Trumpace

I am intermediate and I think intermediates should get this one quite easily (especially as a puzzle, on the table, it is different), so I am hiding it.

If I could ask for a club stopper by bidding 3C i would bid it. Otherwise 4H seems like an reasonable shot. I don't like 4S. We would probably lose control with repeated club leads.

I am not saying that the long run analysis won't work! All I am saying is that there is more to it than just maximising the expected number of IMPS per board. The reason I need to contrive values is that it is very hard to show real bridge situations where the long run analysis might fail. These are not sufficient grounds to declare that the arguments I am making are bogus... As a fair approximation, using the long run analysis is probably good enough (though not in all cases, which is my point), as there are other factors which are more important in deciding the outcome of the match. Don't just blindly use "in the long run it wins hence I use it" approach. Though it might work for most cases, the reasoning is still wrong! That is all. You might turn out to be right, but there could be cases where it is the wrong thing to do! If your opponents just find one such case (which I admit, would probably be pretty hard to do), they can beat you if you blindly stick to the 'in the long run' strategy.

I am not assuming that at all. I am saying that I dont need to assume that.. I can play with such a strategy which will make those 11 8% boards the only boards that count! quoting myself... Basically for boards other than the 8% boards I will play with the same strategy as you do. For the 8% boards I will play safe, in effect giving me a 61% chance of winning. By using your strategy on all but the 8% boards, in effect, I have made these boards decide the outcome of the match!

Suppose we are concerned solely with the boards where there is an 8% chance of throwing away 11 IMPS but 92% chance of gaining 1 IMP (assuming opp plays for safety). Also, assume that of all the bridge deals that are possible (which is a finite number, though very large) around 1.1 percent (I am making this up, just to get a point across) are the 8% 1 vs 11 IMP deals. Consider playing a "fairly long match" of 1000 boards. How many such 8% deals do you expect to occur among the 1000 boards? 11 right? Now if there are 11 such 8% 1 vs 11 IMP boards, the chances of gaining IMPS on these boards by playing safe is 61% (as calculated on a previous post). So if you use your long run strategy (maximising expected IMPS per board) for a 1000 board match, I can beat you (assuming we are equally matched) with 61% chances by playing safe for the 8% 1 vs 11 IMP boards, while using the same strategy as you on the remaining boards! If the match was say a million trillion boards long, you will probably win if I stuck to playing safe on the 8% boards. (Haven't calculated...) The reason the 1%, 2%, 3% IMPS add up is that, in shorter runs too, they actually give more than even chances. The point is that even though the whole match might be long... the number of boards of a particular kind (here 8% boards with 1 gain vs 11 lose IMP) might be small enough to require an approach other than just the long run analysis.

If you run it over a long timeseries, we get closer to the mathematic odds, that is, the example of the insurance company, who is willing to risk to pay a big amount for a very low frequency risk, but cash in in the rest of the cases. I think the example of the insurance company is much better than the example of the coin flipped: the insurance can be one-year only, 2 years or longer, and the risk calculated on a 1 year period can be an analogy to the risk computed of the short-term" match (or set of matches) in bridge. ==== The exmple of the biased coin flip is not well posed, because: 1) at the end of a single set, before we start a new set of coin flips, the % of outcomes are not the same as at the start, because the probability "a priori" has changed because in the previous set(s) the coin exited as tail X times and exited as heads Y times; so if you have won one set, you are almost sure to lose the 2nd and 3rd set; you cannot recompute the odds for the following sets with the original probabilities, the odds must be updated as a function of past results. 2) the % of risk is too high compared to the number of coin throws. If you run the same analysis with every set having, say, 6+ throws, we all know that my side would be a winner. The insurance example isn't right. The money made by the insurance company due to policy holders in that year is _not thrown_ away, unlike the IMPS you win in Bermuda Bowl 2004 are not counted in Bermuda Bowl 2005. Hrothgar has answered your point 1). But just to repeat... Each coin flip is independent of the previous flips. Just because there have been a 1000 tails does not mean the 1001st has higher chances of coming up heads. The chances of heads on 1001st throw are still 75%. No more. No less. About your point 2) Consider a round with 7 flips. If at least 2 heads come up, I make more tokens than you. Probability of this = 1 - (0.75)^7 - 7*(0.75)^6*(0.25) ~ 0.55 I still win with 55% chances if the rounds are 7 flips each. But,(I think, havent done the calculations) the long run analysis wins in the following case: Suppose we pick the length of the round at random say from a very large set of numbers. Then, there is more chance that you will end up making money! You might argue that in Bridge we have something similar... Each match would have a random number of such overtrick or down boards (which correspond to the round length in the coin flip game). But that is incorrect reasoning, since the total number of boards with the overtrick/down scenario are a fixed percentage of all possible bridge deals. Say that percentage is 2%. In a match of length 256, you should do the analysis for around 6 boards (and probably a few more in the neighbourhood of 6), as we expect 2% of the 256 boards to be overtrick or down boards, and based on the results of that, we should pick our strategy. Of course, it depends on how the 256 boards are being generated, which by computer these days is pretty close to being truly random. For 1%, 2%, 3% chances with a 1 IMP gain or 11 IMP loss, it seems that the long run strategy also works in most of the short runs (I have verified for runs upto 23). So the expert is right (play for overtricks to maximise score, if 5% or less chances of losing 11 IMPs while gaining 1 IMP), but by applying the wrong reasoning.

The problem with this line is RHO might duck twice with ♥Kxx, and you are shut off the board. Is this realistic? I think so, he should know the diamond count. <snip> Arend If both E-W follow to 2 rounds of hearts, and when we play a 3rd round and West follows, the odds now favour a 3-3 break, so we go can up with the Ace (of course this is if you think east is capable of ducking with Kxx). If West has the K after all, we can test diamonds and if not, fall back on the spade finesse.

That's the point: 1-IMPS pluses , especially among comparable teams, are not irrelevant, or to throw away at the end of the match. Another way to view this is to ask a top level player: how many times did you lose a match by 1 imp? and how many times did you win a match because you made (or opps failed to make) a safety play catering for a <5% risk ? I think there is a terminology mismatch. By a 'match' I mean the whole of Bermuda Bowl! According to you, Italy vs Egypt is a different match as compared to Italy vs Usa in BB2005, but according to me it is part of the same BIG match... Even so, the long run analysis (just calculating the expected IMPS per board) which you seem to think should work, can lead to incorrect strategies, as the above example of coin flip game shows.

Why do you think it should be over all boards played in a lifetime? For instance, consider the following game. We have a coin which has 75% chances of showing heads and 25% chances of showing tails. I suggest a we play a game as follows. You flip the coin, if it is heads, you get 1.1 tokens. If it is tails I get 3 tokens. We do this in groups of 3 flips. At the end of 3 flips, whoever has the higher number of tokens gets 1$ (paid by the other of course). The tokens are now thrown away and for the next 3 flips, we start fresh with 0 tokens each. Do you play the game with me? If you undertake a long run analysis, over the lifetime... you expect to win 1.1*0.75 - 3*0.25 = 0.075 tokens per flip. Hence for 3 rounds you expect to have more tokens than me. So you take up the challenge... But consider this: Even if there is one tails among the three flips, I end up getting more tokens than you. The chances that all the three flips are heads is (0.75)^3 = 0.421875. i.e. there is a 42% chance that all three flips are heads. So with at least 58% chances, i win at least 0.8 tokens per round of 3 flips, i.e each round I win a $ with at least 58% chances! So even though you expect to win positive tokens per flip, you end up losing money! Why? This is because we throw away the tokens you earned in the previous round and those aren't counted for further rounds. If we kept a running track of tokens won so far, you would win more money. Now consider a similar game with 2 flips per round instead of 3. Here, you expect to win each round with at least 56% chances. So the length of the round matters... The tokens are IMPS and the $ is the championship. Each round is similar to the final match which decides the championship. (assuming the teams start out at 0 each) This shows that you need to analyse per match, rather than over the lifetime... Of course, by a match I just mean the final match which decides the outcome. If we have to play other matches in order to reach the final and there is a victory point kind of system, we need different analysis.

Please don't allow the bb2 vs bb3 argument sway you towards taking the safety play. It is true that the long run analysis has an assumption of carry over of points which does not happen in practice, but, this does not imply that playing for overtricks is wrong. For instance consider the percentage of all such boards (boards with the guard against 5-0 break or overtrick). Assume that it is 2% (I am making this figure up, I have no idea what the right figure is), of all the possible bridge deals. Now consider a 256 board match. Expected number of such boards that would occur is ~6. If we play for overtricks, chances of gaining 6 IMPS on these 6 boards is 78.8%. The chances of losing at least 6 IMPS (lose 11 gain 5) is 22.2%. Based on other considerations of the match, if you think 22.2% is too high, play for safety. If other things are equal, playing for overtricks on each board might be the right way to go. (i.e if you play 1000 256 board matches, you will end up winning 788 of them as opposed to losing 222 of them, if the result is solely based on the 5-0 break deals) In fact you could even vary your tactics. 3 boards you play for safety and 3 you play for overtricks. The chances that you gain IMPS is higher now, but the loss is greater in case you lose. So if you think you need 5 IMPS from the 5-0 boards (because of the other boards), play 1 board for safety and the remaining 5 for overtricks to maximise your chances. Basically my point is... There need not be an "always safe" or "always overtrick" strategy. It could be mixed, in the same match itself. Of course, other considerations might force an "always safe" strategy, but that was not the original poster's question...

I have edited the original post. Looks like RHO has K93.

Playing rubber bridge, you are South in a 3NT contract. [hv=n=s74haqt5dakt65c76&s=saqt52hj92dq3ca84]133|200|[/hv] You reach 3NT, opps passing all the time. 1S-2D-2NT-3NT. West leads club Q. You hold up 2 times, discarding a spade from dummy. East turns up with 3 clubs at least. (EDIT: East overtakes the first club and returns the club 9 and then continues with the 3) What is the best line after winning ♣A? (Please calculate the odds if possible) A ) Lead ♥J (finesse K) B ) Lead ♦Q (finesse J next) C ) Lead low ♦ D ) Lead low ♥ E) other... Assume expert defense. Richard Pavlicek's suit break calculator: http://www.rpbridge.net/xsb2.htm

Not really. If you adopt that reasoning, then you can't really play the odds at all, since they're all "in the long run". That statement is a bit misleading. What it meant was that the analysis works only if you consider a long run of such boards. When the number of boards is cut short, a different analysis might be needed and that the long run analysis might end up giving wrong results. That is all. This does not imply never to play the odds as you seem to have deduced. Which arguments about short matches are you talking about? I have seen multiple! :D

Assume the example was a final match, both teams starting from zero. The example was just to prove a point that the logic, "It works in the long run, hence I will play for it" is not exactly correct from a mathematical standpoint. It had nothing to do with the other factors of bridge. When all else fails, you resort to mathematics! For instance you know west has 5 clubs and East has 3. From a mathematical standpoint you finesse West for the Q. But that is not real bridge, if you know that West cannot have the Q from the bidding and the play so far. Anyway, more often than not, the decision which wins in the long run turns out to be the winning decision for shorter runs too.

The logic that in the long run it works, hence I will play for it is fallacious. That it works in the short run requires a little more math and needs to be taken into consideration! I am repeating what I said before! Sorry about that. For instance say there is an 8% chance of going down when trying for an overtrick. Resulting in a 1 IMP gain or 11 IMP loss. In the long run, this definitely gains. (expected gain 0.04 IMPS per board) But consider a match which has exactly 11 such boards. Other things being equal, you have a 61% chance of losing if you always play for the overtrick. If the same match had exactly 5 such boards by playing for overtricks, your chances of losing are only 35% now. The expert will lose with a 11 board match but win with a 5 board match, even though he makes a winning decision which is right in the long run. The short run decision, depends on the length of the run, though more often than not, the decision which gains IMPS in the long run will also be the decision which gains IMPS on the shorter run.

i think Trumpspace pointed very well the problem. most of the time i play (very) short matches (since i didn't made yet in BB final ;-) and to loose 11 IMPs trying to gain 1 in one board would be crazy. I think if anything then its exactly the opposite, if the match is short you dont want to throw overtricks , because in the long run it will benifht, because the long run wont come, the trunps will not break 5-0 not at this match. All in all the expert is right, take the matematical right play. It is not implied here that the shorter the match the more you should play safe! Only implication is the length of the match plays a factor... Please look at the example in my Dec 19 2005, 01:21 PM reply to whereeagles.

If you follow this strategy... and say we play matches with 17 such board each. You will end up losing more often than winning. (Assuming that losing a 4% 5-0 break board throws away 17 IMPS, which according to your logic odds are around 5% in theory and is not worth playing safe). Well, a 5-0 break doesn't throw away 17 imps but something like 10 or 12. Anyway, if you always want to "play for the contract", you might one day lose an international match 20-10 VPs, the same way I once did. Me and pard kept playing safe while on the other room opps kept trying for overtricks. After 20 boards those peanut imps added and we lost by a substantial margin. The 17 Imps was just an example. By say some scoring change, a game swing is 17IMPS. Your logic will still make you play for the overtrick... My claim is that if the match happens to have exactly 17 such boards you have higher chances of losing the match because of your strategy (other things being equal). This was just an example to prove a point! The point was, there is no "always play for the overtrick" or "always play for safety" rule! For instance if there are 2 such boards per match (4%, 17IMP loss), you are better off playing for overtricks, while, if there are 17 such boards you are better off playing safe! The right strategy depends on the number of such boards in the match and the number of IMPS gained/given away (and various other factors which is hard to determine). But from my calculations, for 4% 5-0 breaks and 11 IMP loss it seems like play for the overtrick will gain more than playing safe. For the long run it is definitely true, but for shorter sized matches also, it seems to be true in most cases.

If you follow this strategy... and say we play matches with 17 such board each. You will end up losing more often than winning. (Assuming that losing a 4% 5-0 break board throws away 17 IMPS, which according to your logic odds are around 5% in theory and is not worth playing safe). The problem with this 'long run'/in theory analysis is that the IMPS won on such boards by USA against Italy in Bermuda bowl 2003 are not counted in USA vs Italy match in the Bermudal Bowl 2004. The long run analysis has an assumption of such a carry over!

If spades are 3-3, I think the following play gives a 100% chance. Win ♣A, cash ♣K and play a low heart off the table. The idea is to ruff a club before the 3rd round (if at all) of trumps are drawn. If we win the 3rd round we can win in hand an play a spade towards QJ. If opps win the third round they are endplayed. Given the bidding, it is likely that east either has 3 or 4 spades and West has 3 or 2 (according to Ben.. if I understood his post correctly) The chances of 3-3 are now: 57.14% The chances of 4-2 are now: 42.86% (using Richard Pavlicek's suit break calculator, giving East 4 spaces and West 3). The chances of a 2-1 heart break: 78% If we do not know that spades are 3-3, playing the A and small (after cashing ♣K) is much better than low heart after cashing ♣K, if you think the opponents will find the spade ruff. Against most beg/intermediate players, I think it is better to play a small heart instead A and small...

Going further on the number of 'Overtrick or die' (OOD) boards in a particular match. Say a 100 board match has 11 OOD boards (which is probably unlikely) What should your strategy be? Say the chances of going down on a single board are 5%. The chances that you gain an IMP on all the 11 boards is (0.95)^11 = 0.568 ~ 57%. The chances that you lose at least one IMP total (by going down at least once) on the 11 boards is ~ 43%. If you think 43% is high enough, play safe. If the chances of going down on a single board were 8% this figure would be a whopping 61% (= 100*(1- (0.92)^11)). Now consider a match where there are 23 OOD boards. The chances that you go down on at least 2 boards is: 1 - (0.95)^23 - 23*(0.95)^22*(0.05) = 0.33 ~ 33% With 35 OOD boards the chance of losing at least one IMP drops to ~25%. (if chances for a single board were 5%) In the long run, the chance of losing IMPs is less than 50% (as shown by earlier analysis) But the long run, might not be long enough... as the 8% case for the 11 boards shows.

Say the chances of going down are 5% if we are trying for the overtrick. Suppose a game swing is worth 11 IMPs. Assume that at the other table they always play safe. if you take the risk and it works you end up making +1 IMPS. if you take the risk and it loses, you end up making -11IMPs. Your expected IMP score per board is 0.95*1 + 0.05*(-11) = 0.4 which is positive, so you must risk the overtrick. Of course this assumes your opponents always play safe. In fact, if the chance of going down when trying for an overtrick is around 9% (100/12 to be precise) or less, the risk must be taken. But the problem with this analysis is the usage of the words "in the long run". The frequency of occurence of such boards in a say 256 board match could be really low. For each board you throw 11IMPs, you need 11 such boards to catch up, what are the chances of that? That needs to be taken into consideration too! In the long run counts only if you are playing a reasonable number of boards which decide the outcome of a match! which could well be over a 1000...

If spades are 4-2 there is a chance that the opponents can manouver a spade ruff. For instance if West has Ax in spades and Kxx of trumps... After A and small heart, west will play A and small spade. East win and return a spade for a ruff. If spades are 3-3, I think there is a 100% line available (assuming clubs are at least 6-2). Also, I think that line also works if opponent do not manouver for a spade ruff in case they are 4-2.

Yes, this is more about the play than counting. I just mentioned the counting lesson, so that someone who remembered the bidding could reply with it...

This hand appeared during yesterday's counting session with hannie, matt and arend. You have reached 2H, assume everyone (except you of course :) ) is intermediate/adv. [hv=n=sqjxxhat8xxdxxcak&s=sxxxhqj9xxdxxcjtx]133|200|[/hv] I wish I remembered the bidding, sadly I don't. Maybe someone can post the bidding here... Opponents start off with two diamonds and switch to clubs which you win with the ♣A. Plan the play. (To make the problem a little more interesting {I hope} assume spades are 3-3)

At first I was confused what in the world is being talked about.... Then i looked closely at the spade suit trying to place the spots.. Nice! It is a wonder how they managed to get some spots out of place!