by chance

from WordNet (r) 3.0 (2006)
by chance
    adv 1: through chance, "To sleep, perchance to dream.." [syn:
           {perchance}, {by chance}]
    2: by accident; "betrayed by a word haply overheard" [syn:
       {haply}, {by chance}, {by luck}]
    3: without advance planning; "they met accidentally" [syn: {by
       chance}, {accidentally}, {circumstantially}, {unexpectedly}]
       [ant: {advisedly}, {by choice}, {by design}, {deliberately},
       {designedly}, {intentionally}, {on purpose}, {purposely}]
    
from The Collaborative International Dictionary of English v.0.48
May \May\ (m[=a]), v. [imp. {Might} (m[imac]t)] [AS. pres. maeg
   I am able, pret. meahte, mihte; akin to D. mogen, G.
   m["o]gen, OHG. mugan, magan, Icel. mega, Goth. magan, Russ.
   moche. [root]103. Cf. {Dismay}, {Main} strength, {Might}. The
   old imp. mought is obsolete, except as a provincial word.]
   An auxiliary verb qualifying the meaning of another verb, by
   expressing:
   (a) Ability, competency, or possibility; -- now oftener
       expressed by {can}.
       [1913 Webster]

             How may a man, said he, with idle speech,
             Be won to spoil the castle of his health!
                                                  --Spenser.
       [1913 Webster]

             For what he [the king] may do is of two kinds; what
             he may do as just, and what he may do as possible.
                                                  --Bacon.
       [1913 Webster]

             For of all sad words of tongue or pen
             The saddest are these: "It might have been."
                                                  --Whittier.
       [1913 Webster]
   (b) Liberty; permission; allowance.
       [1913 Webster]

             Thou mayst be no longer steward.     --Luke xvi. 2.
       [1913 Webster]
   (c) Contingency or liability; possibility or probability.
       [1913 Webster]

             Though what he learns he speaks, and may advance
             Some general maxims, or be right by chance. --Pope.
       [1913 Webster]
   (d) Modesty, courtesy, or concession, or a desire to soften a
       question or remark.
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             How old may Phillis be, you ask.     --Prior.
       [1913 Webster]
   (e) Desire or wish, as in prayer, imprecation, benediction,
       and the like. "May you live happily." --Dryden.
       [1913 Webster]

   {May be}, & {It may be}, are used as equivalent to
      {possibly}, {perhaps}, {maybe}, {by chance},
      {peradventure}. See 1st {Maybe}.
      [1913 Webster]
    
from Moby Thesaurus II by Grady Ward, 1.0
38 Moby Thesaurus words for "by chance":
      accidentally, as it chanced, at haphazard, at intervals, at random,
      by a fluke, by accident, by fits, by good fortune, by hazard,
      by snatches, capriciously, carelessly, casually, desultorily,
      erratically, fitfully, for some reason, fortuitously, haphazardly,
      hit or miss, in snatches, in some way, in spots, incidentally,
      indiscriminately, irregularly, perchance, promiscuously, randomly,
      sloppily, somehow, somehow or other, spasmodically, sporadically,
      unmethodically, unpredictably, unsystematically

    

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