler variant' is more efficient than your standard version! (and may be more efficient than symmetric even - depends on the frequency of certain hands) Quote Link to comment Share on other sites More sharing options...
dake50 Posted April 10, 2008 Report Share Posted April 10, 2008 So, an indexing function to a 'data base' of bal GF hands. Add an index function for 4x singletons; 4x voids; 6x 2-suiters. With, of course, re-indexing that modified data base, eg. bal except for single Spade, or 2-suiter with single Spade. A theoretical exercise I enjoy. But esoteric except to information theorists, isn't it ? Quote Link to comment Share on other sites More sharing options...
jdonn Posted April 10, 2008 Report Share Posted April 10, 2008 1C ! strong----??? you have a GF balanced hand and decided that 2D to 3S is reserved for balanced hand with GF values. I stopped reading after that point. That is such a waste of bids I can barely contain myself. What an inefficient use of precious space! Quote Link to comment Share on other sites More sharing options...
awm Posted April 10, 2008 Report Share Posted April 10, 2008 It seems like with this method the relay is sometimes not the cheapest step (see the sequences for two suiters). This obviously loses some efficiency. What are the other steps used for? Symmetric uses the same amount of space for balanced hands, just gets there differently (starts 1NT then 2♦-3♠ in symmetric, or starts 1♠ then 2♦-3♠ in transfer-oriented version). It does seem like immediately showing balanced shape is poorly thought out -- say opponents are going to crash the auction after the response; if opener knows responder is balanced GF he usually can make an okay decision without the exact shape (so squishing the balanced hands into one bid to unroll later is no big deal) whereas a distributional responder hand (i.e. responder has "clubs") will be harder to deal with. Also, the balanced hand type is a good time for opener to use a relay break and describe his own hand if he has shape (another reason to keep balanced hands low on first response). Quote Link to comment Share on other sites More sharing options...
glen Posted April 10, 2008 Report Share Posted April 10, 2008 1C ! strong----??? you have a GF balanced hand and decided that 2D to 3S is reserved for balanced hand with GF values. I stopped reading after that point. That is such a waste of bids I can barely contain myself. What an inefficient use of precious space! You could think of it as 1♣-1NT(GF bal)-2♣(ask)-then 2♦ etc. following the +chart+ Quote Link to comment Share on other sites More sharing options...
jdonn Posted April 10, 2008 Report Share Posted April 10, 2008 1C ! strong----??? you have a GF balanced hand and decided that 2D to 3S is reserved for balanced hand with GF values. I stopped reading after that point. That is such a waste of bids I can barely contain myself. What an inefficient use of precious space! You could think of it as 1♣-1NT(GF bal)-2♣(ask)-then 2♦ etc. following the +chart+ That is true but it's really not my point. It's a hand that should be shown using one bid since so often opener either doesn't care at all what the shape is, or only cares about one aspect (3 card support for a major, for example). This method uses tons of bids to give information that will so often help the opponents. It would also require shapely hands to start much lower, which puts them at huge risk of preemption. Perhaps inefficient wasn't the right word though. Quote Link to comment Share on other sites More sharing options...
gwnn Posted April 10, 2008 Report Share Posted April 10, 2008 Apparently Dr. Roy Kerr solved some mathematical physics problems that Einstein could not have solved. Dr. Roy Kerr designed Symmetric Relay. erm... Quote Link to comment Share on other sites More sharing options...
the hog Posted April 11, 2008 Report Share Posted April 11, 2008 1C ! strong----??? you have a GF balanced hand and decided that 2D to 3S is reserved for balanced hand with GF values. I stopped reading after that point. That is such a waste of bids I can barely contain myself. What an inefficient use of precious space! I totally agree with Josh. Ben, playing that many bids to show balanced hands is a ridiculous waste of space and unbelievably inefficient. WHY? Quote Link to comment Share on other sites More sharing options...
benlessard Posted April 11, 2008 Author Report Share Posted April 11, 2008 Im not fond of relaying balanced hand so this was purely an example.You could think of it as 1♣-1NT(GF bal)-2♣(ask)-then 2D etc. following the +chart+that why ive started as 2D. In symmetric relay the hands that are showned 0,0,2,3,3,3,3 in my method its 0,0,0,3,5,5,5 if there is an ensemble of less then 13 hands my method isnt optimal with more then 13 my method take the upper hands. Your method goes:ABC = +1, +2, +3D = 5422E = 5431 low shortness (+ 5521, 5512, 5530, 5503)F = 5431 high shortness (+ 6421, 6412, 6430, 6403, 6511)5431 & 5413 is also at D (D,ABD & BCD)Under E or at E i have showned 8 hand wich is the same of sym relay.(D,ABD & BCD) + E,AE,BE+CE+ACEAt F ive showned 13 hand, all the previous+F,AF,BF,CF,ACFAt G ive showned 18 hands wich is 4 more then symm relay. Also the frequency is where my method gain because my hand are in frequency order wich is not always the case in symm relay. Unless im wrong the 5512 exit at 2S while the 5431 are at 2nt. a recap to show you where i exit the hands if my first possible bid is 2D (A=2D) 2Nt= 5422+5431+54133C= 5440+5521+5512+5530+55033D= 6421+6412+6430+6403+6511 3H=6520+6502+7411+7420+7402 Do the same with symm relay and you will see. Quote Link to comment Share on other sites More sharing options...
awm Posted April 11, 2008 Report Share Posted April 11, 2008 It's not clear what's going on because you need to explain how responder shows his two suits and indicates which is longer. It's not going to be the case that your A step on two suiters is 2♦ because that would mean you can somehow always show two suits and indicate which is longer than the other and still have opener's next relay at 2♣. There 12 possible suit pairs (4 longer, then 3 shorter) and not nearly so many sequences where opener's relay is 2♣. Assuming you start in roughly the same style as transfer-oriented symmetric, let's take some example hands: 5♠-4♦-3♥-1♣ Both start 1♥ (spades) .... 2♣ (diams) .... now 2♥ shows the reverser so I guess 2♠ is step A. 5-4-3-1 is 2 on your chart, so you need to bid A (2♠) followed by D (3♦). So you resolve this shape at 3♦. So does symmetric. 5♠-5♦-2♥-1♣ Same start, again 2♠ is step A. Total is 4 (disallow 5440 hands, they are bid via a different start) so you need to bid now E (3♥). You resolve this shape at 3♥ and so does symmetric. 6♠-4♦-2♥-1♣ Same start, again 2♠ is step A. Total now is 9, so you need to bid F (3♠). You resolve this shape at 3♠ and symmetric resolves the same shape at 3♥. 6♠-5♦-0♥-2♣ Same start, again 2♠ is step A. Total now is 14, so you need to bid G (3NT). You resolve this shape at 3NT and symmetric resolves the same shape at 4♣. Basically, you are doing roughly the same as symmetric on these hands. However: (1) You generally do slightly better on the very rare shapes and slightly worse on the very common shapes. This is bad. (2) The scheme seems more complex/harder to remember than symmetric. Quote Link to comment Share on other sites More sharing options...
benlessard Posted April 11, 2008 Author Report Share Posted April 11, 2008 It's not clear what's going on because you need to explain how responder shows his two suits and indicates which is longer. It's not going to be the case that your A step on two suiters is 2♦ because that would mean you can somehow always show two suits and indicate which is longer than the other and still have opener's next relay at 2♣. There 12 possible suit pairs (4 longer, then 3 shorter) and not nearly so many sequences where opener's relay is 2♣.Agree this was just an example to show a 2 suiter after or without the reverser. There is of course no practical need to exit a 7402 at 3H. (1) You generally do slightly better on the very rare shapes and slightly worse on the very common shapes. This is bad. The word slightly is adequate, however showing the common shape earlier isnt that much important compared to showing some critical shapes earlier. If you prefer to go by odds tables the 6421 is before the 5530 and before the 5440 but a 6421 suggest 2 trumps suit while a 5530/5440 suggest 3 trumps suit, a case can be said for showing tough 3suiters shapes before common ones. Anyway the fact that you can put the shapes everyway you want is a nice feature of my method. Remembering A=+1,B=+2,C=+3,D=1,E=4,F=9,G=14 H=19 is easy. The table isnt that hard if you already know your odds tables. For example i can easily do a chart without the reverser 1C---1H (pos with S) 1S?---2C(diamonds could be 4S+longer diamonds)2D ?---- Now 2H is A and 2S is B but there is no reverser. Put purely in odds frequency and without 3-suiter. First column is my method 2nd is symmetric relay(reverser needed with longer D) S+D 2 suiter/no 3 suiters ♠♦♥♣5422=D........3C.......3C 4522=AD......3C.....3D reverser followed by +35431=BD......3C.....3D directly= low shortness4531=E........3D......3D reverse+directly5413=AE......3D......3D high short follwed by step14513=BE......3D......3D reverse +high short +step15521=CE......3D......3H 5512=ACE....3D......3D or 3H im not sure6421=F........3H.......3H4621=AF......3H.......3H6412=BF......3H.......3H4612=CF......3H.......3H5530=ACF....3H.......5503=G........3S.......6430=AG......3S.......4630=BG......3S.......6403=CG......3S.......4603=ACG....3S.....6511=H......3nt.........5611=AH......3nt.......6520=BH......3nt.......5620=CH......3nt.......6502=ACH......3nt.......5602=I......4C....... My practice isnt that good with Symm relay so im sure ive made some mistakes. Please double check and finish the chart if you please thanks in advance. Quote Link to comment Share on other sites More sharing options...
Free Posted April 11, 2008 Report Share Posted April 11, 2008 Im not fond of relaying balanced hand so this was purely an example.You could think of it as 1♣-1NT(GF bal)-2♣(ask)-then 2D etc. following the +chart+that why ive started as 2D. In symmetric relay the hands that are showned 0,0,2,3,3,3,3 in my method its 0,0,0,3,5,5,5 if there is an ensemble of less then 13 hands my method isnt optimal with more then 13 my method take the upper hands. Your method goes:ABC = +1, +2, +3D = 5422E = 5431 low shortness (+ 5521, 5512, 5530, 5503)F = 5431 high shortness (+ 6421, 6412, 6430, 6403, 6511)5431 & 5413 is also at D (D,ABD & BCD)Under E or at E i have showned 8 hand wich is the same of sym relay.(D,ABD & BCD) + E,AE,BE+CE+ACEAt F ive showned 13 hand, all the previous+F,AF,BF,CF,ACFAt G ive showned 18 hands wich is 4 more then symm relay. Also the frequency is where my method gain because my hand are in frequency order wich is not always the case in symm relay. Unless im wrong the 5512 exit at 2S while the 5431 are at 2nt. a recap to show you where i exit the hands if my first possible bid is 2D (A=2D) 2Nt= 5422+5431+54133C= 5440+5521+5512+5530+55033D= 6421+6412+6430+6403+6511 3H=6520+6502+7411+7420+7402 Do the same with symm relay and you will see. Ok, looks like I made an error :) Still I share the opinion that you're losing (slightly) on common hand types. Your simpler variant does not because you save a step (the +3) so common hands are bid an entire step lower. The really extreme shapes can still be bid pretty low (step H = 3NT when you can start at 2♥) but then again, I'll argue that these will get rarely patterned out. I've played symmetric relays for years now, and only once I had a problem: I held a 9220 and opps didn't intervene after my partner's strong 1♣ opening... In every other case where I had an 8-card suit or a 6-6, opponents intervened and relays were off. So I think in practice, the simpler variant is supreme. In theory, no idea :) It also depends on how high you can start relaying: if you start at 2♠, the normal version may be better (to always stay below 3NT if you prefer this). Quote Link to comment Share on other sites More sharing options...
benlessard Posted April 12, 2008 Author Report Share Posted April 12, 2008 I also made a mistake saying symm werent highly efficient. Both ways are efficient and the difference are minimal. Question regarding symm when you are using the reverser (there is no 55 right) its only high shortage and low shortage (in a direct way?) if so where is the 5611 ? Quote Link to comment Share on other sites More sharing options...
jdonn Posted April 12, 2008 Report Share Posted April 12, 2008 I also made a mistake saying symm werent highly efficient. Both ways are efficient and the difference are minimal. Question regarding symm when you are using the reverser (there is no 55 right) its only high shortage and low shortage (in a direct way?) if so where is the 5611 ? After 2 suits, 2♥ is reverser, 2♠ is 5-5 with its own track. 2NT+ (with or without 2♥ first - ergo the symmetry!) is all the 4, 5+ hands. Quote Link to comment Share on other sites More sharing options...
Free Posted April 12, 2008 Report Share Posted April 12, 2008 I also made a mistake saying symm werent highly efficient. Both ways are efficient and the difference are minimal. Question regarding symm when you are using the reverser (there is no 55 right) its only high shortage and low shortage (in a direct way?) if so where is the 5611 ? 6-5 is considered 55+. In the 55+ scheme we have:A = high shortageB = 6511 or 5611 (if possible)C = 5521D = 5530E = 6520F = 5620 (if possible) The rest of the 2-suited scheme is, like Josh says, with exactly a 4 card in one suit, and 5+ in the other, with or without the reverser. Quote Link to comment Share on other sites More sharing options...
akhare Posted April 12, 2008 Report Share Posted April 12, 2008 Basically, you are doing roughly the same as symmetric on these hands. However: (1) You generally do slightly better on the very rare shapes and slightly worse on the very common shapes. This is bad. (2) The scheme seems more complex/harder to remember than symmetric. Agree with the above (and with awm, Free, Josh, Ron, et all). Factor #2 is especially important in a long matches where fatigue comes into the picture -- it's board 55 of a 64 board session -- do you still know what your relays are :)? Quote Link to comment Share on other sites More sharing options...
benlessard Posted April 13, 2008 Author Report Share Posted April 13, 2008 Ive finished the whole chart. I dont think there any mistakes. But please double check A=reverserB=5-5C=High shortD= 5422 equal ----- 5-5 H shortE= low short 1st hand ------55 (6511)F= low short 2nd hand ----- 55 low short 1st hand MY METHOD--------SYMM RELAYS5422=D........3C......3C..........D 4522=AD......3C......3C..........AD 5431=BD......3C......3D..........E 4531=E........3D......3D...........AE 5413=AE......3D......3D...........CE 4513=BE......3D......3D...........ACE5521=CE......3D......3H...........BF 5512=ACE....3D......3H...........BDF 6421=F........3H.......3H...........F4621=AF......3H.......3H...........AF6412=BF......3H.......3H...........CF4612=CF......3H.......3H...........ACF5530=ACF....3H.......3S...........BG5503=G........3S.......3S..........BDG6430=AG......3S.......3S..........G4630=BG......3S.......3S..........AG6403=CG......3S.......3S..........CG4603=ACG....3S.......3S..........ACG6511=H........3nt.......3S...........BEG (3D--3H---3S i assume)5611=AH......3nt.......3Nt..........BEH (3D--3H--3Nt i assume) 6520=BH......3nt.......3Nt.........BH5620=CH......3nt.......4C.........BI6502=ACH....3nt......3Nt.........BDH5602=I..........4C......4C.........BDI Not an important gain but a gain nonetheless.I expect the gain of my method to be smaller with balanced hands or when there is no reverser. Every new method is always more complex then methods you already known. The "core" of my method is certainly much easier then symm relays where you have 3 core(balanced,2 suiters single suiters) + reverser with sub menus everywhere. As for learning 3 full chart i would be kidding myself to say its easy but i dont think its that complicated. You always learn a couple by heart with mnemonics tricks and work downward. Also when you bidding practice on the net you can have them printed and slowly you will learn them by heart. Of course if you screw up you will be more screwed then symm relays because hand and not classified by familiarity. Another downside is if they X for lead and the other guy raise the X you are stuck because the information are worthless if they are not conveyed as a whole (but its quite rare) Quote Link to comment Share on other sites More sharing options...
awm Posted April 13, 2008 Report Share Posted April 13, 2008 You've also misplaced all 7420 hands, which resolve in symmetric at 3NT and for you in 4♣. Basically your scheme is: 3 hands resolve in 3♣; 5 in 3♦; 5 in 3♥; 5 in 3♠; 5 in 3NT; 5 in 4♣; etc. Symmetric is: 2 hands resolve in 3♣; 4 in 3♦; 6 in 3♥; 7 in 3♠; 7 in 3NT So you get one extra hand in 3♣ and one extra in 3♦. But by the time we are counting the number of hands that resolve at 3NT or below, symmetric is ahead by 3 patterns (all 7420s). One of the nice things about symmetric is that virtually all patterns resolve at 3NT or below. It also has the nice properties you mentioned, where you are actually getting useful information at each bid and might be able to stop relaying early, instead of just getting numeric data and having to wait for entire shape to resolve before you really know anything. Quote Link to comment Share on other sites More sharing options...
joshs Posted April 15, 2008 Report Share Posted April 15, 2008 Apparently Dr. Roy Kerr solved some mathematical physics problems that Einstein could not have solved. Dr. Roy Kerr designed Symmetric Relay. erm... Well Roy Kerr solved the field equations for a spinning black hole, and as a coincidence this discussion is making my head spin.... P.S. When was the last time you folded 4 Aces? Quote Link to comment Share on other sites More sharing options...
Zelandakh Posted May 10, 2008 Report Share Posted May 10, 2008 Here's yet another way of handling balanced hands with an assymetric relay method. Comments welcome, flames not :rolleyes: Over 1♣ 1♥ is 4+♠s including 4♠4♥32 hands1♠ is most hands without a 4 card major2♦ is balanced or 3-suited with 4-5♥s and 0-3♠s2♥ is balanced with 4-5♠s and 2-3♥s-- Specifically for balanced hands, after1♣ - 1♥ // 1♠ - 1N // 2♣ - 2♦ // 2♥ - 2♠ // 2N3♣ is 44233♦ is 4432-- 1♣ - 1♠ // 1N - 2♥ is balancedthen after 2♠ relay2N = 5♣3323♣ = 5♦3323♦ = 4♣4♦323♥ = 33343♠ = 3343 + zoom-- After 1♣ - 2♦ // 2♥2N = 5♥3323♣ = 4♥4♦323♦ = 34333♥ = 24343♠ = 3424 + zoom-- After 1♣ - 2♥ // 2♠2N = 5♠3323♣ = 4♠4♦323♦ = 43333♥ = 42343♠ = 4324 + zoom-- Not an attempt to reinvent SR which is just fine, but more designed to move things around within it in order to show/deny majors more quickly in case of 4th seat interference. Notice that is also quite possible to play (as)symmetric relays based around fragments rather than shortages - for me this is easier to remember than either SR or TOSR, for others it wouldn't be :) For example, let's say we have 1-suited club hand. Instead of shortages we might show2S = 6-7♣s, 3♥s2N = 6-7♣s, 3♠s 0-2♥s3♣ = 6-7♣s, 3♦s, 1-2♥s, 1-2♠s3♦ = 2=2=2=73♥ and over = 8+♣s (choice of schemes) and resolve each fragment in turn. I don't see any disadvantage to this approach other than remembering something other than you might be used to if you learnt SR first. There are specific diadvantages - this scheme resolves 7-4 hands at 3♠ but without separating out 7420/7411/7402 for an example given in the thread. And 5431 resolves at a different level to 5413 (3♠ versus 3♦) making the scheme assymmetric under the 'normal' definition of symmetry. As for solving mathematical equations beyond Einstein, it is well established that maths was one of Albert's weakest areas despite his visionary genius. He needed special help with improving his maths ability for some of his proofs. Add to that the general improvements made in maths over the latter half of the 20th century, plus the raw power of modern computers, and it is easy to see why this is not in itself such a majot feat. However, being the first one to solve important (black holes are a pretty critical area of physics) equations amongst contemporaries, that's far more impressive... Quote Link to comment Share on other sites More sharing options...
Recommended Posts
Join the conversation
You can post now and register later. If you have an account, sign in now to post with your account.