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 openended 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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