Texas Holdem mathematical aspects

There are only two opposing cards ranking higher than your jack both of them kings. The
first king makes a call of the forced $15 bring-in bet. This can mean anything from three clubs,
to all high cards with straight possibilities, to just a single buried ace, to a small buried pair, to a
pair of kings, to nothing much at all. Holdem poker players call bring-in bets for all kinds of reasons. Hunches, spontaneous brain surges, you name it.

Player № 1 "completes the bet" by raising to $50 the betting limit on this round. You
call. If you're thinking about folding here, you're probably playing way too tight. Remember, it's
just as bad to throw a hand away that has an expectation of profit than to play a hand that
doesn't. In other words, you lose profit by not taking advantage of hands that are strong enough
and you lose profit by playing hands that are not strong enough. With the king just calling,
another king out of play, a raise from a door card seven, and no higher card left to threaten you,
this hand clearly has a profit expectation. It isn't really a close decision, and if you think it is,
you need to reevaluate how you're playing texas holdem poker.

Anyway, the king calls and the pot is now $245.

On the next betting round, you catch a decidedly unhelpful four. Player №5 bets with kingjack
showing. That's kind of surprising, right? Maybe he had a pair of kings after all. It's not
likely that he made a pair of jacks, because you hold two of them. Maybe he had queen-ten in
the hole and now has an open-end straight draw. Maybe he's just leveraging his high cards,
hoping to chase you and the other opponent out of the pot.
You're just never going to know these things for sure in the absence of tells. And anybody who
says they can figure out exactly what opponents have at these early betting stages of stud,
against typical players who often decide what to do at whim, is just telling you wrong. Player №1 calls without hesitation. You call.

The limits have now doubled from $50 to $100. Player №1 makes an exposed pair of sixes and
checks. You should now consider betting. In fact, I bet most of the time in this situation. Player
№5 caught a nine and might have made a straight, but that's not the most likely thing. He's more
likely to have caught a fourth club or maybe he had a pair of kings all along. Maybe something
else. You've just made aces-up, catching an ace, and when that happens to me, I don't want to let
my opponents get another card for free. I'm probably best and I want them to pay the price. So,
betting is my usual play. But you decide to check. And, you blow what? That's not a bad idea,
either.

In texas holdem poker, you have to mix it up and keep your opponents off guard. Besides, Player №5 bet last round and he's an aggressive opponent, so he might bet this round, too. We give it a try. Sure enough, Player №5 wings out there with a $100 bet. Player №1 calls it. Now you could just call if you wanted, and that's what I'd do sometimes. If you just call, you're not tipping off Player №5 that you have anything. If he's bluffing or betting a weak hand, you'll probably prefer that he not change his mind on the next round. You might want to either check-call or check-raise on the next betting round, but if you check-raise right now, you might have identified your strength prematurely and won't be able to let your opponent tighten his own noose by continuing to bet next.

Of course, other thoughts are going through your head. You might not have the best hand, for
instance. But Player №1 almost certainly doesn't have three sixes, so you feel safe that you have
him trapped. He probably has a straight draw or a flush draw, you figure. Maybe sevens-up.
Maybe something else. You decide to raise, which is probably what you had in mind when you
checked. You get two calls. Fine.

After an uneventful sixth card, which saw Player №5 pick up another club for a not-too-likely
but possible flush and your bet being called by both opponents, we move on to the final
action at the river (last card, facedown). Your card doesn't help, and you still have aces-up
(actually three pair, but the third one doesn't count).
Player №1 suddenly bets. The pot is awfully big and you're getting over 13-to-l odds to call. Of
course, it's not really that good, because Player №5 might now have you beat, even if your hand
is stronger than the bettor's. Still, Player №1 often bluffs and sometimes pushes two pair for
value, so this is a call you're normally going to make. You wouldn't expect to win most of the
time, but you would expect to win enough of the time to show a nice profit. Nobody believes
strongly that you have aces-up, because you have no pair showing. They may consider it a
possibility, but it's not what they expect.
THE TELL. Player №1, who was previously in control, begins to tremble as he places the chips
in the pot. You know what that means. We just talked about it. It doesn't mean that he's nervous
about bluffing. Bluffers bolster themselves. This is a release of tension. The suspense is over.
He's made a very big hand and this is simply nervous excitement. He can't control it. But, look!
There's something else that doesn't even happen in the following photos. He's now gripping the
edge of the table hard, trying to conceal his shaking. Why? He's embarrassed by it, so you can
be sure the shaking wasn't an act. And, in fact, it almost never is unless the player has read
this book.

So, Player №1 made a big hand, pure and simple. You're not sure what it is. It could be
anything from a big flush on up. Maybe a full house. Maybe four of a kind. It's big, though.
Certainly it's bigger than aces-up, so you fold. Excellent!

But Player №5 doesn't know this tell. He's made a flush and raises. He gets reraised and calls.
Maybe he should have called the initial bet on the strength of the ace-high flush, but he should
never have raised. That mistake cost him an extra $200 this time. Player №1 had a straight flush
-but we suspected that, didn't we?