Hijacking in period 3, 5 and 7

In passing, hijack­ing is where one pass­er decides to change what pat­tern they are passing and their actions trans­itions their part­ner into a com­pat­ible pat­tern. One pass­er is mak­ing an act­ive choice, the oth­er is pass­ively respond­ing. All trans­itions involve chan­ging how many clubs are being juggled loc­ally by +/- 1 club (assum­ing the pass­ive part­ner makes the min­im­al caus­al change). If the pass­er who is doing an act­ive trans­ition is gain­ing a club loc­ally then the trans­ition is a "hijack", if the act­ive trans­ition loses a club loc­ally then it is a "low­jack". Col­lect­ively these are also known as "pro­gram­ming" because you are pro­gram­ming your part­ner. Most people use pro­gram­ming and hijack­ing inter­change­ably.

Hijack­ing star­ted in 6 club peri­od 5 pat­terns, these pat­terns are described in Aidan Burns' Highg­ate col­lec­tion https://​passing​.zone/​w​p​-​c​o​n​t​e​n​t​/​u​p​l​o​a​d​s​/​2​0​1​6​/​0​1​/​h​i​g​h​g​a​t​e​.​pdf. If you are new to this type of pat­tern you should start with these (Aidan gives excel­lent instruc­tion which I shall not repeat here, see page 36). How­ever, the Highg­ate col­lec­tion does not go into gen­er­al­it­ies about hijack­ing. Hav­ing become inter­ested in these pat­terns and worked my way through all the pub­licly known hijacks I wanted to gen­er­ate more of them and cap­ture the gen­er­al rules on what are the prop­er­ties that make some­thing a hijack.

General rules of hijacking for two passers

  1. If you have an empty hand because you did not receive a "pass", zip into the empty hand
  2. If you were going to zip into a hand, but there is a pass com­ing to that hand throw a "pass" instead of a zip
  3. A "pass" is defined as the peri­od of the pat­tern + 2 (e.g. in peri­od 5 pat­tern a "pass" is a 7)
  4. The peri­od of the pat­tern before and after the trans­ition must be the same
  5. All pat­terns must have one or more passes (N.B. any pass sat­is­fies this con­di­tion, not just period+2 "passes")
  6. There can be 0 or 1 act­ive trans­ition throws (a "trans­ition throw" is a throw which is not part of the pat­tern you are trans­ition­ing to or from)
  7. All throws made on the pass­ive side must belong to a pat­tern they are trans­ition­ing to or from
  8. The pass­ive respon­der must make a caus­ally min­im­al change to their jug­gling in response to an act­ive trans­ition
  9. All glob­al pat­terns of twice loc­al peri­od are val­id 4 handed siteswaps (N.B. if all pat­terns val­id the loc­al peri­od, each pass­er will always have an integer num­ber of clubs loc­ally. How­ever, if pat­terns are only val­id con­sid­er­ing glob­als that are twice what we have been call­ing the loc­al peri­od then they are integer and half club pat­terns – I believe Brook has writ­ten one of these, but I have not passed it and I have no examples of such pat­terns in this post.)

These are a draft of the rules I have inferred from examples, the list may not be com­plete or accur­ate. If you have counter examples I would love to see them.

Pat­terns may have oth­er passes that are not peri­od + 2, but these are incid­ent­al; only a peri­od + 2 "pass" is suit­able for a hijack­ing trans­ition. A corol­lary of these rules is that a trans­ition res­ults in one pass­er gain­ing a club loc­ally, the oth­er los­ing a club loc­ally. If a trans­ition is val­id and fits these rules then it is part of the class of pat­terns that called "hijacks". These rules are suf­fi­cient to determ­ine if some­thing is a hijack or not, so with enough brute force they could be con­sidered gen­er­at­ive in terms of fil­ter­ing arbit­rary caus­ally val­id strings of num­bers, but I do not con­sider these rules to be well developed enough to be eleg­antly gen­er­at­ive. While I hope to add to the rules, I would wel­come some­body brute for­cing a gen­er­at­or for hijack­ing trans­itions.

Notation for transitions

Much of the work­ing out of the pat­terns is done in 4 handed glob­al, how­ever for describ­ing trans­itions I have found it effect­ive in work­shops to write [pat­tern 1 in local]transition throw if any[pattern 2 in loc­al] with the pat­tern 1 and pat­tern 2 writ­ten in the order required such that the entire string is what you do loc­ally going through the trans­ition. A cor­res­pond­ing string for the pass­ive response appro­pri­ately off­set is gen­er­ally provided in work­shops, although for my own notes I gen­er­ally don't both­er as the pass­ive respon­der will just respond nat­ur­ally.

One nice thing that drops out of this nota­tion is that it becomes clear that when the pat­terns are het­ero­gen­eous the min­im­al glob­al is twice the length of the min­im­al when the pat­tern is homo­gen­eous. This can be treated as a clue when it comes to con­sid­er­ing how to go about rep­res­ent­ing these pat­terns when attempt­ing to gen­er­ate them auto­mat­ic­ally. Anoth­er little clue is when there is an act­ive trans­ition throw that does not belong to either pat­tern, which indic­ates that states of the pat­terns we are trans­itiong between are not the same – state diagrams/​representations might be a good way to look at find­ing these trans­itions.

When I am work­ing things out, my stand­ard approach is to find the three (or four) pat­terns needed in glob­al and once I have them I switch to loc­als and intu­it what and where the trans­ition is, and if there is a trans­ition throw what that trans­ition throw is. The absence of any form­al pro­cess for this is some­thing I would like to solve.

Due to the way I work with both loc­al and glob­al, I will some­times be using num­bers in loc­al instead of hefflish.

Hijacking in period 3

If the peri­od is 3, then the hijack­able passes are zaps: 3+2=5. There was some con­cern that a zap might not be enough warn­ing to know you aren't going to have an empty hand, but that turned out not to be an issue.

855

The act­ive pass­er here is hijack­ing, by throw­ing an 8 instead of a 5. There are no act­ive (out of pat­tern) trans­ition throws. 

Transitioning out of 855

[855][885] act­ive trans­ition goes up 1 club (hijack)

[585][582] pass­ive response goes down 1 club

The return transition

[885][855] act­ive trans­ition goes down 1 club (low­jack)

[582][585] pass­ive response goes up 1 club

The is a minor vari­ation, you can ini­tially make either 5 into an 8 (trans­ition­ing from 855). How­ever the same is not true of the return, the 5 you turned into an 8 to enter the pat­tern will dic­tate which of the 8s can be thrown as a 5 to make the return trans­ition. Oth­er than that, the two options are the same.

Holy grail 975

Holy hijack­ing Bat­man! is this pat­tern really easy enough to do hijack­ing in? Appar­ently it is.

Transitioning out of 975

[579][879] act­ive trans­ition goes up 1 club (hijack)

[957][927] pass­ive response goes down 1 club

The return transition

[879][579] act­ive trans­ition goes down 1 club (low­jack)

[927][957] pass­ive response goes up 1 club

Hijacking in period 5

If the peri­od is 5, then the hijack­able passes are singles: 5+2=7. Aidan's two per­son hijacks fall into this cat­egory, so there was little new from me with 6 clubs in peri­od 5. I was able to make an addi­tion­al trans­ition into Maybe on Aidan's dia­gram to make a loop. There was also some pri­or work by Brook Roberts with 7 club pat­terns which has the excit­ing option of hijack­ing from 7 clubs to 8vs6 to 9vs5 loc­ally.

Classic hijacks and the 6 club loop

Aidan wrote up the trans­itions for most of these in the highg­ate col­lec­tion, with the only nov­el addi­tion being the trans­itions between "Maybe" and "Pop­corn Vs 5 club y not". I've found it help­ful to lay the pat­terns out in the fol­low­ing graph­ic­al rela­tion­ship.

Fig­ure 1. The ver­tic­al axis of this graph indic­ates the num­ber of passes each pat­tern has, with 1 pass at the bot­tom and 4 passes at the top. "Up" and "Down" refer to increas­ing or decreas­ing the num­ber of passes respect­ively. From each sym­met­ric pat­tern there are two routes out as either pass­er may take the act­ive role. Funky bookends vs parsnip has two trans­itions up to Martin's one count, but only the funky bookends pass­er can make them. Martin's one count has two dif­fer­ent trans­itions (self or heff) back down to funky bookends vs parsnip, either pass­er may take either route down, so in total there are four ways of leav­ing this pat­tern.

This video cov­ers the main loop from Maybe, up to Funky bookends vs parsnip down to 6 club y not, down Pop­corn vs 5 club y not and up to Maybe again. Below is a list of all the trans­itions shown on fig­ure 1, the trans­itions used in the video are marked with a *.

Maybe to Popcorn Vs 5 Club Y Not

[87762][88766] act­ive trans­ition goes up 1 club (hijack)

[62877][62827] pass­ive response goes down 1 club

Popcorn Vs 5 Club Y Not to Maybe*

[87668][77628] act­ive trans­ition goes down 1 club (low­jack)

[28276][28776] pass­ive response goes up 1 club

Maybe to Parsnip Vs Funky Bookends*

[62877]4[72772] act­ive trans­ition goes down 1 club (low­jack)

[77628][77678] pass­ive response goes up 1 club

Parsnip Vs Funky Bookends to Maybe

[72772]4[87762] act­ive trans­ition goes up 1 club (hijack)

[76787][76287] pass­ive response goes down 1 club

6 Club Y Not to Popcorn Vs 5 Club Y Not*

[76782][76688] act­ive trans­ition goes up 1 club (hijack)

[82767][82762] pass­ive response goes down 1 club

Popcorn Vs 5 Club Y Not to 6 Club Y Not

[76688][76782] act­ive trans­ition goes down 1 club (low­jack)

[82762][82767] pass­ive response goes up 1 club

6 Club Y Not to Parsnip Vs Funky Bookends

[82767]4[77272] act­ive trans­ition goes down 1 club (low­jack)

[67827][67877] pass­ive response goes up 1 club

Parsnip Vs Funky Bookends to 6 Club Y Not*

[77272]6[76782] act­ive trans­ition goes up 1 club (hijack)

[78776][78276] pass­ive response goes down 1 club

Parsnip Vs Funky Bookends to Martin's one count A

[78776][77772] act­ive trans­ition goes down 1 club (low­jack)

[72727][72777] pass­ive response goes up 1 club

Martin's one count to Parsnip Vs Funky Bookends A

[77772][78776] act­ive trans­ition goes up 1 club (hijack)

[72777][72727] pass­ive response goes down 1 club

Parsnip Vs Funky Bookends to Martin's one count B

[77678][77772] act­ive trans­ition goes down 1 club (low­jack)

[72772][72777] pass­ive response goes up 1 club

Martin's one count to Parsnip Vs Funky Bookends B

[77772][77678] act­ive trans­ition goes up 1 club (hijack)

[72777][72772] pass­ive response goes down 1 club

Going up into Martin's one count and back down into funky bookends allows you to change which pass­er has the Parsnip side of the pat­tern. So, as well as being a little loop of its own, it also would allow you to change who is able to take the routes down from Parsnip. (no foot­age found)

Hijacking out of Funky Bookends with 7 clubs

Ini­tially pro­posed by Brook and mod­i­fied by me so that it is 5 club Y not at the bot­tom rather than 5 club not Y. This base pat­tern allows you to do 7 clubs each, 8 clubs vs 6 clubs and 9 clubs vs 5 clubs. Ori­gin­ally Brook had this going through 6 club y not. Based on my modi­fic­a­tions to the 6 club loop I also looked for a Maybe ver­sion of this and was able to add it. I don't believe any his­tor­ic­al foot­age of the Brook's ori­gin­al set of trans­itions through to 5 club not y exists, but Camer­on and I had it run­ning nicely in Novem­ber 2018 (Leeds con­ven­tion?) and didn't film it because Camer­on had to go an tech for the show.

Fig­ure 2. Trans­ition dia­gram for hijack­ing in peri­od 5 with 7 clubs from Funky Bookends through to 5 Club Y Not.

UP AND DOWN ON THE MAYBE SIDE

Pre­lim­in­ary work mak­ing sure we can go to 9 clubs vs 5 clubs through maybe as this side was brand new in Ker­lin­gen. This is down and up on the left side of Fig­ure 2. 

THE SEVEN CLUB LOOP USING MAYBE AND 6 CLUB Y NOT

Funky Bookends to PHPHT vs 6 Club Y Not

[77678][A7878] act­ive trans­ition goes up 1 club (hijack)

[78776][78276] pass­ive response goes down 1 club

PHPHT vs 6 Club Y Not to PHTTT vs 5 Club Y Not

[78A78][AAA78] act­ive trans­ition goes up 1 club (hijack)

[76782][76282] pass­ive response goes down 1 club

PHPHT vs 6 Club Y Not To funky bookends

[A7878][77678] act­ive trans­ition goes down 1 club (low­jack) – trans­ition not shown in either video

[78276][78776] pass­ive response goes up 1 club

PHTTT vs 5 Club Y Not to PHPHT vs 6 Club Y Not

[AAA78][78A78] act­ive trans­ition goes down 1 club (low­jack) – trans­ition not shown in either video

[76282][76782] pass­ive response goes up 1 club

PHTTT vs 5 Club Y Not to PPSTT vs Maybe

[A78AA][776AA] act­ive trans­ition goes down 1 club (low­jack)

[28276][28776] pass­ive response goes up 1 club

PPSTT vs Maybe to Funky Bookends

[AA776][78776] act­ive trans­ition goes down 1 club (low­jack)

[76287][76787] pass­ive response goes up 1 club

Funky Bookends To PPSTT vs Maybe

[78776][AA776] act­ive trans­ition goes up 1 club (hijack)

[76787][76287] pass­ive response goes down 1 club

PPSTT vs Maybe to PHTTT vs 5 Club Y Not

[776AA][A78AA] act­ive trans­ition goes up 1 club (hijack)

[28776][28276] pass­ive response goes down 1 club

Hijacking in period 7

This the real bleed­ing edge of where hijack­ing is at the end of 2019. Over the year I man­aged to achieve a proof of prin­ciple for hijack­ing in peri­od 7. Not hav­ing any par­tic­u­lar sys­tem for gen­er­at­ing hijacks I quite prob­ably have not star­ted with easy pat­terns. One thing I did find while try­ing to com­pose these hijacks is that there is numer­ic­al issue mak­ing it hard to start with 6 clubs and go to 7vs5 because the passes are 9s. I'm not say­ing there aren't any 6 club peri­od 7 hijacks just that they are tough to find. Sim­il­arly I found it use­ful to put some 7s into the pat­terns even though these are not hijack­able passes in these pat­terns they keep the pat­terns pleas­ingly linked when there is only one 9 (I was not in favour of a sev­en count pat­tern).

Hijacking out of 9788827 a.k.a period 7 hijacking 1

As far as I am aware none of these pat­terns have names so they go by their glob­als in the sec­tion head­ings. The 6 club pat­tern is a very good test of how met­ro­nom­ic your jug­gling is in pat­terns with zips. If it the tim­ing is not met­ro­nom­ic it makes the 6 club pat­tern remark­ably dif­fi­cult to the extent that in some prac­tices, a part­ner and I struggled when we were both doing the 6 club pat­tern for prac­tice, but with the same part­ner it was much smooth­er when they were doing the 8 club pat­tern against me doing the 6 club pat­tern.

9788827 to 9797226 vs 9797888

[8298877]4[9926772] act­ive trans­ition goes down 1 club (low­jack)

[8778298][8778998]

9797226 vs 9797888 to 9788827

[9926772]6[9887782] act­ive trans­ition goes up 1 club (hijack)

[7789988][7782988]

Hijacking out of 9968827 a.k.a period 7 hijacking 2

As with the pre­vi­ous set of pat­terns, I don't think any of these have names. Also, the 6 club pat­tern is chal­len­ging – quite prob­ably also due to minor tim­ing errors that can be intro­duced when zip­ping which can become major tim­ing errors as this 6 club pat­tern has a zip flip loc­ally.

There is no video for this one yet, but all the trans­itions have been imple­men­ted so I can say with con­fid­ence that they are cor­rect. It would be nice to have a the­ory way of find­ing these trans­itions and/​or prov­ing their cor­rect­ness!

9968827 to 9922497 vs 9968897

[8296879]4[9924792] act­ive trans­ition goes down 1 club (low­jack)

9922497 vs 9968897 to 9968827

[9924792]6[9687982] act­ive trans­ition goes up 1 club (hijack)

Feedback, additions and corrections

I had hoarded some of the new mater­i­al for too long wait­ing to find and pub­lish the eleg­antly gen­er­at­ive rules for gen­er­at­ing hijacks. Writ­ing this post has helped things along a little bit, but it is time to share what I have and give oth­ers a leg up on tack­ling the the­ory chal­lenge. Some of it is not great, but I wanted to get things out rather than wait­ing for them to be per­fect.

I would hope this entire post is error free, but it is pretty long, so it seems reas­on­able there will be a mis­take or two I haven't caught some­where. If you find any errors, par­tic­u­larly in the act­ive trans­itions, please let me know ASAP. If you can sug­gest what should be there, all the bet­ter.

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