Poker is a game of incomplete information; you don't know what your opponents have
until the hand is over, and many times not even then. The best you can do is put your opponents on ranges of
hands based on their playing styles, actions in the hand,
tells, and other factors, and refine your ranges as you get more information.
PokerCruncher enables you to deal with incomplete information by letting you specify
hand ranges (sets of hands with optional weights) for players, not just specific hands.
Weights are an important feature because
different hands in a hand range may have different likelihoods, for
example, "I think he has AA 75% of the time in this situation and KK 25%".
Hand ranges are a powerful feature that you won't find in most other odds
calculators, including desktop, online, and website calculators. We're happy to
bring you hand ranges in a mobile app.
An Example
Say in a 2/5 no-limit game where everyone has 400
stacks, it gets folded to the button, who raises to 30. The small blind
calls, and you are the big blind and have QQ. Let's say that all three
of you are solid tight-aggressive players, capable of bluffing but no
one is a maniac or frequent bluffer. So far the button's range of hands
is pretty wide in your view; he could have a strong hand or he could be
playing his position and raising with a mediocre hand. You put the small
blind on a stronger range of hands than the button, but not super-strong
because he didn't re-raise. So you think you probably have the best hand
with QQ and re-raise to 125 to try to take down the pot preflop. But the
button then goes all-in for 275 more. The small blind folds so it's now
you and the button.
The button's range of hands has gotten much
narrower and stronger now; you put him on AA, KK, or AK. Your first instinct may be to fold because at best you're in a coin-flip situation.
(By the way, is QQ vs. AK really a 50/50 coin flip?; this is one of PokerCruncher's library and odds tests
scenarios; hint: it's closer to 60/40 than 50/50.) But this opponent likes to play AK strongly like this very often
preflop so you estimate he has AK about 50% of the
time, and AA/KK 25% of the time each.
There is another possibility - he could be bluffing. He could have say JJ or a lower
pair, AQ/AJ/etc., a suited connector, or even nothing i.e. a complete
bluff. For simplicity we'll pick JJ as the representative bluff case.
But you think the bluff case is low probability based on how this
opponent plays, say 10% of the time. We'll move AK down from 50% to 40%
and put him on JJ 10% of the time. Let's model this in PokerCruncher
using hand ranges to see
what your equity is with QQ in this situation:
The opponent's hand range is specified as "AsAc:25,KsKc:25,AsKc:40,JsJc:10",
a comma-separated list of hands with optional integer weights (which default to
1). In this example the weights sum to 100 but they can sum to any
positive number. We picked just JJ to represent the bluff case but you
can include as many hands as you'd like; a hand range can have any
number of hands.
Then you simulate this scenario:
... and see that your equity with QQ is about 41%,
not bad at all. You will want to call the all-in if you're getting better than about 60:40, or 3:2, pot odds on your final call.
Your 125, the button's matching 125, and the small
blind's 30 are already in the pot, for a total of 280. The button raised
all-in for 275 more, so it's 275 to you to win 280+275=555. So you're
getting 555:275 odds on your final call or about 2:1 odds. This is
better than the 3:2 odds you need so this is a profitable call; so your
decision: call the button's all-in with QQ.
Some Follow-Up Examples
The above analysis is for a solid tight-aggressive opponent
who can play AK like AA and KK very often preflop.
Where would you stand against a much tighter opponent who would have AA/KK most of the time in this
situation? Re-run the simulation but give AA and KK a weight of 2 or 3 (or
even higher) and give AK the default weight of 1 (or 0 for a player who would never play AK like
this) and eliminate JJ (the bluff case) as a possibility altogether. Your equity with QQ will of course go down from
41%, but by how much? Will your equity go down enough to make folding the correct
play? What's the breakeven point?
Where would you stand
against a loose-aggressive opponent or a frequent bluffer or a maniac? Would you be
in the lead with QQ against these players'
ranges of hands? How much in the lead?
The
above examples are simple heads-up preflop situations. You can specify
hand ranges in multi-player scenarios; you can give multiple players
their own distinct hand ranges; you can use hand ranges in postflop situations,
with partial simulation, etc. That is, PokerCruncher's features are
independent and can be used in any combination with each other,
resulting in a powerful Hold'em analysis and modeling system.
