# alias: Lebensohl2
# button-text: Lebensohl2
# scenario-title: --- Lebensohl2
# gib-works: true
# bba-works: true
# auction-filter: Auction.....\n1N +2[DHS].*(2[HS]|2NT|3[CDHSN])
# convention-card-ns: 21GF-SPECIALS
# convention-card-ew: 21GF-GIB
/*@chat
--- Lebensohl
After we open 1N and RHO overcalls 2!D, 2!H, or 2!S...
• A suit at the 2-level is natural and not forcing.
• 2N is a relay to 3!C and after the opener's 3!C bid...
◦ Pass to play 3!C.
◦ A new lower-ranking suit is to play.
◦ A cue bid is Stayman WITH A STOP.
◦ A new higher-ranking suit is constructive.
◦ 3N is to play WITH A STOP.
• A new suit at the 3-level is game-forcing.
• A cue bid is Stayman WITHOUT a stop.
• 3N is natural, WITHOUT a STOP -- opener should pass or scramble.
https://www.larryco.com/bridge-articles/lebensohl
https://www.larryco.com/bridge-articles/transfer-lebensohl
@chat*/

# Lebensohl
dealer south

# South opens 1N, Robot style
sOpens = hcp(south)>14 and hcp(south)<18 and shape(south,any 4333 +any 4432 +any 5332 -5xxx-x5xx)

# Good Suits West -- QJT or better
GSW = top4(west,spades)>1 and top5(west,spades)>2 and spades(west)>3
GHW = top4(west,hearts)>1 and top5(west,hearts)>2 and hearts(west)>3
GDW = top4(west,diamonds)>1 and top5(west,diamonds)>2 and diamonds(west)>3
GCW = top4(west,clubs)>1 and top5(west,clubs)>2 and clubs(west)>3

wStrong = hcp(west)>15
w2Suit = (GSW + GHW + GDW + GCW)==2 and shape(west,any 64xx+any 55xx+any 54xx) and hcp(west)>8 and hcp(west)<16
w1Suit = (GSW or GHW or GDW or GCW) and shape(west,any 7xxx+any 6xxx+any 5xxx) and hcp(west)>8 and hcp(west)<16 and not w2Suit

wCompetes = (wStrong or w2Suit or w1Suit)

# Good Suits North -- 5+ to the QJT or better
GSN = top5(north,spades)>2 and shape(north,6xxx+5xxx+any 1xxx+any 0xxx)
GHN = top5(north,hearts)>2 and shape(north,x6xx+x5xx+any 1xxx+any 0xxx)
GDN = top5(north,diamonds)>2 and shape(north,xx6x+xx5x+any 1xxx+any 0xxx)
GCN = top5(north,clubs)>2 and shape(north,xxx6+xxx5+any 1xxx+any 0xxx)

n0Suit = shape(north,any 4432+any 4333+any 4441) and hcp(north)>9
n1Suit = (GSN or GHN or GDN or GCN) and hcp(north)>8
nForces = (n0Suit or n1Suit)

# ---------------------------------------------------------------------------
# North's Lebensohl branches -- one per bullet of the convention description.
# NOTE ON CONSUMERS: BBA bids the direct branches but never uses 2NT as a weak
# relay (0 of 136 tested weak auctions; in the strong pool its 2NT always runs
# on to 3NT). The relay branches therefore serve the dealer script -- players
# generating hands and bidding them themselves -- and are dropped downstream by
# the auction filter, so the bba-filtered lesson/quiz pool stays honest.
# ---------------------------------------------------------------------------
# West's presumed overcall suit. The auction filter admits only 2D/2H/2S, so
# clubs never appears; a 2-suiter is attributed to its longer good suit.
wOvS = GSW and spades(west)>=hearts(west) and spades(west)>=diamonds(west)
wOvH = GHW and not wOvS and hearts(west)>=diamonds(west)
wOvD = GDW and not (wOvS or wOvH)

# Stopper in West's suit -- GIB's definition: A, QJx, 5+ hcp, or length+hcp >= 7
nStpD = hcp(north,diamonds)>4 or diamonds(north)+hcp(north,diamonds)>5
nStpH = hcp(north,hearts)>4 or hearts(north)+hcp(north,hearts)>5
nStpS = hcp(north,spades)>4 or spades(north)+hcp(north,spades)>5
nStop = (wOvD and nStpD) or (wOvH and nStpH) or (wOvS and nStpS)

# Strength bands opposite a 15-17 notrump
nWeakHcp = hcp(north)<8
nInvHcp = hcp(north)>7 and hcp(north)<10
nGFHcp = hcp(north)>9

nLongS = spades(north)>4
nLongH = hearts(north)>4
nLongD = diamonds(north)>4
nLongC = clubs(north)>4

# 1/2 -- weak with a long suit. Above the overcall it is bid naturally at the
# 2 level; below it, the 2NT relay is the only way to reach it (a long club
# suit is reached by passing the 3!C relay).
nWeakAbove = nWeakHcp and ((wOvD and (nLongH or nLongS)) or (wOvH and nLongS))
nWeakBelow = nWeakHcp and ((wOvH and nLongD) or (wOvS and (nLongD or nLongH)) or nLongC)

# 3 -- invitational with a 5-card major ranking above the overcall
nInvite = nInvHcp and ((nLongS and (wOvD or wOvH)) or (nLongH and wOvD))

# 4 -- game force with a 5-card major, bid at the 3 level
nGF5M = nGFHcp and ((nLongS and not wOvS) or (nLongH and not wOvH))

# 5/6 -- Stayman: game-going with a 4-card major and no 5-card major.
# Slow (2NT then the cue) shows a stopper, fast (direct cue) denies one.
nStayShape = (wOvD and (hearts(north)>3 or spades(north)>3)) or (wOvH and spades(north)>3) or (wOvS and hearts(north)>3)
nStayman = nGFHcp and nStayShape and spades(north)<5 and hearts(north)<5
nStayStop = nStayman and nStop
nStayNoStop = nStayman and not nStop

# 7/8 -- straight to notrump: game-going, no 4-card major.
# Slow (2NT then 3NT) shows a stopper, fast (direct 3NT) denies one.
n3NTish = nGFHcp and spades(north)<4 and hearts(north)<4
n3NTStop = n3NTish and nStop
n3NTNoStop = n3NTish and not nStop

nAnyBranch = (nWeakAbove or nWeakBelow or nInvite or nGF5M or nStayStop or nStayNoStop or n3NTStop or n3NTNoStop)

# Imported Leveling Code
c1 = hascard(west,2C)
c2 = hascard(east,2D)
c3 = hascard(west,3C)
c4 = hascard(east,3D)

keep06 = c1 and c2 // this is used later w/c3 & c4 expressions
keep44 = c3 or c4 // this is used later w/c1 & c2 expressions

keep015 = keep06 and c3
keep03 = keep06 and keep44
keep045 = keep06 and not c3
# ####6 = c1 and c2
keep11 = c1 and keep44
keep14 = c1 and not keep44
keep19 = c1 and not c2
keep25 = c1
keep30 = keep06 or c3
keep33 = c1 or (c2 and keep44)
# ####44 = c3 or c4
keep47 = keep44 or keep06

keep53 = not keep47
keep56 = not keep44
keep67 = not keep33
keep70 = not keep30
keep75 = not keep25
keep81 = not keep19
keep86 = not keep14
keep89 = not keep11
keep94 = not keep06
keep955 = not keep045
keep97 = not keep03
keep985 = not keep015
keep = 1
keep0 = 0

# End of Imported Leveling Code
# Reduce West's 1-suited hands
levStrong = wStrong and keep
lev1Suit = w1Suit and keep03
lev2Suit = w2Suit and keep
levelTheDeal = (levStrong or lev2Suit or lev1Suit)

# Level the eight branches. Their natural rates span 100:1 -- the weak long-suit
# hands are common, while a game-going North holding a stopper in West's own
# good suit is the rarest thing on the table.
# These gates are built from South's low cards, NOT from script/Leveling's
# keep* values. Those are built from West/East cards and are already spent on
# West's hand types; reusing them couples the two dimensions and skews both.
r1 = hascard(south,2C)
r2 = hascard(south,2D)
r3 = hascard(south,2H)
r4 = hascard(south,2S)

nk75 = not r1 // 75%
nk32 = not (r1 or r2 or r3 or r4) // 32%
nk25 = r1 // 25%
nk05 = r1 and r2 and not r3 // 4.7%
nk03 = r1 and r2 and (r3 or r4) // 2.7%

// Gates chosen by measuring every branch x gate pair on the ungated pool and
// picking, per branch, the gate landing nearest a common rate. Natural rates
// span 116:1 (weak-below 23.3%, 3NT-with-stopper 0.20%); this brings the eight
// branches to roughly 2:1. 3NT-with-stopper is the scarcest and so runs
// ungated -- it sets the ceiling every other branch is levelled down to.
levWeakAbove = nWeakAbove and nk05
levWeakBelow = nWeakBelow and nk03
levInvite = nInvite and nk25
levGF5M = nGF5M and nk25
levStayStop = nStayStop and nk75
levStayNoStop = nStayNoStop and nk32
lev3NTStop = n3NTStop and keep
lev3NTNoStop = n3NTNoStop and nk32

levelNorth = (levWeakAbove or levWeakBelow or levInvite or levGF5M
or levStayStop or levStayNoStop or lev3NTStop or lev3NTNoStop)

# Now do it
sOpens and wCompetes and levelNorth
and levelTheDeal

action printoneline,
average "South HCP " hcp(south),
average "North HCP " hcp(north),
average "North Balanced " 100 * n0Suit,
average "North 1 Suit " 100 * n1Suit,
average "West Strong " 100 * wStrong,
average "West 2-Suited " 100 * w2Suit,
average "West 1-Suited " 100 * w1Suit,
average "b1 weak above " 100 * nWeakAbove,
average "b2 weak below " 100 * nWeakBelow,
average "b3 invitational" 100 * nInvite,
average "b4 GF 5cM " 100 * nGF5M,
average "b5 Stayman stop" 100 * nStayStop,
average "b6 Stayman none" 100 * nStayNoStop,
average "b7 3NT stop " 100 * n3NTStop,
average "b8 3NT none " 100 * n3NTNoStop,
average "any branch " 100 * nAnyBranch,