“The best throw of the dice is to throw them away” is a very old gambling adage that is still popularly cited. “The best throw upon the dice is to throw them away” was credited as an old Italian proverb in a book published in 1790.
 
“There is but one good throw upon the dice, which is, to throw them away” was written by “Paul Chatfield” (the pen name of Horace Smith, 1779-1849) in his book, The Tin Trumpet, or Heads and Tales, for the Wise and Waggish (1836). However, the proverb was likely in use before Horace Smith was born in 1779.
 
   
Wikiquote: Gambling
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There is but one good throw upon the dice, which is, to throw them away.
. Chatfield.
 
GIGA Quotes—Gambling
There is but one good throw upon the dice, which is, to throw them away.
—Paul Chatfield (a/k/a Horace Smith)
 
Google Books
Elegant Extracts:
or, useful and entertaining passages in prose, selected for the improvement of young persons, begin similar in design to Elegant Extracts in Poetry
By Vicesimus Knox
London: Charles Dilly
1790
Pg. 928:
Old Italian Proverbs.
(...)
The best throw upon the dice is to throw them away.
 
30 May 1810, Anti-Monarchist, and Republican Watchman (Northampton, MA) “Italian Proverbs,” pg. 4, col. 2:
The best throw with dice is to throw them away.
 
Google Books
4 December 1827, The Kaleidoscope: or, Literary and Scientific Mirror, pg. 180, col. 3:
A HINT TO GAMESTERS.
Accept this advice, you who sit down to play.
The best throw with dice is to throw them away.
 
Google Books
The Tin Trumpet, or Heads and Tales, for the Wise and Waggish:
to which are added Poetical Selections
By the late Paul Chatfield (1779 - 1849; it is not clear why he is being called “the late”—ed.)
Edtied by Jefferson Saunders
London: Whittaker & Co.
1836
Pg. 236:
There is but one good throw upon the dice, which is, to throw them away.
     
Google Books
Pearls;
Or, The World’s Laconics: Being Choice Thoughts of the Best Authors, in Prose and Poetry
By Tryon Edwards
Boston, MA: B. B. Russell
1872
Pg. 68:
DICE.—The best throw with the dice, is to throw them away.— Old Proverbs.
 
Google Books
A Dictionary of Thoughts:
Being a Cyclopedia of Laconic Quotations
Edited by Tryon Edwards
Detroit, MI: F. D. Dickerson Co.
1908
Pg. 190:
The best throw with the dice is to throw them away. — C. Simmons.
   
Google Books
20,000 Quips & Quotes
By Evan Esar
New York, NY: Barnes & Noble Books
1995, ©1968
Pg. 336:
The best throw of the dice is to throw them away.
 
Google Books
And I Quote, Revised Edition:
The Definitive Collection of Quotes, Sayings and Jokes for the Contemporary Speechmaker
By Ashton Applewhite, William R. Evans III and Andrew Frothingham
New York, NY: St. Martin’s Press
2003
Pg. 333:
The best throw of the dice is to throw them away. — Austin O’Malley
       
Google Books
The Little Black Book of Casino Games:
The Smart Player’s Guide to Gambling
By John Hartley
White Plains, NY: Peter Pauper Press, Inc.
2005
Pg. 131:
The best way to throw the dice is to throw them away.
Anonymous
 
Google Books
Compelling Conversations:
Questions and quotations on timeless topics - an engaging ESL textbook for advanced students
By Eric H. Roth and Toni Aberson
Los Angeles, CA: Chimayo Press
2008
Pg. 103:
The best throw with the dice is to throw them away.—t-shirt sold in Las Vegas.