Example

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   Assume you are playing against three opponents and you were initially dealt  2♦ 3♠ 4♥ 5♥ 5♣.
   The software displays under your hand: You hold one pair and an open-ended straight.
   It also displays the following suggestions and odds: 

   1) You may keep the pair and discard the rest, playing for:
   - two pair (probability: 15.985%, odds: 7.75 : 1) or
   - three of a kind (probability: 11.433%, odds: 7.75 : 1) or
   - full house (probability: 1.017%%, odds: 97.33 : 1) or
   - four of a kind (probability: 0.246%, odds: 405.50 : 1).
   The probability of succeeding is 28.683% (2.49 : 1 odds). 

   2) You may keep the four straight cards and discard the card left, playing for straight. The probability of succeeding is 17.021% (4.88 : 1 odds). 

   Simultaneously, the following odds tables are displayed: 

   One opponent holding: 

Formation

Probability

Odds

higher pair

35.994%

1.78 : 1

two pair

4.804%

19.82 : 1

three of a kind

2.156%

45.38 : 1

straight

0.439%

226.72 : 1

flush

0.185%

539.50 : 1

full house

0.148%

674.45 : 1

four of a kind

0.025%

3962.67 : 1

straight flush

0.002%

61356.56 : 1

a higher formation than yours

43.750%

1.29 : 1

   These are the odds of one specific opponent holding the listed formations at that moment of the game.

   At least one opponent holding: 

Formation

Probability

Odds

higher pair

73.778%

0.36 : 1

two pair

13.729%

6.28 : 1

three of a kind

6.330%

14.80 : 1

straight

1.312%

75.24 : 1

flush

0.554%

179.50 : 1

full house

0.443%

224.48: 1

four of a kind

0.076%

1320.55 : 1

straight flush

0.005%

20451.84 : 1

a higher formation than yours

82.202%

0.22 : 1

   These are the odds of at least one of your three opponents holding the listed formations at that moment of the game.

    Now assume you ignore both suggestions you keep 4♥ 5♥ 5♣ and discard 2♦ 3♠. Your replacements come 4♣ J♠. Your hand is now:  4♣ 4♥ 5♥ 5♣ J♠.
   The software displays under your hand: You hold two pair. Simultaneously, the above odds tables are displayed again with the updated information:

    One opponent holding: 

Formation

Probability

Odds

higher two pair

4.781%

19.92 : 1

three of a kind

2.207%

44.32 : 1

straight

0.437%

227.62 : 1

flush

0.178%

559.95 : 1

full house

0.153%

654.45 : 1

four of a kind

0.027%

3723.87 : 1

straight flush

0.002%

58178.00 : 1

a higher formation than yours

7.781%

11.85 : 1

   These are the odds of one specific opponent holding the listed formations at that new moment of the game.

    At least one opponent holding: 

Formation

Probability

Odds

higher two pair

13.688%

6.32 : 1

three of a kind

6.475%

14.44 : 1

straight

1.306%

75.54 : 1

flush

0.534%

186.32 : 1

full house

0.457%

217.82: 1

four of a kind

0.081%

1240.96 : 1

straight flush

0.005%

19392.32 : 1

a higher formation than yours

21.573%

3.64 : 1

   These are the odds of at least one of your three opponents holding the listed formations at that new moment of the game.  

   You can use all the above odds to make decisions on discarding and driving the betting dialogue, to evaluate the strength of your hand in front of your opponents or evaluate the chances of one opponent bluffing.
   And all these odds are real probabilities, returned by precise probability formulas and not by partial simulations!

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