This article is not going to tell you anything you didn't already know! However (pace Rumsfeld) it may tell you something you didn't know you knew, namely the mechanism by which you come to decide between different sets of possible moves. It also provides a technique to assist you to make a decision when the "correct" choice is not intuitively obvious.
The technique is not specific to Diplomacy, nor even to gaming in general. It merely formalises a thought-process which occurs intuitively whenever you make any decision in life where one of a range of possible options will interact with something as-yet unknown to produce an outcome of greater or lesser desirability. It even applies, for example, to a choice of marriage partner!
However, for reasons that will become apparent, it is of particular applicability to the no-press variety of Diplomacy (which is where I spend nearly all my Diplomatic time). In this article, therefore — unless otherwsise specified — assume my thinking and examples relate to no-press games.
I should emphasise that this article is solely concerned with short-term tactical decisions. Strategy is at least as important as tactics — probably more so — but I make no attempt to assess competing strategies, and strategic thinking is only relevant here insofar as it influences the value you assign to a given board position.
I'll illustrate my points by using a fully worked example. This may look daunting, but don't be put off by this; the number of times you'll need to actually do full longhand workings in anger can be counted on the fingers of one foot. However, it's the best way to show how thought processes can be numerically converted into decisions.
Ok. Disclaimers over, I'm now going to have to bore you with a wee bit of mathematician-speak…
Given any decision d that you make from the set of possible decisions D, and any decision x that the opponent(s) can make simultaneously from the set of interacting decisions X, the outcome (Odx) of d with any specific x can be measured as:
where Px is the probability of the opponent making decision x, and Vdx is the resulting value to you of the interaction of d with x.
The Expected Outcome (Od) of the decision d is merely the total of all Odx summed over the range of possible values of x, i.e.
And the "correct" decision is the selection d with the maximum value for Od.
Or, in English, the outcome of any decision an opponent might make reflects (a) how likely he is to make it, and (b) how good or bad the outcome is if he does. Nothing more than cost-benefit analysis, or risk analysis under another guise.
There… told you it wouldn't take long. Now I suppose you want to know what this gobbledegook actually means, and you'll be delighted to hear that this is best done by dropping the maths-talk and reverting to Diplomatese.
The first thing to do is establish what the possibilities are, both for your own moves and those of the opponents.
Yes, I know… if you have 5 units on the board, and each has 20 possible options (including moves, convoys, supports, and hold) there are 95,367,431,640,625 possible decision sets, and it will take a wee bit of time to write down and evaluate each of these. Furthermore, if you have 5 units the opponents have 29 units or thereabouts between them, and the number of possibilities there is 176 billion billion billion. So you may need to lay in a good stock of ink and paper.
Calm down, breathe deeply, take a chill-pill, it ain't really that bad… of the numpty-squillion possibilities, only a handful actually matter. Let's see what we can eliminate:
Having cut out all the dross, we end up with a reasonably manageable set of possibilites. For my example, I'll use the Russian Fall '01 position in the northern theatre, with a fleet in the Gulf of Bothnia, an army in St Pete's, a German fleet in Denmark, and English fleets in the North and Norwegian Seas. I'm assuming that Austro-Turkish manoeuvres in the south are not so immediately threatening that the army in the Winter Palace needs an immediate return ticket to the Kremlin, and that the strategy implied by the opening moves — a concentrated assault on Scandinavia — can therefore be pursued. I'll also ignore any possibility of opponents going NMR, on the grounds of eliminating improbable moves.
For your own moves, the fleet has three realistic possibilities: move to Swe, move to Bal, or hold (probably communicating in some way to Germany). The army too has three realistic possibilities: move to Nwy, move to Fin, or hold (probably communicating in some way to England). This gives a total of 9 combinations of move to consider. However, it's highly unlikely you'll want to leave one force on hold whilst the other fails to attack a centre. This narrows it down to 6 pairs of moves to consider for this sector.
This part of the job is vitally important in no-press. It's far from rare in press games to overlook possible moves for yourself, but you have allies to point them out to you. There's no such luxury in no-press: you need to think for yourself!
As to the opposition moves, we've already established that for our purposes Germany has three options. The English position is slightly more complicated. We can discount anything which doesn't involve a move to Norway (even if old Clemenceau is sitting in the Channel and Picardy, the cold-water fleet still has nothing better to do than try and grab a centre). We also don't for the time being need to distinguish between the Norwegian Sea fleet moving to Norway, the North Sea Fleet moving in, or the Yor/Edi army being convoyed there; as with the Kaiser's none-of-the-above options, this will be a consideration for Spring '02, not Fall '01. However, there are four potential variations: the unopposable supported move into Norway; an unsupported move from the Norwegian Sea, with the North Sea staying out-of-sector (for instance, convoying Yorkshire to Belgium); an unsupported move from the Norwegian Sea, with the North Sea slipping into the Skagerrak; and an unsupported move from the North Sea, with the Norwegian Sea steaming into the Barents Sea. However, whilst the latter two will call for different approaches in the spring, I'm going to conflate them for this analysis as both being "full-frontal assault on Scandinavia", and both equally undesirable (the Barents sea option is more immediately hostile to Russia and friendly to Germany, and the Skagerrak move vice versa; however, in no circumstance is an English general in Scandinavia likely to leave Russia undisturbed in St Pete's when it's so easy to capture and retain from the north). There are therefore three English possibilites to consider, alongside the six Russian and three German.
The bad news is that this gives us 54 (ie 6*3*3) combinations to consider. The good news is that this is about as complex as it ever gets.
The way to proceed from here is to lay all the possible combinations out in "Decision Tables", which look like this.
These tables form the basis of the remainder of the analysis.
This is a relatively easy stage in the process. In the example we're using, we only have to assess two sets: one for Billy-boy and one for King Teddy.
Statisticians will tell you that probability is expressed as a real number between zero (representing no possibility whatever) and one (meaning total certainty). Forget it, we aren't doing a stats exam here!
What matters to us is not the absolute probability, but the relative probability of the various options the opponent can take. These can indeed be expressed as a numbers between 0 and 1, but could equally well be percentages, or even numbers in any other range. For my own part, I like to use percentages, as they're easiest to understand.
Statisticians will also tell you that the sum of the probabilities for an exhaustive list of mutually-exclusive options is 1 (ie a 100% certainty that one of the options will occur). Again, forget it; we're only concerned about relative values (though as a matter of personal choice I do normally make my probabilities add up to 100%, just as a failsafe check on my sums).
The important thing in this stage is the exercise in judgment. How — without access to the inner workings of the opponents' minds (and, in a Gunboat game, without even knowing who they are) — can you put a number on the probability of a particular choice being made? There are several things which can assist in this process.
I'll make a probability assessment of my own here. In the next game you start, predict the sets of orders every movement phase for every other player with three or more units. I would assign a 99.9% probability that the number of phases where you make totally correct predictions — between fall '01 and the time a stalemate line is approaching completion — is a nice round zero!
As you see, assigning probabilities is a highly subjective judgement call. This is one of the several reasons why computer artificial intelliegence Diplomacy programs are so notoriously pathetic: computers follow rules, they don't and can't exercise human judgement (and won't do so in your lifetime or mine).
The reason this aspect of the analysis is particularly relevant to no-press Diplomacy is simply because the unknowns are fewer when press is exchanged. In no-press, every single opponent's moves for every single phase of the entire game are matters of conjecture until the results of the phase are posted. With press, on the other hand, you are likely to know with 100% certainty (barring a stab) what your allies intend to order in your theatre of interest. Furthermore, you'll be using every diplomatic trick in the book to know — or at least to have a very good idea about — the enemy's intentions as well. This removes the vast bulk of the need to exercise probabilistic judgement.
So, let's get back to the example I've been using. What probabilities would I assign to the German and English orders?
Assuming no better information (and in Fall '01 in no-press you rarely will have better information), and assuming also that French spring openings don't point to an English change of heart, I would suggest the following probabilites:
|Supported attack||60%|| ||Sweden||45%|
|Unsupported attack||10%|| ||Baltic||5%|
(Note, however, that if the spring moves have guaranteed the Kaiser a build from Belgium, as well as the near-certainty of Holland, then I would increase the probability of the Baltic move to 10% or even 15%, since the build from Denmark would then be less pressing; conversely, if he failed to open Berlin to Kiel I would count it as a non-option, since it would wholly foreclose the German chance of a Danish build).
This is, as I can't emphasise enough, a judgement call not an observable fact. You may well deem the probabilites to be very different, and you're perfectly entitled so to do.
We can now plug these figures into the Decision Tables. Remember when assessing the combined probability of two independent variables that you merely have to multiply the two probabilities together. If you express them as percentages, don't forget to divide by 100 at the end (50% of 60% is 30%, not 3,000%). They now look like this.
The last section was all about judging what the opponent might do; we can now return to the comparative comfort of our own heads.
Having listed the possible combinations of moves (54 of them in our example), we now need to assess the outcome of each combination. Before even attempting to put values against this, it is advisable to simply state the impact of the moves in factual terms according to the objective state of the board which results from the orders. Remember always that this examines the board as it will be after the results are in (including retreats and, for a fall analysis, adjustments). So in looking at our example we're asking, for each combination of orders, what will the map look like at the start of 1902?
The aspects I may look at here include:
The first three of these will almost always be vital considerations. The latter three are much more dependent on circumstances and personality. You might also have other issues you wish to consider, depending on the circumstances. Feel free. This is a guidance note, not a Rulebook!
As with the probability assessments, this stage of the exercise has a particular relevance to no-press; but this time it's for a dfferent reason. Even in full-press Diplomacy, you still need to go through the outcome assessment and evaluation process (albeit normally intuitively); however, you don't always need to painstakingly think through all the possible ramifications of a set of moves. What do you have clever allies for if not to bounce ideas off them?
Let's now look at the impacts in more detail, using our example.
The alliance structures are probably the most complicated factor to assess in the early phases, before alliances and enmities are fixed (it gets easier the nearer we are to the end of the war).
Looking first at Anglo-Russian relations, I will read a full-frontal English attack as as sign of near-certain hostility, a supported attack on Norway as a mark of probable hostility, and an unsupported attack as indicating possible alliance. I also expect him to interpret my moving to Norway as hostile, to Finland as neutral, and holding as friendly. If we assume that a hostile move on my part will worsen his disposition towards me by one level (if possible), and a friendly move will improve it, we get the following matrix:
|England\Russia||StP - Nwy (hostile)||StP - Fin (neutral)||StP hold (friendly)|
|Full-frontal (hostile)||Near-certain English Enemy||Near-certain English Enemy||Probable English Enemy|
|Supported attack (unfriendly)||Near-certain English Enemy||Probable English Enemy||Possible English Enemy|
|Unsupported attack (friendly)||Possible English Enemy||Possible English Ally||Probable English Ally|
Similar considerations apply to Russo-German relations, as shown below:
|Germany\Russia||Bot - Bal (hostile)||Bot - Swe (neutral)||Bot hold (friendly)|
|Den - Bal (hostile)||Near-certain German Enemy||Near-certain German Enemy||Probable German Enemy|
|Den - Swe (unfriendly)||Near-certain German Enemy||Probable German Enemy||Possible German Enemy|
|Neither (friendly)||Possible German Enemy||Possible German Ally||Probable German Ally|
Dot counting is a simple factual assessment in the fall: either a dot is unowned, or someone owns it. Counting potential dots in a spring move is somewhat more problematic, but that's an exercise I'll leave for you to do yourself when the need arises. I'm your mentor not your nanny!
Defensive coherence is also a simple factual assessment, especially on a small front. Our front here only has two units, and defensive coherence can only be in one of three possible states: two-way mutual defence, one-way defence, or uncoordinated. With a longer front line it may be harder to work out, and you may have to include a count of supporting units in some form or other; this is another job for you to devise your own solution if and when required.
Offensive coherence measures the number of provinces that can be threatened by two or more forces in combination. In our example, providing we forget about possible builds in St Pete's in the winter, then the Spring '02 choice is binary: the units can either fail to coordinate offensively at all, or can combine to attack Sweden or Norway, but not both. Note that in other circumstances this is more than a binary question: an army in Warsaw can move to Ukraine to support an army in Serbia into Rumania (or to receive Serbian support for this attack); however, it could also move to Galicia to threaten both Rumania and Budapest, which (all else being equal) would be a more flexible and constructive position thus favouring the move to Galicia over the move to Ukraine. Of course, rarely is all else ever equal!
I don't, however, want to discount the extra flexibility available from a build. When looking at offense you want to consider best cases, whereas defensive considerations involve worst cases. So I'll measure offensive coherence on the basis of an additional army in St Pete's if it's vacant for the build, giving me a target count of zero, one, or two potential targets. (To say it's a target is not to say it's necessarily winnable — the enemy may have supporting defenders — merely that it is capable of being attacked with support).
In some circumstances offensive coherence is a non-issue. If you're trying to manage a controlled withdrawal to avoid a rout, you ain't gonna wanna attack!
The momentum/security considerations will vary depending on both circumstances and style. As a simple example of circumstances dictating, if you are trying to merely maintain a tricky position until other forces (your own or an ally's) can come riding over the horizon to the rescue, then momentum will be of no significance. Your own playing style will also greatly influence the factors you consider: if you like an expansive game or are dashing for a solo you'll place great weight on momentum and very little on security; conversely, if you favour caution and survival you'll emphasise security at the expense of momentum. As with everything else in this article, there's no escaping the human element. I'll come on to the evaluation in a moment, but for now lets try to keep things simple and factual. We need some sort of measurement of momentum, and I'm going to use the simplest possible measure available: the number of your units which actually move (as opposed to supporting, holding, convoying, bouncing, or otherwise sitting parked in the same bivouac). Security issues will vary with circumstances, and there's really little in the way of a generalised unit of measure we can apply. Instead, it's probably best to list any specific features of concern. In certain circumstances this will involve issues like opponents' forward retreats behind your front line, or indefensible dots, but in our particular example the only potential security weakness is a vacated St Pete's, or the variant of full-frontal where there is an Englishman in both the Barents Sea and Norway. With security considerations (as with defensive cohesion but unlike offensive cohesion) you're having to consider worst-case positions, so in my evaluation I'll assume I'm unable to build in St Pete's in the winter.
Let's now plug some text into the example, to see how we might assess the outcomes. Sadly, this is the really ballsaching part of the exercise, since all 54 combinations need separate consideration. The tables now look like this.
Having worked out the factual impact of the various move combinations, we can now try and put numbers against each. This is, yet again, a subjective judgemental exercise. You must be getting used to that idea by now!
There are several ways you could go about this. One method would be a simple linear scale, for example from +10 ("this is better than sex with Marylin Monroe"), through zero ("did somebody say something?"), to -10 ("not only have I just died an unpleasant painful death, but Beelzebub has now condemned me to spend all eternity covering political conferences"). Nothing whatever is wrong with this method.
Another way is to look at the individual elements you've identified, and evaluate each one separately before combining them to reach a final figure. This appears to be more scientific; actually, it isn't (and does in addition have some inbuilt pratfalls), but it does make life easier when you're looking at a lot of separate factors. It also helps when you want to give just one of the factors exceptional weight — for instance, if a possible forward retreat would be devastating, you could weigh it at a disproportionately negative value compared to all the other factors.
Another advantage of this approach is that it forces you to make explicit judgements. I suspect that for many players their natural "style" — especially in relation to the caution/expansiveness factor — is quite frequently allowed to overcome better judgement. A cautious player may well think "I could lose a centre doing this, so I won't do it" when in fact the potential short-term loss is outweighed by the medium-term potential advantages the move yields. Conversely the expansive player may be unduly neglectful of his soft underbelly. By putting a figure on the elements in the analysis, this risk of subjective misjudgement is minimised.
A third benefit is that it may reveal "gaps" in your first attempt at assessing the factors significant to the outcomes. For instance, I haven't in this example looked at the risk of letting someone in for a solo, or of letting someone whittle me out of a draw. In other circumstances, though, factors like this may need separate evaluation. Another potential factor is of particular relevance to no-press: the freedom to communicate. There may be a pressing need to transmit a message (such as "get your tanks off my lawn" or "stop France before he solos") using the normal no-press method of an impossible convoy. If this were the case, you might add separate factor to represent sets of orders which include a static fleet capable of giving the desired message. Overall, the list of relevant factors is wholly for you to identify and assess; I've only given examples, not an exhaustive checklist.
Now the warning. It's very possible that factors which you've isolated as separate are actually different aspects of the same thing. For example, the move from St Pete's to Finland has an equivalent impact on offensive coherence and momentum and security. There's nothing actually wrong with "double counting" — this isn't a polling booth — but you do need to be aware of it and avoid attaching too much weight to double-counted factors.
Time now to get back to the Tsar's conundrum and paly with some numbers.
At this stage of the war, with much fluidity in the position, I view the alliance structures as of primary importance. Furthermore, the English and German positions must be looked at jointly. Overall I prefer to attack Germany than England, both since he's nearer to me and more vulnerable early on to a squeeze, and since I've already defended against an English assault with the Mos-StP move in the spring. This isn't, however, a strong preference. I most certainly don't want two enemies in the north, though, and would prefer not to have two allies (since I will have to turn on one, and don't need a reputation as a stabber this early in the game). Also, whilst I don't mind how much one hates me if the other is well-disposed, the extent of hate certainly does come into play if I don't have a potential ally. This lot will take a bit of assessing!
The way I'll "score" for this is as follows: If my assessment shows I have one ally and one enemy, irrespective of intensity, I'll score it +4. If the enemy happens to be Germany, I'll add a further point making it +5 to indicate the preference. If I have two allies of any intensity I'll mark it as -1. All other combinations involve 2 potential enemies, but if I've only marked one or other as a "possible enemy" there's still clearly fluidity in the relationship, so I'll score it as zero. Anything else is very nasty, so I'll score -2 for each probable enemy and -3 for each near-certain enemy.
I'm not going to be occupying Norway this fall; so do I care whether it's occupied by England this year or not? Well, English occupation is immaterial for now — I plan to kick him out next year unless Germany is my target — but if the King is hostile I don't want him gaining a build. However, I'm not going to overemphasise its importance, since any build won't be able to reach the front line till next fall at the earliest, so I'll allow just -1 for English occupation, and even then only if he's a probable or near-certain enemy.
Sweden is another kettle of fish. I can envisage no circumstances whatever in which I'd rather not gain the build from Sweden. However, the exact value of it to me depends on events elsewhere on the map. If things are going well for me in the south, with Rumania assured and no threats to Sevastopol or Warsaw, then the build from Sweden is no more than a nice-to-have (and possibly not even that if it sets off a burst of penis-envy — sorry, early-leader-syndrome — amongst the others). On the other hand, if things are threatening to turn sour in the Pripyet Marshes I may need the northern build merely to shore up the southern defences. For now I'll assume that one of Austria or Turkey is firmly onside, so I'll value the Swedish build at +2 (if things were tougher down there I'd make this +3 or even +4, but if both are friendly I'd reduce this to +1 to reflect the risk of being seen to grow too fast).
If Bothnia is hitting the Baltic, Germany may or may not occupy Sweden. I hope he does. If he gets Sweden he won't get Denmark, and will have an isolated unit in the north (in theory he could get both centres, with Kiel following up into Denmark, but he won't do this as he doesn't expect me to not try for Sweden myself). So I will value a German in Sweden as a positive good to me, worth +1. However, if the German is in Sweden because I stood pat the signal is mixed; I won't score for this.
I'm not overly concerned about defensive coherence in this position. The army is under no serious threat in spring '02 unless it advanced to Finland, and Germany occupied Sweden, and England convoyed an army to Norway. The fleet can only be threatened (following a German fleet build) if it advanced to the Baltic, or if it moved to Sweden without the army concurrently moving to Finland and with the English in occupation of Norway. I'll deduct 2 points in these specific circumstances, and otherwise ignore this factor (in some cases both risks apply; very nasty, so make it cumulative and deduct 4).
Offensive potential, momentum, and security largely go hand-in-hand in this example. Whenever both units move there are two potential targets. The opposite, though, does not apply - if the only unit to move is StP-Fin, then the build I've assumed in St Pete's allows two targets. Where two potential targets exist, therefore, I'm not going to separately count momentum; instead, I'll value the agressive potential of the position at +3.
If I have one potential target only, it perforce means I'm already in occupation of Sweden and the target is Norway. Since I've already counted the benefits of having a build from Sweden, and since occupying Sweden means Norway is targetted irrespective of what the St Pete's army did, I'm not going to score this potential any further.
If I fail to move, the impact is very much bound up with the alliance structure, which I've already considered. It also means that St Pete's remains secure for now. There's clearly no benefit in standing still, but it's not an automatic disadvantage either. I'll count it at zero.
Security is only an issue in two circumstances. The first is when the army moves to Finland and the back door is temporarily left open. However, it's then also free for a build to plug the gap, and will only be significant if I fail to get a build from either Sweden or Romania. Since this is early in the war I'm not going to be paranoid about possibly losing centres; I'm still thinking of winning, not mere survival! So I'll wholly discount this consideration.
Where there is a concern, as noted before, is a full-frontal attack with English forces in Norway and the Barents Sea, and the Russian fleet in Sweden and hence isolated from St Pete's. This will only show up in 50% of full-frontals, but is such an unpleasant possibility I feel I need to allow for it. In this case (and in this case only) I really need to distinguish between the two full frontals. In an ideal world I'd mark it as -4 for the Barent's variety of full-frontal, but not relevant to the Skaggerak variety. However, I don't want to do this — isn't 54 combinations enough already? — so I'll average things out and count this feature as worth -2.
All this can go into the Decison Tables, which are now like this.
This stage doesn't require the exercise of judgement, merely the multiplication of the assessed probability times the calculated outcome for every line. This gives a line-by-line "expected outcome" of the interaction of the decisions (Odx in the formal bit), and by adding these up for each of the 6 choices you can make yourself you get the expected outcome of your own decision (Od).
If you have an iota of sense you'll get a spreadsheet — or, if you happen to be a senior executive, your sidekick — to do the arithmetic for you. I have neither sense nor a sidekick, so I've done it longhand.
This gives us the final Decision Tables, looking like this.
The final step is to interpret the results and make your decision accordingly.
The rule-of-thumb is to pick the decision set with the best total expected outcome.
But… (there's always a "but", isn't there?)
Exercise common sense. If the outcomes look strange, improbable, or just plain wrong, then it's likely they are exactly that.
and the only place you didn't exercise judgement was in doing the arithmetic. So if it seems a weird outcome, then you probably misjudged some of the inputs. Look at them again. Do they still make sense? Are the probabilities reasonable? Are you over- or under-compensating some factors at the expense of others? Have you failed to consider a key factor? Don't be afraid to rethink and try again. Remember always that the high-probability opponents' decisions contribute disproportionately to the calculations; in our example, although 9 combinations are considered, just 4 of them make up 85.5% of the weightings. So these are the ones to revisit in particular.
Maybe the figures do make sense. Maybe it's just your intuitive "common sense" that actually misjudged what the good and bad plays really are!
It may be that after doing this exercise, you're still in a quandry. Maybe the vote is too close to call. In this case, a further option is to look at is the spread of numbers that make up the total. If it's a large spread — some very big positive numbers and/or very big negative ones — the implication is that it's an all-or-nothing throw of the dice. You'll either break the bank or file for bankruptcy. If, on the other hand, the spread is small, it implies a safety-first option; win small or lose small. Pick whatever best suits your temperament and strategy.
|Bot-Swe + StP-Nwy||+20½|
|Bot-Swe + StP-Fin||+320½|
|Bot-Swe + StP hold||+98½|
|Bot-Bal + StP-Nwy||-625|
|Bot-Bal + StP-Fin||-225|
|Bot hold + StP-Nwy||+117½|
This is a pretty clear call for moving to Sweden and Finland, and gratifyingly matches common sense (my common sense anyway) in that it gives good forward movement, good attacking potential, and doesn't commit you to any specific ally or enemy. The sums also make it crystal clear that there's no point dashing for the Baltic: it's going to hurt, and probably hurt bigtime. (This is, of course, no-press. In a press game, if you've got a firm agreement with England to mount a joint attack on Germany, the big minus numbers dissolve in the 0% probability part of the equation, leaving a modest but not unreasonable positive prognosis).
I'm a little surprised intuitively that the option where Bothnia holds is preferable, albeit marginally, to the option where St Pete's holds. I suspect I may have not got the impact of alliance structures quite right. This certainly wouldn't surprise me — it's both the most complicated factor in this example and the one that weighs most heavily on the outcomes — but I don't feel inclined to revisit the figures. After all, any tweaking I do is unlikely to change the winner… it won by a street!
Right: that's all the work done. You now know how you decide between competing decisions. You've done it all your life. You work out what the possible outcomes of the decisions are, and how likely those outcomes are to take place, and decide from that on the "best" decision overall. You normally do it wholly intuitively, without for a moment analysing the computation processes that went on inside your head. And — unless you have congenitally poor judgement — you normally decide correctly.
What you now have, though, which you may not have had before, is a technique to help you arrive at a decision when it's not immediately and intuitively obvious what's the best way to jump.
Hope it helps!
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