Poker -- from Wolfram MathWorld

title

Poker is a card game played with a normal deck of 52 cards. Sometimes, additional cards called "jokers"
are also used. In straight or draw poker, each player is normally dealt a hand of
five cards. Depending on the variant, players then discard and redraw cards,
trying to improve their hands. Bets are placed at each discard step. The number of
possible distinct five-card hands is equal to the number of possible ways of picking
five cards out of a deck of 52, namely

where is a binomial
coefficient.

There are special names for specific types of hands. A royal flush is an ace, king, queen, jack, and 10, all of one suit. A straight flush is five consecutive cards all of the same suit (but not a royal flush), where an ace may count as either high or low. A full house is three-of-a-kind and a pair. A flush is five cards of the same suit (but not a royal flush or straight flush). A straight is five consecutive cards (but not a royal flush or straight flush), where an ace may again count as either high or low.

The probabilities of being dealt five-card poker hands of a given type (before discarding and with no jokers) on the initial deal are given below (Packel 1981). The "computation"
and "counts" columns give the numbers of possible five-card hands of each
type, and how this number is computed. As usual, denotes a
binomial coefficient. The odds
of a hand with probability are .

Gadbois (1996) gives probabilities for hands if two jokers are included, and points out that it is impossible to rank hands in any single way which is consistent
with the relative frequency of the hands.

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How President Trump Is Like A Terrible Poker Player

title

I was playing poker in Atlantic City this weekend, so I’ve had poker on the brain as I’ve been thinking about President Trump’s tactics during the partial government shutdown, which ended on Friday after Congress passed a three-week continuing resolution to fund the government. What will happen at the end of the next three weeks is very much up in the air. But the way Trump has played his hand so far on the shutdown has a lot in common with how bad poker players tend to cost themselves money.

If you read the headline of this post, you may have assumed that it refers to Trump’s getting outmaneuvered on the shutdown by House Speaker Nancy Pelosi. I do think Trump was outmaneuvered by Pelosi, but the analogy to poker is a little different from that. It has more to do with Trump’s overall strategy toward the presidency.

In general, the strategic goal of poker is to put your opponent to tough decisions. If you see one of those hands on TV where one player is thinking for several minutes about whether to call or fold on the river, that usually means the other player has played his or her hand well, putting the opponent in a no-win position by leaving just the right amount of doubt about whether it’s a bluff or a real hand.

As a corollary, good players play in such a way as to avoid putting themselves to tough decisions. Bad players, conversely, tend to paint themselves into corners. They’ll curse their luck when they suddenly realize that a hand they’d assumed was a winner might be no good. But more often than not, it reflects a mistake they made earlier in the hand, such as playing a weak hand that they should have folded to begin with.

Sound familiar? It sounds a lot like Trump, who didn’t have a lot of good choices on the shutdown. He could have:

• Caved to Pelosi and agreed to reopen the government without a border wall. But that would have risked undermining perceptions that Trump is a strong negotiator and leader and risked disappointing his base.


• Maintained the shutdown. But that was getting more costly by the day for Trump, as his approval ratings got worse and more and more Americans blamed him for the shutdown — and as federal workers went without paychecks and the entire air traffic system was on the verge of chaos.


• Struck a deal with Democrats. But because Democrats had all the leverage — the shutdown was hurting Trump a lot more than it was hurting them — it would have had to be a far more generous deal than the one that presidential adviser/son-in-law Jared Kushner had cooked up, generous enough that it would entail serious policy concessions and perhaps lead to a backlash from his base.


• Declared a national emergency to build a border wall — an option that very much remains on the table. But that would likely be extremely unpopular, would create a precedent that a future Democratic president could exploit, might not be held up by the courts, and would trigger at least some objections from other Republican lawmakers and perhaps also from parts of the military.

I tend to agree with my colleague Perry Bacon Jr. that conceding to Pelosi was Trump’s least-worst option. In fact, I think Trump probably would have been better off just conceding on the border wall completely, instead of kicking the can down the road for three weeks. But I’m far from certain of that conclusion. The point is that all of Trump’s options stunk, and like in the case of a bad player who limped into the pot with 7-2 offsuit (the worst hand in poker) and then got caught up in a huge pot with a bad hand, it was 100 percent Trump’s fault.

Nor was the shutdown a case where things unexpectedly took a rough turn for Trump.

It’s been obvious the whole time that it was liable to end in political (if not also literal) disaster. Trump was an unpopular president using an unpopular technique to push for an unpopular policy, and he was doing it just after Republicans had lost 40 seats to Democrats in the midterm elections while Trump tried to scaremonger voters on immigration. I can certainly think of lapses in presidential judgment that were more consequential in hindsight than the shutdown, but not all that many that were so obvious in advance.

And this isn’t the first time that Trump and Republicans have gotten themselves in trouble by picking a fight over an unpopular policy. GOP efforts to undo Obamacare were similar to the shutdown, since Republicans risked either passing a massively unpopular repeal bill or breaking a promise they’d made to voters in 2016. The dynamics over the Republican tax bill were also similar in several respects. Republicans ultimately passed their bill in that case, but they paid a price for it in the midterms in congressional districts with high state, local and property taxes, which can no longer be deducted beyond $10,000 under the new law. Confirming Brett Kavanaugh to the Supreme Court after he was accused of committing sexual assault when he was in high school, when Republicans could have withdrawn his name and chosen a less controversial nominee, is another case in which Republicans had to choose from among several difficult options.

Part of this is just a way of saying that public opinion does have consequences: Sometimes it prevents you from passing unpopular policies, and sometimes you pass them but suffer electorally. And sometimes, it’s both: Republicans didn’t get their full Obamacare repeal, but health care was a huge issue in the midterm campaign nonetheless.

If Trump doesn’t believe the polls showing himself and his policies, such as the border wall, to be unpopular, then maybe that’s part of the problem. (There are a lot of ways to be bad at poker, but probably the most common one is to play too many hands because you overestimate your own abilities.) This being FiveThirtyEight, I feel obligated to point out that the notion that polls systematically underestimate Trump is on shaky ground. But if Trump thinks polls are fake news and if he hires advisers who encourage that perception, that could explain why he constantly puts himself in such politically untenable positions.

There’s something else about those bad poker players that I think might apply to Trump.

Some of them (not all by any means) actually do have decent people-reading skills. They can sometimes suss out, through body language and table talk, whether your hand is relatively strong or relatively weak and make better decisions on that basis. It’s almost never enough to overcome poor strategic and technical play; poker is mostly a mathematical game. But those talents can help to stem losses, especially at lower stakes where opponents are more likely to exhibit tells. The bad players have their fair share of winning days when they’re catching cards.

Trump, similarly, has gotten a long way on the basis of hustle and luck — he was lucky in several important respects to be elected president. There are some cases in which he has displayed solid (if unconventional) tactical instincts, from his negotiations with foreign leaders to his handling of the media to his belittling of his primary opponents. That’s not to say he always gets these decisions right or even does so anywhere near approaching a majority of the time. But he gets enough “wins” — he became president of the United States! — to sustain his ego and not prompt a lot of self-reflection.

But Trump has no sense for which battles to pick and seemingly little awareness of his own unpopularity and the consequences it has for the presidency. Moreover, although Trump sometimes seems to realize when he has gotten himself into a no-win position, he doesn’t recognize how often his own decisions are responsible for putting him there. The presidency is a long game, and a much harder one than being a real-estate developer or a reality television host. The scary possibility for Trump — and I do mean merely a possibility — isn’t that the chaos of the shutdown, coming on the heels of the midterms and as the Russia investigation still looms over him, is a new low for him. It’s that it’s the new normal.

Source

Basic Poker Rules

title



Poker is a game of chance. However, when you introduce the concept
of betting, poker gains quite a bit of skill and psychology.
(This isn"t to say that there isn"t skill at poker when nothing is
at risk, there just isn"t nearly as much). This is meant as
a very basic primer into the rules of poker, for more information,
get a book on the game (or start playing with a group of people who
know how. It"s more expensive than reading a book, but the group
won"t mind. *Snicker*).

This list is currently broken into several parts:

1. The Very Basics
   
2. How the Hands are Ranked
   
3. Descriptions of Hand Ranks
   
4. Betting
   
5. An Example 5-Card Draw Hand
   

The Very Basics

Poker is played from a standard pack of 52 cards. (Some variant games
use multiple packs or add a few cards called jokers.) The cards are
ranked (from high to low) Ace, King, Queen, Jack, 10, 9, 8, 7, 6, 5,
4, 3, 2, Ace. (Ace can be high or low, but is usually high). There
are four suits (spades, hearts, diamonds and clubs); however, no suit
is higher than another. All poker hands contain five cards, the highest
hand wins.

Some games have Wild Cards, which can take on whatever
suit and rank their possessor desires. Sometimes jokers will be
used as wild cards, other times, the game will specify which cards
are wild (dueces, one-eyed jacks, or whatever).

How the hands are ranked

Hands are ranked as follows (from high to low):

• Five of a Kind
  
• Straight Flush
  
• Four of a Kind
  
• Full House
  
• Flush
  
• Straight
  
• Three of a Kind
  
• Two Pair
  
• Pair
  
• High Card
  

Descriptions of Hand Ranks

Five of a Kind

A five of a kind (which is only possible when using wild cards)
is the highest possible hand. If more than one hand has five of a kind,
the higher card wins (Five Aces beats five kings, which beat five queens,
and so on).

Straight Flush

A straight flush is the best natural hand. A straight flush is
a straight (5 cards in order, such as 5-6-7-8-9) that are all of the
same suit. As in a regular straight, you can have an ace either high
(A-K-Q-J-T) or low (5-4-3-2-1). However, a straight may not "wraparound".
(Such as K-A-2-3-4, which is not a straight). An Ace high straight-flush
is called a Royal Flush and is the highest natural hand.

Four of a Kind

Four of a kind is simply four cards of the same rank. If there
are two or more hands that qualify, the hand with the higher-rank four of a
kind wins. If, in some bizarre game with many wild cards, there are two
four of a kinds with the same rank, then the one with the high card outside
the four of the kind wins. General Rule: When hands tie on the rank
of a pair, three of a kind, etc, the cards outside break ties following
the High Card rules.

Full House

A full house is a three of a kind and a pair, such as K-K-K-5-5.
Ties are broken first by the three of a kind, then pair. So K-K-K-2-2
beats Q-Q-Q-A-A, which beats Q-Q-Q-J-J. (Obviously, the three of a kind
can only be similiar if wild cards are used.)

Flush

A flush is a hand where all of the cards are the same suit, such as
J-8-5-3-2, all of spades. When flushes ties, follow the rules for
High Card.

Straight

A straight is 5 cards in order, such as 4-5-6-7-8.
An ace may either be high
(A-K-Q-J-T) or low (5-4-3-2-1). However, a straight may not "wraparound".
(Such as Q-K-A-2-3, which is not a straight). When straights tie,
the highest straight wins. (AKQJT beats KQJT9 down to 5432A). If
two straights have the same value (AKQJT vs AKQJT) they split the pot.

Three of a Kind

Three cards of any rank, matched with two cards that are not a pair (otherwise
it would be a Full House . Again, highest three of
a kind wins. If both are the same rank, then the compare
High Cards.

Two Pair

This is two distinct pairs of card and a 5th card. The highest pair wins
ties. If both hands have the same high pair, the second pair wins. If
both hands have the same pairs, the high card wins.

Pair

One pair with three distinct cards. High card breaks ties.

High Card

This is any hand which doesn"t qualify as any one of the above hands.
If nobody has a pair or better, then the highest card wins. If multiple
people tie for the highest card, they look at the second highest, then
the third highest etc. High card is also used to break ties when
the high hands both have the same type of hand (pair, flush, straight,
etc).

Betting

So, how do you bet?
Poker is, after all, a gambling game. In most games, you
must "ante" something (amount varies by game, our games are
typically a nickel), just to get dealt cards. After that
players bet into the pot in the middle. At the end of the
hand, the highest hand (that hasn"t folded) wins the pot.
Basically, when betting
gets around to you (betting is typically done in clockwise order),
you have one of three choices:
Call
When you call, you bet enough to match what has been
bet since the last time you bet (for instance, if you bet a
dime last time, and someone else bet a quarter, you would owe
fifteen cents).
Raise
When you raise, you first bet enough to match what has
been bet since the last time you bet (as in calling), then
you "raise" the bet another amount (up to you, but there
is typically a limit.) Continuing the above example, if
you had bet a dime, the other person raised you fifteen
cents (up to a quarter), you might raise a quarter (up
to fifty cents). Since you owed the pot 15 cents for
calling and 25 for your raise, you would put 40 cents
into the pot.
Fold
When you fold, you drop out of the current hand (losing
any possibility of winning the pot), but you don"t have to
put any money into the pot.

Betting continues until everyone calls or folds after a raise
or initial bet.

Some Standard Betting Rules

In the group I play in, we ante a nickel. The maximum first
bet is fifty cents, and the maximum raise is fifty cents. However,
during one round of betting, raises may total no more than one dollar.

An Example Five Card Draw Hand.

Five card draw is one of the most common types of poker hands. Each
player is dealt five cards, then a round of betting follows. Then
each player may discard up to 3 cards (4 if your last card is an ace
or wild card, in some circles) and get back (from the deck) as many
cards as he/she discarded. Then there is another round of betting,
and then hands are revealed (the showdown) and the highest hand wins
the pot. So you are the dealer at a five card draw game (against four
other players, Alex, Brad, Charley and Dennis (seated in that order
to your left). Everyone puts a nickel into the pot (Ante) and you
deal out 5 cards to each player.

You deal yourself a fairly good hand Ks-Kd-Jd-5c-3d. A pair of kings
isn"t bad off the deal (not great, but not bad). Then the betting
starts...

• Alex "Checks" (checking is basically calling when you don"t owe
  anything to the pot).
  
• Brad bets a dime.
  
• Charley calls (and puts a dime into the pot).
  
• Dennis raises a dime (and puts twenty cents into the pot).
  
• Well, it"s your turn. Twenty cents to you. You can fold, call
  or raise. Like I said before, pair of kings isn"t bad, not good but
  not bad. You call and put twenty cents into the pot.
  
• Back to Alex, who grumbles and tosses his cards into the center
  of the table, folding. (Note, when folding, never show your cards
  to anyone).
  
• Brad calls. The total bet is twenty cents, but he had already
  bet a dime, so he owes a dime, which he tosses into the pot.
  
• Charley is in the same position as brad, and tosses a dime into the
  pot.
  

The round of betting is over. After Dennis"s raise, everyone else folded
or called (there weren"t any raises) so, everyone is all square with the
pot. Now everyone can discard up to 3 cards. Brad discards 3 cards,
Charley discards one card, Dennis discards two cards. (You deal replacements
to everyone) and now it"s your turn. You have a pair of kings, three
spades, and no chance for a straight. It"s best to just keep the two kings
and hope to get a 3rd or fourth king. You discard three cards, and your
new hand is: Ks-Kd-Kc-4c-8h. Three Kings! A nice little hand.

What do you suppose the others were trying for? Well, Brad kept two cards,
so he probably had a pair (just like you) but it probably wasn"t aces, so
even if brad got a three of a kind, you probably beat him. Charley
kept four cards, so he was probably trying for a straight or flush.
(If Charley had four of a kind, he might have bet much harder). The
big problem is Dennis. He raised earlier, and only drew two cards.
He might be bluffing, but he could have had three of a kind off the deal...
In any case, the second round of betting starts (with dealers left).

• Brad bets a nickel.
  
• Charley folds (I guess he didn"t get his straight or flush).
  
• Dennis raises twenty cents (to a quarter total).
  
• You call.
  
• Brad looks at his cards, then calls (betting twenty cents).
  
• Again, everyone called Dennis"s raise, so the round of betting
  is over.
  

Well, the betting is over, everyone reveals his hand:

• You had Ks-Kd-Kc-4c-8h.
  
• Brad had Jh-Jd-3c-3s-Ah.
  
• Dennis had Qh-Qs-Qd-As-7s.
  

Well, the highest hand is three of a kind, and the highest three of
a kind is your three kings. You win!

Conclusion

After this and an hour of play, you"ll be right at home playing poker.
(Maybe not very good, but right at home). If you ever get bored with
basic 5 card draw, look at our List of Poker Variants.

Source

PELEMBAGAAN PARTAI POLITIK DI TINGKAT LOKAL (Studi tentang Pelembagaan Partai Golkar di Kabupaten Sinjai Pasca Kekalahan pada Pemilu 2009) | Muhammad Lutfi

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PELEMBAGAAN PARTAI POLITIK DI TINGKAT LOKAL
(Studi tentang Pelembagaan Partai Golkar di Kabupaten Sinjai
Pasca Kekalahan pada Pemilu 2009)

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(Studi tentang Pelembagaan Partai Golkar di Kabupaten Sinjai
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