[han]

I completely agree with the expert. Taking a safety play that expects to lose IMPs in the long run (and in the short run too) is bad bridge. Teammates should be able to appreciate it when you make the right play. Teammates who complain when you make the RIGHT choice are very bad teammates indeed, and they would probably also complain when you do make the safety play and it costs an IMP. Just make the plays that have the highest expected wins. And yes, that sometimes means risking a contract for an overtrick, as long as the risk is very small.

[Trumpace]

whereagles, on Dec 19 2005, 07:25 AM, said:

Trumpace, on Dec 19 2005, 11:47 AM, said:

whereagles, on Dec 19 2005, 06:07 AM, said:

The odds for a 5-0 break are around 4%. The overtrick costs 1 imp out of 10. That's 10%, so indeed in theory it doesn't pay to play for the 5-0 break.

If the match is close, play for the overtrick. If you're winning and just want to avoid big swings, play for the 5-0 break.

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.

[Trumpace]

Flame, on Dec 19 2005, 08:14 AM, said:

vang, on Dec 19 2005, 06:48 AM, said:

Trumpace, on Dec 19 2005, 11:14 AM, said:

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...

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.

[Trumpace]

Hannie, on Dec 19 2005, 12:57 PM, said:

I completely agree with the expert. Taking a safety play that expects to lose IMPs in the long run (and in the short run too) is bad bridge. Teammates should be able to appreciate it when you make the right play. Teammates who complain when you make the RIGHT choice are very bad teammates indeed, and they would probably also complain when you do make the safety play and it costs an IMP. Just make the plays that have the highest expected wins. And yes, that sometimes means risking a contract for an overtrick, as long as the risk is very small.

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.

[awm]

But then again, all else is not equal. In the eleven board match, if you always play for the overtrick you may "lose" 61% of the time, but almost all of these "losses" are by one imp when you score +1 on ten boards and -11 on one board. On the other hand, when you "win" 39% of the time, you will score +1 on every board and win by 11 imps. So while I agree that if these eleven boards are the entire match and it's win/loss and not VPs, and I know in advance that every board will be like this, it would be better to take safety plays... this is not how real bridge works.

I think a lot of good players take safety plays for three main reasons:

(1) They believe they are superior to the field. In many fields this may be true. Also, many good players have big egoes and think they are superior to all fields even when this may not be true. Anyways, if you are the best team in the field, then lowering variance is often a good tactic. Taking safety plays may be a net loss, but it's a very small expected loss in exchange for reducing the variance of your results.

(2) Being a good bridge player doesn't mean you can compute exact probabilities at the table. There may be a few players who can do this (I hear Michael Rosenberg is good at it) but the majority of top players can't. The probabilities in these situations are very small, and it can be hard to work out exactly what your expectation is. At IMPs it is "more often right" to take safety plays and a lot of good players do this by default.

(3) Psychological reasons -- particularly playing with a client, going down in a makeable contract may be bad mojo. In general I'd rather win more often, than make my contracts at a slightly higher rate, but I can see why people might not look at the issue this way. Also see reason (1).

[Trumpace]

awm, on Dec 19 2005, 02:20 PM, said:

But then again, all else is not equal. In the eleven board match, if you always play for the overtrick you may "lose" 61% of the time, but almost all of these "losses" are by one imp when you score +1 on ten boards and -11 on one board. On the other hand, when you "win" 39% of the time, you will score +1 on every board and win by 11 imps. So while I agree that if these eleven boards are the entire match and it's win/loss and not VPs, and I know in advance that every board will be like this, it would be better to take safety plays... this is not how real bridge works.

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.

[arrows]

think about this:

People know that insurance companies make money of them, but people keep buying insurance, why?

People know that the odds of winning lottery is against them, but people keep
buying lotteries, why?

Are they all idiots?


Typcially in a IMP team game. there are lots of swings that cost much more
than 1 imp. Hence the cost of losing 1 imp more neglectable. That's why
you should stick to the safe play.

mathematically correct doesn't mean it's practically correct.
Here, the key point is that most people are risk averse, that's why they pay premium for insurance. The 1 imp is your premium.

[awm]

arrows, on Dec 19 2005, 02:39 PM, said:

think about this:

People know that insurance company make money of them, but people keep buying insurance, why?

People know that the odds of winning lottery is against them, but people keep
buying lotteries, why?

Are they all idiots?

The reason is that money doesn't value linearly. To give an easy example:

Suppose you are given a choice. Either you will be given $10 million... or you can flip a fair coin. If the coin comes up heads, you get $30 million. If it comes up tails, you get nothing. What do you pick? The expectation from the coin flip is higher, but most rational people will take the guaranteed money.

The point is, there is a threshold of money which will allow me (or most people) to be pretty much set for life. There wouldn't be much difference in my life between winning $10 million and $30 million, since either means I could retire and do pretty much whatever I wanted to do. Just the earnings from a safe investment on this money would yield a nice yearly salary. So even though the $30 million is "three times higher" it isn't really worth three times as much.

On the other hand, if you get rid of the "million" I would take the coin flip. $30 is worth three times more than $10 to me. A really rich person (say Warren Buffet or Bill Gates) would probably take the coin flip for the $30 million too, since these numbers are basically pocket change to them.

As for the lottery, the effective value of $10 million (or whatever the lottery pays) is really high and the cost ($1 or so) is very small. The relative values are not equal to the monetary values for most people. There's also the enjoyment gained by actually playing, which may be worth a small amount. You won't see people like Bill Gates (for whom even the winning value of the lottery is pocket change) playing the lottery.

As for insurance, I know that I buy insurance because it's required by law.

I think the same reasoning applies in reverse though. A cost of $500-$1000 a year is annoying, but affordable. If I lose everything to an earthquake or fire, I'm pretty much screwed for life, so it may be worth the insurance premium even though it's expected negative.

I'm not sure how much this applies to bridge, where an IMP is pretty much an IMP, other than in the "strength of field" and "state of match" constraints mentioned before, which can create a situation where IMPs don't really scale linearly either.

[Fluffy]

I'm a damn matematician and wouldflip the coin

[barmar]

Trumpace, on Dec 19 2005, 04:14 AM, said:

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...

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".

While playing the odds might not result in winning any particular match, the long run also includes all the matches you ever play. If you adopt a strategy that has a 5% improvement, then (all else being equal) you can expect to win 5% more matches.

As a simplified example, suppose the only swing boards in any of your matches are the ones where you have to make this safety play decision, and you push all the other boards. If you don't make this decision correctly, you can expect to lose more of those deciding boards than if you do, so you'll lose more matches.

In real life, of course, there are lots of swing boards, so no single board is likely to decide a long match (sometimes it *feels* like it does, as in the final board of the USA-Italy match last year, but there were many other big swings in the match that could have won Italy the championship despite that slip at the end). But it's not really helpful to think about that -- to decide what to do on a particular board, you should normally consider it in isolation, and go with the odds on it. There are some occasions where "state of the match" allow some deviation (if you're up 50 IMPs with 10 boards to go, swings of 1-2 IMPs probably don't matter any more), but most of the time you don't have this information and you have to play each board best.

[cherdano]

I think the arguments about short matches in this thread are exactly wrong. When you are playing a very short match against an equally good team, the 1 IMP from the overtrick will decide the match more often than 1/11 * the number of times the 11 IMPs will decide the match. If you don't believe me, just think about a one board match

The argument about VP is also wrong. 11 IMPs will swing around 3 IMPs usually, while as for 1 IMP there is about a 25% of swinging an IMP, so the ratio of expected gain vs loss is still the same. (Unless, of course, you are in the last board and your feeling about the state of the match is precise enough that you are, say, well within the 3-8 IMPs range of 16-14. Not that I would believe anyone who thinks he knows the SOM that exactly.)

Arend

[Trumpace]

barmar, on Dec 19 2005, 03:41 PM, said:

Trumpace, on Dec 19 2005, 04:14 AM, said:

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...

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.

Cherdano, on Some day in the past,some time, said:

I think the arguments about short matches in this thread are exactly wrong. When you are playing a very short match against an equally good team, the 1 IMP from the overtrick will decide the match more often than 1/11 * the number of times the 11 IMPs will decide the match. If you don't believe me, just think about a one board match

Which arguments about short matches are you talking about? I have seen multiple!

[luke warm]

very interesting thread, i've never really thought about this... i've "taken on authority" that at imps, the safety play is better "in the long run"

having read all the arguments, two sway me toward always taking the safety play.. first was mikeh's argument about the likely contracts at both tables... i agree with him that you don't have to risk a contract for 1 imp, the very fact(?) that different contracts will be played on, say, 50% of the boards will make taking the safety play a better bet

2nd, trumpace's argument concerning the "long run"... what he said about bb2 vs. bb3 is correct... the 'long run' would include both of those final matches, but would have nothing to do with what to do while actually playing bb3... imo

[Trumpace]

luke warm, on Dec 19 2005, 07:52 PM, said:

very interesting thread, i've never really thought about this... i've "taken on authority" that at imps, the safety play is better "in the long run"

having read all the arguments, two sway me toward always taking the safety play..

first was mikeh's argument about the likely contracts at both tables... <Snipped>

2nd, trumpace's argument concerning the "long run"... what he said about bb2 vs. bb3 is correct... the 'long run' would include both of those final matches, but would have nothing to do with what to do while actually playing bb3... imo

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...

[Chamaco]

I would like to ask a question:

don't you think that the analysis should *not* be restricted to the single match (whatever the no. of boards) ?


It seems to me, on afterthought, that the +1 imps pickups shopuld be accounted over ALL OF THE MATCHES where we will avoid safety playes vs a low %.

The cost-benefit should not be restricted over a single match, but should include *all the imps TEAM matches in our life* where we shall adopt the same tactics refusing a low-risk safety play.

[Chamaco]

arrows, on Dec 19 2005, 07:39 PM, said:

think about this:

People know that insurance companies make money of them, but people keep buying insurance, why?

We can also think the other way around:

Insurance companies are ready to pay a big prize once in a while if a disaster occurs, if they can cash in a moderate amount on a regular basis.
And insurances companies do have a sound budget, so, on balance, their approach should payoff: indeed, on many instances, they reckon that the low-occurrence disaster they cover, NEVER occurs at all during a lifetime.

This suggests that even the opposite reasoning can be defended: we might want to cash in on a regular basis our 1-IMP pluses, ready to payoff to the low-occurrence 11 imps losses, just as the insurance companies do.

This analysis should not be restricted to the single match, but, if we consistently adopt the same tactics, to all of the team matches in our life.

[whereagles]

Fluffy, on Dec 19 2005, 08:14 PM, said:

I'm a damn matematician and wouldflip the coin

that's the spirit!

[Trumpace]

Chamaco, on Dec 20 2005, 03:23 AM, said:

I would like to ask a question:

don't you think that the analysis should *not* be restricted to the single match (whatever the no. of boards) ?


It seems to me, on afterthought, that the +1 imps pickups shopuld be accounted over ALL OF THE MATCHES where we will avoid safety playes vs a low %.

The cost-benefit should not be restricted over a single match, but should include *all the imps TEAM matches in our life* where we shall adopt the same tactics refusing a low-risk safety play.

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.

[Chamaco]

Trumpace, on Dec 20 2005, 10:31 AM, said:

Why? This is because we throw away the tokens you earned in the previous round and those aren't counted for further rounds.

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 ?

[Trumpace]

Chamaco, on Dec 20 2005, 05:47 AM, said:

Trumpace, on Dec 20 2005, 10:31 AM, said:

Why? This is because we throw away the tokens you earned in the previous round and those aren't counted for further rounds.

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.