AXMAS

[Xlambda]

AXMAS , AX two Xmas's trees design.
AX is a "tree" that is already decorated, does not call any other lambda. The ornaments are embedded in the function.
AXMAS is an undecorated one. We can choose our own ornaments array "or". Call AFLAT.
AFLAT , flattens the ornament array, and gives us the versatility to deal with arrays of any shape, size, dimensions, with blanks/null strings, ranges, or other array formulas.
Both designs, randomly, change the display of ornaments every time spreadsheet recalculates, or if we hit F9.
Both lambdas share same concept design, creating a Xmas tree shape, a "triangular" array that can be filled with random values.
A triangular array is like designing a symmetric staircase, it has stairs or steps, and has 2 input parameters "ht", the approximate total height, and "sh", each stair height. Each stair width or depth is by default 1. Knowing these parameters, the function knows how to calculate nr. of steps, exact total height to accommodate nr. of steps and total width footprint of the "staircase".
Both lambdas share same ornament topper (2 parts), and same tree base, (last row) where presents boxes are placed. First variables after LET.
AXMAS(ht,sh,or)

=LAMBDA(ht,sh,or,
     LET(t,UNICHAR(11088),i,UNICHAR(9618),p,UNICHAR(127873),
        o,AFLAT(or),n,ROWS(o),h,MAX(9,ht),s,MAX(3,sh),ns,ROUNDUP(h/s,0),y,ns*s+1,x,2*ns-1,r,SEQUENCE(y),c,ABS(SEQUENCE(,x)-ns),
        a,QUOTIENT(r-1,s)>=c,b,INDEX(o,RANDARRAY(y,x,1,n,1)*a),w,SWITCH(r,1,t,2,i,y,IF(c<ns-2,p,""),b),
       IF(a,w,"")
    )
)

AX(ht,sh)

=LAMBDA(ht,sh,
    LET(t,UNICHAR(11088),i,UNICHAR(9618),p,UNICHAR(127873),q,SEQUENCE(44,,10035),o,UNICHAR(IF(q>10058,q+117698,q)),
        n,44,h,MAX(9,ht),s,MAX(3,sh),ns,ROUNDUP(h/s,0),y,ns*s+1,x,2*ns-1,r,SEQUENCE(y),c,ABS(SEQUENCE(,x)-ns),
        a,QUOTIENT(r-1,s)>=c,b,INDEX(o,RANDARRAY(y,x,1,n,1)*a),w,SWITCH(r,1,t,2,i,y,IF(c<ns-2,p,""),b),
        IF(a,w,"")
    )
)

AXMAS.xlsx
	A	B	C	D	E	F	G	H	I	J	K	L	M	N	O	P	Q	R	S	T	U	V	W	X	Y	Z	AA	AB	AC	AD	AE	AF	AG	AH	AI	AJ	AK	AL	AM	AN	AO	AP	AQ	AR	AS
1	AXMAS(ht,sh,or)																							ornaments array sample
2	ht: approx.. height; if ht ignored or <9 => ht=9, (min tree height=9)																							❀	❁	❂	❃	❅	❆	?	?	✿	✽	✾
3	sh: each "step" height; if ignored or <3 =>sh=3 (3 min."stair" height=3 )																								smallest tree								ht,15,sh,4
4	or: ornaments array, any array, any shape, any values																								ht,,sh,,(ignored)								=AXMAS(15,4,X2:AH2)
5	Increasing sh value makes triangle's top angle smaller, (higher tree "slope")																								=AXMAS(,,X2:AH2)											⭐
6	For better visual experience, change the grids width to tiny squares, all centered aligned.																										⭐									▒
7	Predetermined ornaments, topper, 2 parts, tree base,present boxes.																										▒									✿
8	If you want to change them, just after LET, variables t,i,p																										?									❁
9																										❅	❃	❀							✽	❅	✽
10	11088	⭐	topper 1																							❃	❆	?							?	?	?
11	9618	▒	topper 2																							❃	❆	❅							✽	✽	❀
12	127873	?	base																						✽	?	❂	✿	❂						❅	❀	❅
13																									❂	✽	❅	✾	❁					✾	❀	❆	✿	✾
14	Ornaments array values used by these trees in next post.																								?	✾	✾	❀	❀					❆	❁	❆	❆	✿
15	Note: Ornaments shape, color, can look different on your spreadsheet.																										?							?	❅	❂	❀	❃
16																																		✿	?	❂	❂	❃
17		ht,30,sh,4																															❀	✾	❀	?	❁	❅	❅
18		=AXMAS(30,4,BH17:CU20)																															❃	?	❃	❃	❃	✿	✽
19									⭐											ht,20,sh,,													❆	✾	?	❃	✿	❀	❃
20									▒											=AXMAS(20,,BH17:CU20)													❂	✽	✽	❂	❅	❃	✿
21									⏬																	⭐									?	?	?
22									?																	▒
23								?	?	?																?
24								?	?	?															?	?	♕							ornaments array as numbers
25								⏬	?	?															?	✼	?								=AXMAS(13,4,SEQUENCE(9))
26								?	?	?															?	?	?											⭐
27							?	?	?	❀	?													?	?	?	?	?										▒
28							✷	?	?	?	?													?	?	?	?	?										5
29							?	?	?	?	?													⚽	?	?	?	?										3
30							❊	❇	?	❉	?												?	?	?	?	❄	?	?								6	4	1
31						✻	?	?	?	✅	?	?											?	?	⏪	?	⭕	?	?								6	5	2
32						?	?	?	⭕	?	⚓	?											?	?	✺	?	?	?	✴								3	9	7
33						?	?	?	?	❌	?	?										?	?	?	?	❎	?	?	❄	?							2	5	4
34						?	⏩	✼	?	⭕	✴	?										?	?	?	❈	?	?	?	?	?						4	6	9	4	4
35					?	?	?	?	?	❇	?	?	?									?	⭕	✻	?	❆	?	✻	?	?						5	3	6	3	7
36					✺	⏩	❂	?	⛄	?	?	✺	?								?	?	?	?	?	?	?	?	?	⚡	⚡					5	3	2	3	9
37					?	?	?	?	?	⚓	?	?	?								❈	?	?	?	?	✿	?	✾	?	❂	?					2	8	2	2	8
38					?	?	?	✸	?	?	?	✿	?								?	?	?	?	❁	?	?	?	❁	?	?				2	7	7	3	4	8	4
39				?	❉	?	?	?	?	?	✿	?	♕	❉						?	?	❎	?	?	✶	?	?	?	⏩	?	?	❀			1	3	9	7	6	9	5
40				?	?	?	?	?	?	?	?	?	?	?						✻	?	?	?	?	❂	?	?	?	❉	?	?	❂			6	1	9	6	1	8	2
41				?	✼	?	?	❅	❈	?	❃	✅	✅	?						❆	✹	⚓	?	?	⭐	⏬	❊	?	?	?	⚡	?			6	2	1	4	9	8	3
42				?	?	?	?	?	?	?	?	?	?	?								?	?	?	?	?	?	?	?	?							?	?	?
43			?	?	?	?	✅	?	?	?	⛄	?	?	?	?
44			?	?	?	❄	?	?	❄	?	✼	⏬	?	?	?																			Note: This values can be used with CF
45			?	?	?	?	?	?	?	?	?	?	?	♔	❅
46			?	?	❊	?	?	?	?	?	?	?	?	❀	?
47		?	?	?	?	?	?	?	?	?	?	?	?	?	?	⚡
48		?	?	⚽	?	?	?	?	?	?	✾	?	❊	?	?	?
49		?	?	✵	✵	?	?	?	❊	?	❃	?	?	?	?	?
50		?	✶	?	?	✻	?	?	?	?	?	❈	?	?	?	?
51				?	?	?	?	?	?	?	?	?	?	?
52
AXMAS 1

Cell Formulas
Range	Formula
AG4,AI25,T20,B18,Y5	AG4	=FORMULATEXT(AG5)
AG5:AM21	AG5	=AXMAS(15,4,X2:AH2)
Y6:AC15	Y6	=AXMAS(,,X2:AH2)
B10:B12	B10	=UNICHAR(A10:A12)
B19:P51	B19	=AXMAS(30,4,BH17:CU20)
T21:AF42	T21	=AXMAS(20,,BH17:CU20)
AI26:AO42	AI26	=AXMAS(13,4,SEQUENCE(9))
Dynamic array formulas.

 

[Xlambda]

Simulating Slot machine, mechanical, with Form Controls.
To be able to see the form controls, also inserted a screen capture.

AXMAS.xlsx
	A	B	C	D	E	F	G	H	I	J	K	L	M	N	O	P	Q	R
1
2
3		Simulating Slot machine, mechanical, with Form Controls. (can be done with 3 or 5 reels)
4
5									=IF(AND(NOT(N11),N10=1),INDEX($D$7#,,1),I9#)
6		reel array		=ASLOT(B7:B19,,3)					↓	=IF(AND(NOT(O11),N10=1),INDEX($D$7#,,2),J9#)
7		?		?	?	?			↓	↓	=IF(AND(NOT(P11),N10=1),INDEX($D$7#,,3),K9#)
8		?		?	BAR	?			↓	↓	↓
9		?		?	?	?			?	?	?			cell link option buttons form control
10		?							?	?	?			1
11		?							?	?	?			TRUE	TRUE	FALSE
12		?										↑		cell links check box form control
13		?							↑	↑	↑	↑
14		?						block reel from spinning				↑	slot machine lever
15		?
16		?
17		?
18		?
19		BAR
20
ASLOT 3

Cell Formulas
Range	Formula
I5	I5	=FORMULATEXT(I9)
D6	D6	=FORMULATEXT(D7)
J6	J6	=FORMULATEXT(J9)
D7:F9	D7	=ASLOT(B7:B19,,3)
K7	K7	=FORMULATEXT(K9)
I9:I11	I9	=IF(AND(NOT(N11),N10=1),INDEX($D$7#,,1),I9#)
J9:J11	J9	=IF(AND(NOT(O11),N10=1),INDEX($D$7#,,2),J9#)
K9:K11	K9	=IF(AND(NOT(P11),N10=1),INDEX($D$7#,,3),K9#)
Dynamic array formulas.

 

[Xlambda]

Digital or virtual slot machine with a deck of cards. Poker slot machine. Mechanical vs digital.

AXMAS.xlsx
	A	B	C	D	E	F	G	H	I	J	K	L	M	N	O	P	Q	R	S	T	U	V	W
1	Slot machine (mechanical or digitalized) with a deck of cards. Can we simulate dealing poker hands?
2	reel, deck of cards in order
3	=ADECK(1)		- using ASLOT (mechanical)
4	2♠		As we see does not make a lot of sense when the cards are in order.
5	2♣		Vertically order is kept whatever we use as reels, ADECK(1) or ADECK(), horizontally, 2 or more reels can be aligned,
6	2♥		meaning there will be lines with dups, fact that is not acurate with simulating dealing hands in a poker game
7	2♦
8	3♠		all reels unfolded						cheking for dups "byrow" , if values <5 we have dups
9	3♣		=ASLOT(ADECK(1),5)						=BYROW(C10#,LAMBDA(a,COUNTA(UNIQUE(a,1))))
10	3♥		Q♦	Q♠	7♠	6♥	7♠		4
11	3♦		K♠	Q♣	7♣	6♦	7♣		4		- using ANDECK (digital, no mechanical reels possible)
12	4♠		K♣	Q♥	7♥	7♠	7♥		4		The only way to simulate poker hands slot machine is to
13	4♣		K♥	Q♦	7♦	7♣	7♦		4		digitalize it with ANDECK using a single deck of cards, to be sure
14	4♥		K♦	K♠	8♠	7♥	8♠		4		will not have dups
15	4♦		2♠	K♣	8♣	7♦	8♣		4
16	5♠		2♣	K♥	8♥	8♠	8♥		4		all rounds for single deck						digital poker slot machine with a 3x5 "window"
17	5♣		2♥	K♦	8♦	8♣	8♦		4		=ANDECK(1,5)						=INDEX(K18#,SEQUENCE(3),SEQUENCE(,5))
18	5♥		2♦	2♠	9♠	8♥	9♠		4		6♥	7♣	3♣	A♦	10♥		6♥	7♣	3♣	A♦	10♥
19	5♦		3♠	2♣	9♣	8♦	9♣		4		7♠	9♠	5♠	2♠	3♠		7♠	9♠	5♠	2♠	3♠
20	6♠		3♣	2♥	9♥	9♠	9♥		4		2♥	2♣	K♦	5♣	J♦		2♥	2♣	K♦	5♣	J♦
21	6♣		3♥	2♦	9♦	9♣	9♦		4		6♦	K♠	8♠	8♥	10♠
22	6♥		3♦	3♠	10♠	9♥	10♠		4		9♦	10♦	6♣	J♠	Q♥		or
23	6♦		4♠	3♣	10♣	9♦	10♣		4		Q♠	9♥	A♥	7♦	Q♣
24	7♠		4♣	3♥	10♥	10♠	10♥		4		K♥	6♠	J♥	9♣	4♠		=ANDECK(1,5,3)
25	7♣		4♥	3♦	10♦	10♣	10♦		4		7♥	8♦	5♦	8♣	A♠		8♠	7♠	10♥	K♠	8♣
26	7♥		4♦	4♠	A♠	10♥	A♠		4		4♦	10♣	K♣	3♥	A♣		8♦	4♥	3♣	A♥	3♦
27	7♦		5♠	4♣	A♣	10♦	A♣		4		4♣	Q♦	5♥	3♦	2♦		6♥	5♠	Q♥	4♦	4♣
28	8♠		5♣	4♥	A♥	A♠	A♥		4		4♥	J♣
29	8♣		5♥	4♦	A♦	A♣	A♦		4								hit F9 to "spin"
30	8♥		5♦	5♠	J♠	A♥	J♠		4
31	8♦		6♠	5♣	J♣	A♦	J♣		4
32	9♠		6♣	5♥	J♥	J♠	J♥		4
33	9♣		6♥	5♦	J♦	J♣	J♦		4
34	9♥		6♦	6♠	Q♠	J♥	Q♠		4
35	9♦		7♠	6♣	Q♣	J♦	Q♣		4
36	10♠		7♣	6♥	Q♥	Q♠	Q♥		4
37	10♣		7♥	6♦	Q♦	Q♣	Q♦		4
38	10♥		7♦	7♠	K♠	Q♥	K♠		4
39	10♦		8♠	7♣	K♣	Q♦	K♣		4
40	A♠		8♣	7♥	K♥	K♠	K♥		4
41	A♣		8♥	7♦	K♦	K♣	K♦		4
42	A♥		8♦	8♠	2♠	K♥	2♠		4
43	A♦		9♠	8♣	2♣	K♦	2♣		4
44	J♠		9♣	8♥	2♥	2♠	2♥		4
45	J♣		9♥	8♦	2♦	2♣	2♦		4
46	J♥		9♦	9♠	3♠	2♥	3♠		4
47	J♦		10♠	9♣	3♣	2♦	3♣		4
48	Q♠		10♣	9♥	3♥	3♠	3♥		4
49	Q♣		10♥	9♦	3♦	3♣	3♦		4
50	Q♥		10♦	10♠	4♠	3♥	4♠		4
51	Q♦		A♠	10♣	4♣	3♦	4♣		4
52	K♠		A♣	10♥	4♥	4♠	4♥		4
53	K♣		A♥	10♦	4♦	4♣	4♦		4
54	K♥		A♦	A♠	5♠	4♥	5♠		4
55	K♦		J♠	A♣	5♣	4♦	5♣		4
56			J♣	A♥	5♥	5♠	5♥		4
57			J♥	A♦	5♦	5♣	5♦		4
58			J♦	J♠	6♠	5♥	6♠		4
59			Q♠	J♣	6♣	5♦	6♣		4
60			Q♣	J♥	6♥	6♠	6♥		4
61			Q♥	J♦	6♦	6♣	6♦		4
62
ASLOT 4

Cell Formulas
Range	Formula
A3,Q24,Q17,K17,I9,C9	A3	=FORMULATEXT(A4)
A4:A55	A4	=ADECK(1)
C10:G61	C10	=ASLOT(ADECK(1),5)
I10:I61	I10	=BYROW(C10#,LAMBDA(a,COUNTA(UNIQUE(a,1))))
K18:O28	K18	=ANDECK(1,5)
Q18:U20	Q18	=INDEX(K18#,SEQUENCE(3),SEQUENCE(,5))
Q25:U27	Q25	=ANDECK(1,5,3)
Dynamic array formulas.

 

[Xlambda]

Simulating a poker digital slot machine makes sense to also cover poker hands rankings (PHR).
PHR: straight flush (royal flush when 10-A same suit), 4 of a kind, full house, flush, straight, 3 of a kind, 2 pairs, 1 pair, high card (I will consider it as "nothing"). See attached picture.
Came out with PHR, Poker Hand Rankings function.
PHR(a,[t]): arguments and functionality:
a: array of n rows x 5 clms, each row representing an accurate poker hand (no dups)
[t]: type argument
- t, 0 or omitted, total occurrences of each rank for whole array of hands "a" => result array 10x1 array (10 ranks)
- t,1 rank of each row (hand, round) => result array rows(a)x1
- t,2 => array result 10x2, 1st clm rank names, 2nd clm ranking occurrences of "a"
- t,3 ranking names only => 10x1
Only one thing about the concept, main trick for checking all possibilities was using the arguments functionality of UNIQUE function "by_col" and "exactly_once".

=LAMBDA(a,[t],
    LET(k,{"rf";"sf";"4k";"fh";"f";"s";"3k";"2p";"1p";"n"},IF(t=3,k,
       LET(b,BYROW(a,LAMBDA(r,LET(f,COUNTA(UNIQUE(RIGHT(r,1),1))=1,k,LEFT(r,LEN(r)-1),v,SWITCH(k,"A",14,"K",13,"Q",12,"J",11,--k),
         x,MAX(v)=14,q,SORT(v-MIN(v)+1,,,1),s,AND(q=SEQUENCE(,5)),u,COUNT(UNIQUE(q,1)),o,UNIQUE(q,1,1),n,IF(AND(ISERR(o)),0,COUNT(o)),
         SWITCH(n,0,"fh",3,"1p",2,"3k",1,IF(u=2,"4k","2p"),5,IF(s,IF(f,IF(x,"rf","sf"),"s"),IF(f,"f","n")))))),p,MAP(k,LAMBDA(a,SUM(--(a=b)))),
      SWITCH(t,0,p,1,b,2,IF({1,0},k,p))))
   )
)

AXMAS.xlsx
	A	B	C	D	E	F	G	H	I	J	K	L	M	N	O	P	Q	R	S	T	U	V	W	X	Y	Z	AA	AB
1	Poker Hand Ranking, PHR function															t,1				t,omitted			t,2
2										sample						ranking/hand		t,3 ranking names		all ranking ocurrences in "a"			array ranking names and their occurrence in "a"
3		ranking	name	examples										a		=PHR(J4:N22,1)		=PHR(D4:H13,3)		=PHR(J4:N22)			=PHR(J4:N22,2)
4		royal flush	rf	10♣	J♣	Q♣	K♣	A♣		10♣	A♣	J♣	Q♣	K♣		rf		rf		1			rf	1
5		straight flush	sf	2♥	3♥	4♥	5♥	6♥		5♥	6♥	7♥	8♥	9♥		sf		sf		2			sf	2
6		4 of a kind	4k	9♠	9♥	9♣	9♦	Q♥		2♠	3♠	4♠	5♠	6♠		sf		4k		2			4k	2
7		full house	fh	A♠	A♥	A♦	J♠	J♦		K♠	K♣	K♥	K♦	8♣		4k		fh		2			fh	2
8		flush	f	2♠	4♠	5♠	6♠	7♠		10♣	9♥	10♠	10♥	10♦		4k		f		2			f	2
9		straight	s	4♦	5♣	6♦	7♣	8♥		J♣	7♣	7♦	7♥	J♥		fh		s		2			s	2
10		3 of a kind	3k	10♠	10♥	10♦	3♣	2♦		5♥	A♥	3♥	Q♥	9♥		f		3k		2			3k	2
11		2 pair	2p	K♠	K♥	Q♠	Q♦	3♠		4♣	10♣	Q♣	7♣	J♣		f		2p		2			2p	2
12		1 pair	1p	8♦	8♠	6♣	3♦	J♥		7♠	8♥	9♦	10♠	J♦		s		1p		2			1p	2
13		nothing	n	K♦	8♣	4♣	5♦	7♥		6♠	8♠	7♥	10♣	9♦		s		n		2			n	2
14										K♠	3♦	K♣	3♥	K♥		fh
15										Q♦	8♦	5♣	Q♥	Q♠		3k
16										10♥	10♣	2♦	A♣	10♦		3k
17										A♥	6♦	J♠	A♦	J♣		2p
18				To simulate dealing a shuffled						2♣	Q♣	Q♥	10♠	2♥		2p
19				deck of cards, 5 cards/round						K♥	6♥	K♣	4♥	A♣		1p
20				we can use ANDECK(1,5)						3♣	5♦	3♥	9♠	7♦		1p
21				To eliminate last row of 2 cards						10♥	9♠	J♠	5♦	Q♠		n
22				we can extract only 10 rounds						8♦	5♣	6♥	3♣	K♥		n
23				with:
24										ranking/hand(round)				distribution/whole deck
25				=ANDECK(1,5,10)				a		=PHR(D26#,1)				=PHR(D26#,2)
26				3♣	K♠	10♠	3♠	7♦		1p				rf	0
27				J♠	Q♣	Q♦	3♦	3♥		2p				sf	0
28				2♠	9♠	A♥	9♦	2♥		2p				4k	0
29				8♦	2♣	K♦	5♦	4♦		n				fh	0
30				8♠	5♥	A♠	10♣	K♣		n				f	0
31				6♣	J♥	2♦	7♥	9♣		n				s	0
32				7♠	5♣	7♣	6♥	Q♠		1p				3k	0
33				9♥	4♥	A♣	8♣	J♦		n				2p	2
34				10♥	4♠	J♣	A♦	8♥		n				1p	3
35				Q♥	K♥	6♦	10♦	6♠		1p				n	5
36
PHR 1

Cell Formulas
Range	Formula
P3,R3,T3,N25,J25,D25,W3	P3	=FORMULATEXT(P4)
P4:P22	P4	=PHR(J4:N22,1)
R4:R13	R4	=PHR(D4:H13,3)
T4:T13	T4	=PHR(J4:N22)
W4:X13	W4	=PHR(J4:N22,2)
D26:H35	D26	=ANDECK(1,5,10)
J26:J35	J26	=PHR(D26#,1)
N26:O35	N26	=PHR(D26#,2)
Dynamic array formulas.

 

[Xlambda]

AXMAS.xlsx
	A	B	C	D	E	F	G	H	I	J	K	L	M	N	O	P	Q
1	PHR for more decks (5). Cumulative stats of rankings distribution
2	To be sure that no hands(rounds) can have duplicates we need to create a stack of single decks shuffled randomly.
3											rankings
4									rankings/round		distribution/all 5 decks			distribution values only
5									=PHR(C6:G55,1)		=PHR(C6:G55,2)			=PHR(C6:G55)
6	deck 1	=ANDECK(1,5,10)	8♦	2♣	3♥	Q♥	5♣		n		rf	0		0
7			Q♠	7♠	10♥	4♣	10♠		1p		sf	0		0
8			A♥	2♥	8♣	5♠	A♣		1p		4k	0		0
9			10♣	7♥	K♠	3♦	7♦		1p		fh	0		0
10			A♠	4♠	6♥	K♥	J♥		n		f	0		0
11			5♦	7♣	J♣	Q♣	2♠		n		s	1		1
12			K♣	4♥	2♦	3♣	10♦		n		3k	0		0
13			5♥	J♦	9♠	Q♦	9♣		1p		2p	1		1
14			6♠	3♠	9♥	4♦	8♥		n		1p	25		25
15			8♠	K♦	J♠	A♦	6♣		n		n	23		23
16	deck 2	=ANDECK(1,5,10)	8♠	A♥	8♦	4♠	5♦		1p
17			3♥	6♦	7♦	Q♣	5♠		n
18			J♣	9♠	9♦	7♥	4♣		1p
19			4♥	4♦	9♥	6♠	2♥		1p
20			K♦	K♠	3♦	J♠	9♣		1p
21			8♥	3♣	3♠	2♣	Q♠		1p
22			A♣	A♠	K♥	2♠	7♠		1p
23			5♥	10♥	10♠	8♣	6♣		1p
24			10♦	2♦	J♦	Q♦	7♣		n
25			5♣	10♣	A♦	K♣	J♥		n
26	deck 3	=ANDECK(1,5,10)	Q♣	J♥	5♣	A♣	10♠		n
27			7♣	J♠	8♥	K♦	5♥		n
28			6♦	J♦	8♣	10♣	2♣		n
29			2♦	4♠	A♠	4♣	3♥		1p
30			5♦	7♠	9♠	8♠	6♥		s
31			4♥	9♣	Q♦	7♥	3♦		n
32			K♠	10♥	9♥	2♥	A♦		n
33			K♥	7♦	6♠	Q♠	J♣		n
34			6♣	A♥	2♠	10♦	8♦		n
35			K♣	4♦	3♣	3♠	Q♥		1p
36	deck 4	=ANDECK(1,5,10)	10♥	10♠	3♥	7♣	J♦		1p
37			6♣	K♣	2♠	6♠	A♣		1p
38			A♥	8♦	4♦	10♣	5♣		n
39			8♠	9♥	3♣	6♦	10♦		n
40			9♣	9♦	K♠	Q♠	A♠		1p
41			5♦	3♦	9♠	Q♦	K♦		n
42			Q♣	Q♥	7♥	4♠	J♥		1p
43			5♥	7♠	J♣	K♥	4♥		n
44			8♣	A♦	8♥	2♥	4♣		1p
45			2♦	6♥	7♦	2♣	3♠		1p
46	deck 5	=ANDECK(1,5,10)	K♦	A♥	K♠	4♣	J♠		1p
47			2♦	3♣	2♥	3♥	4♥		2p
48			9♦	2♣	A♠	7♥	5♠		n
49			8♦	Q♦	10♦	2♠	Q♣		1p
50			6♥	J♣	5♦	8♥	A♦		n
51			5♥	10♠	7♠	5♣	6♠		1p
52			6♣	6♦	3♠	Q♠	4♠		1p
53			9♠	7♣	K♣	4♦	A♣		n
54			J♦	10♥	9♣	10♣	Q♥		1p
55			8♠	3♦	8♣	9♥	7♦		1p
56
PHR 2

Cell Formulas
Range	Formula
I5,K5,N5	I5	=FORMULATEXT(I6)
B6,B46,B36,B26,B16	B6	=FORMULATEXT(C6)
C6:G55	C6	=ANDECK(1,5,10)
I6:I55	I6	=PHR(C6:G55,1)
K6:L15	K6	=PHR(C6:G55,2)
N6:N15	N6	=PHR(C6:G55)
Dynamic array formulas.

 

[Xlambda]

Noticed that creating a big stack of shuffled decks, and hitting F9 a considerable number of times, the higher rankings like royal flush and straight flush, did not register occurrences. How many virtual decks we must shuffle until will start to get a straight flush or even a royal flush? This will represent one of many ways we can evaluate the "performance" of the randomizing "engine" in general, with a fun experiment like a virtual deck of cards.
So, why not to "automate" the process and create a virtual "stack" of large nr. of decks and accumulate the results. Here is the function, main engine, mighty REDUCE again:
Note: MAKEARRAY is used here only for cosmetics, the presentation of the result.
NPHR(n): N decks of cards, cumulative Poker Hands Rankings distribution.
n: integer >=1, nr. of virtual decks

=LAMBDA(n,
    LET(k,PHR(1,3),nk,REDUCE(0,SEQUENCE(n),LAMBDA(v,i,LET(d,ANDECK(1,5,10),v+PHR(d)))),
      MAKEARRAY(12,2,LAMBDA(r,c,SWITCH(r,1,IF(c=1,"Decks",n),12,IF(c=1,"Hands",SUM(nk)),IF(c=1,INDEX(k,r-1),INDEX(nk,r-1)))))
    )
)

AXMAS.xlsx
	A	B	C	D	E	F	G	H	I	J	K	L	M	N	O	P	Q	R
1	NPHR(n). The function. Cumulative rankings distribution for "n" decks of cards.
2
3	=NPHR(10)			=NPHR(50)			=NPHR(100)			=NPHR(500)			=NPHR(1000)			=NPHR(5000)
4	Decks	10		Decks	50		Decks	100		Decks	500		Decks	1000		Decks	5000
5	rf	0		rf	0		rf	0		rf	0		rf	0		rf	0
6	sf	0		sf	0		sf	0		sf	0		sf	0		sf	0
7	4k	0		4k	0		4k	0		4k	1		4k	4		4k	9
8	fh	0		fh	1		fh	0		fh	9		fh	10		fh	73
9	f	0		f	1		f	2		f	4		f	20		f	95
10	s	0		s	2		s	5		s	25		s	33		s	213
11	3k	2		3k	7		3k	26		3k	101		3k	230		3k	1052
12	2p	4		2p	30		2p	66		2p	243		2p	496		2p	2285
13	1p	39		1p	205		1p	426		1p	2050		1p	4199		1p	21206
14	n	55		n	254		n	475		n	2567		n	5008		n	25067
15	Hands	100		Hands	500		Hands	1000		Hands	5000		Hands	10000		Hands	50000
16
17
18				After"dealing" 5,000 decks, 50,000 hands, still no "rf" royal flush or "sf" straight flush
19
NPHR 1

Cell Formulas
Range	Formula
A3,P3,M3,J3,G3,D3	A3	=FORMULATEXT(A4)
A4:B15	A4	=NPHR(10)
D4:E15	D4	=NPHR(50)
G4:H15	G4	=NPHR(100)
J4:K15	J4	=NPHR(500)
M4:N15	M4	=NPHR(1000)
P4:Q15	P4	=NPHR(5000)
Dynamic array formulas.

 

[Xlambda]

Let's raise the stakes for up to 200,000 virtual decks or 2,000,000 hands!

AXMAS.xlsx
	A	B	C	D	E	F	G	H	I	J	K	L	M	N	O	P	Q	R
1	For values of n>10000, calculation time takes some time (seconds for 10,000 and for 200,000 decks, or 2M hands close to 3min),
2	so the following data are all copies as values of NPHR function results.
3
4	Decks	10,000		Decks	20,000		Decks	30,000		Decks	40,000		Decks	50,000
5	rf	0		rf	0		rf	0		rf	0		rf	1
6	sf	1		sf	3		sf	4		sf	5		sf	10
7	4k	31		4k	44		4k	63		4k	100		4k	117
8	fh	147		fh	290		fh	428		fh	616		fh	694
9	f	215		f	399		f	573		f	784		f	1017
10	s	378		s	730		s	1055		s	1381		s	1780
11	3k	2083		3k	4280		3k	6287		3k	8459		3k	10670
12	2p	4765		2p	9530		2p	14242		2p	18922		2p	23692
13	1p	42316		1p	84334		1p	126376		1p	168785		1p	211706
14	n	50064		n	100390		n	150972		n	200948		n	250313
15	Hands	100,000		Hands	200,000		Hands	300,000		Hands	400,000		Hands	500,000
16
17
18	Decks	60,000		Decks	70,000		Decks	80,000		Decks	90,000		Decks	100,000		Decks	200,000
19	rf	2		rf	0		rf	1		rf	3		rf	1		rf	6
20	sf	9		sf	10		sf	10		sf	9		sf	18		sf	20
21	4k	135		4k	152		4k	177		4k	216		4k	237		4k	492
22	fh	823		fh	991		fh	1175		fh	1205		fh	1493		fh	2879
23	f	1155		f	1399		f	1486		f	1673		f	1946		f	3909
24	s	2032		s	2444		s	2816		s	3209		s	3438		s	7188
25	3k	12444		3k	14931		3k	16937		3k	19008		3k	21302		3k	42001
26	2p	28602		2p	33158		2p	38251		2p	42801		2p	47251		2p	95213
27	1p	253750		1p	296243		1p	338088		1p	380358		1p	422144		1p	844838
28	n	301048		n	350672		n	401059		n	451518		n	502170		n	1003454
29	Hands	600,000		Hands	700,000		Hands	800,000		Hands	900,000		Hands	1,000,000		Hands	2,000,000
30
31				Notes:
32				- "nothing" occurrences almost half of all hands, all other rankings, the other half
33				- first "sf" for 10,000 decks
34				- first "rf" for 50,000 decks or half million hands
35				- 200,000 or 2,000,000 hands, exceeds physical real estate of a spreadsheet
36
NPHR 2

 

[Xlambda]

Great news!! Remember post #7, this thread? Quote:
"I believe in Santa, Excel's Santa. So, the other day, I wrote him a letter. It was a secret wish, but now I am going to disclose it. I've wished for more recursive iterations."
Check this out, latest MrExcel YT: New Excel Formula Editor Debuts - 2466
Among other nice "gifts" we received the one with "better recursion limits, 16x larger". How cool is that!!!
Thanks Excel Team, excellent work!!!! I think this forum, in the near future, will get its deserved traction. Thanks MrExcel.com team for creating this fabulous leading-edge lambda environment!!!!
(Seems that these gifts were lost in "transportation", that's way they did not get to us sooner) ✌????

 

[Xlambda]

Happy 2022 Holidays All !!
This year Mike was so kind to choose my lambdas as his traditional Xmas tree video.
Check this out. It also has the downloadable workbook link in the description or here
PS: Just seen on previous posts here a lot of ornaments not printed (apear as "?") and I remember they were ok 1 year ago. Something happened. I will check them later.

 

[Xlambda]

XMAS , same like AXMAS, replaced my good old AFLAT to TOCOL
XMAS same arguments as AXMAS

=LAMBDA(ht, sh, or,
    LET(
        t, UNICHAR(11088),
        i, UNICHAR(9618),
        p, UNICHAR(127873),
        o, TOCOL(or),
        n, ROWS(o),
        h, MAX(9, ht),
        s, MAX(3, sh),
        ns, INT(h / s),
        y, ns * s + 1,
        x, 2 * ns - 1,
        r, SEQUENCE(y),
        c, ABS(SEQUENCE(, x) - ns),
        a, QUOTIENT(r - 1, s) >= c,
        b, INDEX(o, RANDARRAY(y, x, 1, n, 1) * a),
        w, SWITCH(r, 1, t, 2, i, y, IF(c < ns - 2, p, ""), b),
        IF(a, w, "")
    )
)

and predefined array of ornaments "storage box" argument free lambda:
AO()

=LAMBDA(LET(q,SEQUENCE(44,,10035),UNICHAR(IF(q>10058,q+117698,q))))

Checking ornaments in mini-sheet, work OK

EIF Xmas Tree 2022.xlsx
	A	B	C	D	E	F	G	H	I	J	K	L	M	N	O	P	Q	R	S	T	U
1
2			=XMAS(28,3,AO())
3											⭐
4											▒
5											🌐
6										🌞	🌚	❄
7										🌕	✾	🌛
8										❇	❇	✾
9									❁	🌕	🌍	✶	🌜
10									🌏	❂	✺	❊	✻
11									❀	✻	❅	🌜	🌠
12								❉	🌕	🌙	🌑	✴	✳	🌍
13								🌗	✽	❇	❃	❈	🌠	❆
14								✾	🌖	🌒	✸	❊	🌝	🌑
15							🌙	✴	🌕	❉	✾	✾	🌠	✷	✸
16							✸	🌒	✿	✷	✾	🌎	🌎	❅	🌕
17							🌙	✳	🌜	❉	✴	🌟	🌙	✺	❃
18						✺	✶	✿	🌔	🌘	🌙	🌏	❄	✾	🌛	🌚
19						🌓	🌞	✽	🌜	🌑	✺	✸	✽	❅	❄	🌝
20						🌙	🌓	🌗	✽	✽	✿	🌓	🌝	✵	✿	🌑
21					🌚	🌙	❈	❈	❆	❁	🌞	🌘	❀	🌕	✷	❅	✽
22					❅	✼	✻	🌛	🌠	🌞	✶	✼	❂	❁	❉	❆	✴
23					✻	✼	❊	✽	🌜	❈	✶	🌕	✹	🌏	🌙	❅	🌏
24				✿	❅	🌒	❉	✴	❈	🌗	✿	❅	🌎	🌝	❄	🌟	✸	✺
25				❃	🌖	✶	❄	✾	✷	❄	🌛	🌗	🌞	✳	🌐	✾	✵	✴
26				✴	🌓	❃	🌠	❁	🌙	🌔	🌛	🌠	🌔	🌎	🌞	✶	🌍	❄
27			🌚	✹	✾	🌐	❇	❂	🌒	❆	❈	✾	✻	✴	🌖	🌓	✵	✽	🌘
28			🌖	🌏	🌘	❄	🌞	✿	🌜	🌙	🌍	✾	❇	❊	🌝	✸	🌝	❉	✽
29			🌠	✿	🌚	❂	✾	❁	✵	🌓	❁	🌘	✶	❄	✷	❅	🌓	🌛	🌏
30					🎁	🎁	🎁	🎁	🎁	🎁	🎁	🎁	🎁	🎁	🎁	🎁	🎁
31
32
Sheet2

Cell Formulas
Range	Formula
C2	C2	=FORMULATEXT(C3)
C3:S30	C3	=XMAS(28,3,AO())
Dynamic array formulas.

 

[Xlambda]

Also, only CF that works (can be displayed in mini-sheet) is Color Scales

EIF Xmas Tree 2022.xlsx
	A	B	C	D	E	F	G	H	I	J	K	L	M	N	O	P	Q	R	S	T	U	V	W	X	Y	Z	AA	AB	AC	AD	AE	AF	AG	AH	AI	AJ	AK	AL	AM	AN	AO	AP	AQ	AR	AS	AT	AU	AV	AW	AX	AY	AZ	BA	BB	BC	BD	BE
1																				CF color scales
2
3		=XMAS(27,,AO())																		=XMAS(27,,SEQUENCE(20))																			=XMAS(27,,SEQUENCE(20))
4										⭐																		⭐																			⭐
5										▒																		▒																			▒
6										❄																																					4
7									✶	🌔	🌑																																			6	14	11
8									🌕	🌙	✷																																			15	10	17
9									❅	✸	🌙																																			12	1	15
10								🌠	🌠	❆	❇	🌐																																	7	5	9	18	2
11								🌏	❅	✴	✵	✽																																	1	3	14	1	3
12								✵	🌐	🌘	🌕	❈																																	12	8	8	12	8
13							🌗	✻	✻	🌚	🌕	🌎	❂																															8	15	3	20	4	10	14
14							❃	🌝	❉	🌎	🌏	✼	❉																															1	14	19	8	12	13	20
15							✶	❁	🌙	🌙	❇	✾	🌗																															2	12	5	14	12	5	5
16						✺	🌖	🌝	✽	🌍	🌑	✴	🌐	🌛																													17	1	10	3	5	12	10	20	13
17						🌖	🌓	❆	🌗	🌗	❉	🌏	🌚	❁																													3	17	9	14	7	3	12	12	11
18						🌏	🌚	✹	🌕	✻	❅	🌙	❆	🌗																													13	14	8	10	1	2	2	15	8
19					🌖	🌗	🌔	🌠	🌗	✶	❈	🌒	🌑	🌗	✾																											14	12	11	5	12	10	9	8	18	4	2
20					🌗	✺	❂	❆	🌑	✺	✳	❀	✷	✻	🌚																											10	1	13	17	17	2	9	13	1	20	3
21					🌗	🌏	✾	🌙	🌟	🌛	🌑	✿	✷	✴	✽																											18	17	9	1	16	11	3	13	3	19	7
22				🌒	❈	🌟	✶	❇	✽	🌍	✷	🌘	🌠	🌖	❇	🌝																									2	15	12	3	5	3	15	3	6	3	5	1	1
23				✿	❅	✷	❂	🌔	✼	🌒	🌗	❈	🌎	🌙	✹	❃																									7	5	2	4	8	1	4	19	13	6	2	20	10
24				🌑	✷	🌐	✼	❈	✷	🌞	✶	✻	🌠	❄	✷	✽																									16	14	16	8	15	16	14	16	16	6	3	14	11
25			🌛	✵	✷	🌏	🌛	✻	✷	🌕	✾	🌒	🌍	✵	🌑	✸	🌗																							14	8	14	4	6	15	8	4	6	6	16	6	5	5	11
26			🌎	❈	✳	🌟	🌏	🌘	🌟	🌓	🌒	🌖	🌕	✾	✿	✵	✸																							13	11	4	20	4	15	11	8	11	5	5	10	11	4	20
27			🌙	🌐	🌏	✴	✳	🌜	✺	🌙	🌚	🌞	✶	🌟	🌖	🌐	❄																							5	6	1	13	7	3	17	17	11	19	8	9	1	6	8
28		🌓	✹	✶	🌍	✳	❇	🌔	🌜	🌠	🌝	🌚	🌚	✵	🌕	🌔	✻	🌘																					3	16	20	1	6	12	18	17	14	6	9	19	10	1	18	18	8
29		❈	🌝	🌘	✹	✹	🌛	🌘	❅	🌘	🌓	✹	🌓	🌔	✳	🌗	❉	✸																					8	10	15	3	1	11	11	13	17	4	5	7	9	9	19	7	12
30		❀	🌔	✴	✺	✸	✺	❉	❇	🌟	🌛	❈	🌐	✶	❀	🌖	❁	🌙																					18	11	1	4	3	11	17	2	1	20	12	14	20	8	6	4	8
31				🎁	🎁	🎁	🎁	🎁	🎁	🎁	🎁	🎁	🎁	🎁	🎁	🎁						🎁	🎁	🎁	🎁	🎁	🎁	🎁	🎁	🎁	🎁	🎁	🎁	🎁							🎁	🎁	🎁	🎁	🎁	🎁	🎁	🎁	🎁	🎁	🎁	🎁	🎁
32
Sheet3

Cell Formulas
Range	Formula
B3,AM3,T3	B3	=FORMULATEXT(B4)
B4:R31	B4	=XMAS(27,,AO())
T4:AJ31,AM4:BC31	T4	=XMAS(27,,SEQUENCE(20))
Dynamic array formulas.

Cells with Conditional Formatting
Cell	Condition		Cell Format	Stop If True
AM4:BC31	Other Type	Color scale		NO
AM4:BC31	Other Type	Color scale		NO
T4:AJ31	Other Type	Color scale		NO