Random deal for A♠ A♥ (2013-11-23, pre-opening)


How it works:

Each day, Mike Caro deals a hold ’em starting hand, which is displayed on the Poker1.com home page.

When you click the link, you come to a page (like this one) that provides the statistics for that category of hand.

Then we ante $1 million and deal a five-player showdown.

IMPORTANT: This Poker1.com home-page feature is experimental. I haven’t decided whether it will appear daily after P1 officially opens, whether it will appear occasionally, or whether it will be abandoned. The decision will depend largely on the number of visits it receives.

Hands are posted soon after being dealt. Please let me know about any glitches. — Mike Caro


→ Jump down to today’s $5 million showdown

→ Choose a previous random hand

Anatomy of today’s hold ’em hand


Category1: A-A pair

Expected win rate2 vs. a random hand (heads up): 85% (50% is average)

Expected win rate2 vs. eight random hands (nine-handed): 35% (11.11% is average)

Odds against being dealt a hand in this category3: 220 to 1

MCU4 ranking against few opponents (limit): 1 of 169

MCU4 ranking against many opponents (limit): 1 of 169

MCU4 composite ranking (limit / all situations): 1 of 169

COPS5 units6 won or lost (limit / nine-handed): +6.38

COPS5 units6 won or lost (no-limit / nine-handed): +9.17


NOTE: Unlike the precisely accurate Mike Caro statistics found elsewhere at Poker1, the chart below was generated by simulating 1,000,000 deals randomly by computer.

When you compare today’s distribution chart to other days, you’ll notice slight differences in statistics that should be exactly the same. Keep this in mind next time you play poker:

Your luck probably won’t stabilize, even after a million deals.


Distribution chart of outcomes7
Outcome
(final strength)
Chance of finishing
with this outcome
Heads-up win-loss
with this outcome
Straight flush 0.01% 96%
Four of a kind 0.84% 100%
Full house 8.55% 99%
Flush 1.98% 97%
Straight 1.22% 81%
Three of a kind 11.8% 91%
Two pair 39.7% 85%
One pair 35.9% 80%1
No pair 0%

1This percentage is only provided for paired starting hands, because most other hands results can be heavily skewed by the possibility of board pairs. Although similar issues affect other final hand strengths, the statistics for them usually aren’t quite as misleading.

NOTES: *For ties (i.e., “split pots”), chances are prorated in accordance with the share of the pot won. *This chart doesn’t differentiate between results using both starting cards, one starting card, and no starting cards (“playing the board”). *The win/loss rate for hands in a category ignores ties.

ANATOMY NOTES:

1CATEGORY: There are 169 categories of hold ’em starting hands: 13 for pairs, 78 for non-paired cards of mixed suits, and 78 for cards of the same suit.

Categories have various numbers of members, depending on the suits and the order the cards arrive.

Therefore, there are 2,652 hold ’em starting hands that can be displayed at Poker1, assuming, as an example, that K-7 and 7-K are different. But, because order of arrival doesn’t really matter for hold ’em starting hands, there are actually only half as many combinations — 1,326 — that the 169 categories comprise.

2WIN RATE is based on computer simulation of one million deals through the showdown using Mike Caro’s Poker Probe software or another program based on the Mike Caro Poker Engine. When a hands ties, a portion of a win is credited. (Rounded to nearest percent.)

3ODDS AGAINST: There are only three possible likelihoods for any category of hand. They are 220-to-1 against a specific pair, 330.5-to-1 against any specific ranks of the same suit, and 109.5-to-1 against any specific unpaired ranks of mixed suits.

4MCU is Mike Caro University of Poker, Gaming, and Life Strategy.

The MCU rankings are for limit hold ’em. No-limit rankings are similar and often identical.

The composite category is a compromise between many and few opponents. So, it may seem strange that sometimes it can be higher or lower than both. That’s because it was determined by the actual strength relative to other composite hands, not by adding the two other rankings and dividing by two.

5COPS is Caro Online Poker Solutions — the cheating prevention system for online poker developed by Mike Caro and Bill Handy. Here’s a link to a Poker1 entry about COPS: → Go there.

6UNITS: The big blind is one unit. Therefore, +2.1 “units won or lost,” if applied to a $10 big-blind game, means the hand averages a $21 profit; -0.4 means it averages a $4 loss.

The units were calculated from a COPS database of hands played online. Some hands that are higher on the MCU rankings are misplayed and, therefore, lose more than worse hands (such as 7-2 of mixed suits) that are more often folded.

Unit information was supplied by Bill Handy, my COPS-project colleague. It is subject to revision.

7CHART OF OUTCOMES: The distribution chart lists the likelihood of outcomes from a royal flush down to no pair. The statistics reflect the final strength of the hand after all five board cards are dealt, whether both starting cards are used, one is used, or the board is played. To save time, I simulated 1,000,000 deals and, so, the statistics aren’t as precise as others found at Poker1.com that I personally calculated.


→ Jump up to anatomy of today’s hand

→ Choose a previous random hand

Today’s $5 million showdown


— Introduction —


Now we enter today’s hold ’em hand in our $5,000,000 showdown.
Yes, it’s imaginary.

You can treat it two ways:

  • as a substitute for astrology, signaling the kind of luck
    you can expect today
    ; or
  • as amusement, like I do.

Your choice. Remember that — similar to real life — you might
only need to be lucky once in five days to break even.

TABLE TALK

Some days, you’ll find comments from me and other players, while we await the flop, turn, and river.

The table talk is sometimes about poker, but often about life, politics, or whatever. We might get sidetracked, and you can just scroll down to see the next cards dealt, if you choose.

A player personality guide is provided in “Showdown notes,” near the bottom. As for “Mike Caro,” I’ll say almost anything — motivational, trivial, or controversial.

Please promise not to get mad at me. I’m just sharing.

So, let’s ante $1 million and see what happens…


Today’s starting hands…


↓ Our hand ↓ ↓ Amy ↓ ↓ Bob ↓ ↓ Cal ↓ ↓ Deb ↓
58% chance 12% chance 7% chance 11% chance 12% chance

(Note: A 20 percent chance is average at all stages.)

Starting hand comments

I can’t believe I just dealt that hand to us. I shuffle and deal randomly and fairly every time. And whatever happens, happens. There’s no changing anything to make the cards more interesting at any stage of the action.

Here’s what surprises me about the hand: It’s a one in 2,652 shot. I know, that figure seems wrong to you if you’re mathematically astute. So, let me tell you why it’s right.

As I explain in many places at P1, there are 169 categories of starting hands, and a pair of aces is one of them. So, why don’t I say one in 169? It’s because I keep a list of each hand by suits separately, so I know what’s been dealt at Poker1. In reality, each pair has six exact-suit combinations, meaning K♦ K♣ is different from K♥ K♦ — even though they’re both in the pair-of-kings category. Additionally, there are four combinations for each suited-hand category, like J-3 or 8-7. And there are 12 combinations if the hand is not paired and not suited.

Add it up and you get 1,326 combinations of hands. Fine. So, why am I saying today’s hand is one in 2,652? It’s because I keep track of the way the hands are displayed on the home page. I don’t sort them high to low. They’re shown in the order they were dealt.

So, here’s what got me so excited. Any two-card sequence is just as rare as any other. The odds against being dealt 2♦ 7♥ are the same as the odds against being dealt K♠ A♠. Each is 2,561-to-1 against (one in 2,562). Poker is just a game of patterns. We give special meaning to some and not to others. So, in five-card draw poker, if you’re dealt A♣ K♣ Q♣ J♣ 10♣, you’ll hold the best possible hand, but it’s no rarer than Q♦ 9♣ 7♠ 4♥ 2♠. We’ve simply agreed to make the royal flush pattern special.

Anyway, I list all 2,652 two-card starting hands in the order they’re dealt from “best” to “worst.”. I list them first by pairs, then by suited cards, then by non-suited, non-pairs. And within those three categories, they’re ordered by ranks first and then by suits. How can you order by suits? You do it by using a poker convention that breaks ties in some games. Mostly, this is is used in games like seven-card stud, where the high exposed card must act first. If there are two kings, then spades is considered higher than hearts, which is higher than diamonds, which is higher than clubs (the lowest suit). If you want to remember easily, the suits rank high-to-low in reverse alphabetical order: SHDC.

Now that you understand all that, what is at the very top of my list of high hands? It’s A♠ A♥ — a pair of aces of exactly those suits in exactly that order. On average, a daily showdown will only provide us with that hand every seven years and three months. And here we are only seven days into the competition and look for yourself!

Now, let’s talk about our chances, since we haven’t won a showdown yet. We’re none out of six and $6,000,000 out of pocket.

We’re not safe today, either. Despite none of our opponents having a pair or even suited cards, we still have a 42 percent chance of losing. Usually, you’ll be in more trouble than this with aces. So, you shouldn’t get emotionally upset when you get aces cracked. It’s quite common.

Nobody else has nearly a 20 percent chance, which would be average in a five-handed showdown. Bob is in worst shape, because his king is duplicated in Amy’s hand and she holds a higher kicker — a nine.

Starting hand table talk (while awaiting the flop)

BOB: Wow! Great hand, Mike. At least I’m better off than Cal and Deb.

MIKE CARO: No, you’re not. You’re much worse off than either of them, sorry to say.

BOB: Are you trying to tell me you’d rather have eight-deuce than king-three? That defies common sense. Show us some cards.

Let’s see the flop…

↑ FLOP ↑


↓ Our hand ↓ ↓ Amy ↓ ↓ Bob ↓ ↓ Cal ↓ ↓ Deb ↓
67% chance 5% chance 1% chance 20% chance 6% chance

Flop comments

Even though Cal paired his eight, our chances got better. We’ll win this kind of race about two out of three times.

Our improvement is due to the fact that the flop seems like garbage to Amy, Bob, and Deb.

Flop table talk (while awaiting the turn)

Everyone is quiet now.

Show us the turn card…

↑ FLOP ↑                 ↑ TURN ↑


↓ Our hand ↓ ↓ Amy ↓ ↓ Bob ↓ ↓ Cal ↓ ↓ Deb ↓
76% chance 0% chance 10% chance 13% chance 0% chance

Turn comments

That paired Bob, so now we have two players, Bob and Cal, to worry about who can make three-of-a-kind or two pair. However, our chances got better, because there’s only one card left to survive.

If you’re wondering why Cal’s chances are better than Bob’s, it’s because Amy holds a king, which reduces the chances of Bob making kings-up by one-third.

Amy and Deb have been eliminated.

Number of winning river cards: 29 of 38 remaining

Turn table talk (while awaiting the river)

AMY: I knew I should have said a prayer before you shuffled. I’ve already lost all six days and this makes seven. I don’t even have a chance. So, sad.

CAL: Your prayer wouldn’t have changed anything, Amy. Ask Mike. He’s not religious.

MIKE CARO: Amy’s right. Her prayer would have almost certainly changed the cards and probably the winner.

DEB: That’s impossible. God has better things to do than worry about our stupid five million dollar showdown.

MIKE CARO: Every prayer changes everything, Deb — whether you think God cares or if there even is a god. That’s because we all have total power to change everything. The future is totally rewritten anytime you shrug your shoulders.

MIKE CARO: Your act changes your mindset and you react differently in the future — maybe in obvious ways, maybe subtly. Other people are also unconsciously influenced by everything they see you do. Different thoughts flit through their heads. Different interactions occur. It ripples through the world. Different people will be born, different ones will die.

AMY: I have that power? O-M-G!

MIKE CARO: Everyone has that power. There are two problems with it. One is that you can’t choose not to use it. And the other is that you can’t predict the ways your tiniest actions will change the world. You just know that they will. It’s really like shuffling. You’re definitely changing what cards will appear, but you don’t know what they’ll be. So, let’s see the last card and find out.

We’re ready to ride the river…

↑ FLOP ↑                 ↑ TURN ↑    ↑ RIVER ↑


↓ Our hand ↓ ↓ Amy ↓ ↓ Bob ↓ ↓ Cal ↓ ↓ Deb ↓
— WON — Lost Lost Lost Lost

We won the $5,000,000 pot — a $4,000,000 profit

Results after 7 days




  Us Amy Bob Cal Deb
Wins 1 0 1 2 3
Result -$2,000,000 -$7,000,000 -$2,000,000 +$3,000,000 +$8,000,000
Days since
last win
0 4 1 3

Final poker words

Our first win! The river card didn’t help anyone.

It paired Deb’s queen, but she was already out of contention.

By the way, I was cheering for Amy today, because she hasn’t won yet. Cheering for your opponents at poker is something I teach.

Even though it sounds strange, it really doesn’t change your chances. And psychologically, it keeps you from being upset by bad luck. If you cheer for your opponents, only two things can happen. One, they win and you were rooting for the right side. Or two, they lose and you get a consolation prize — the pot.

That simple mental trick may seem silly, but it can keep you from getting frustrated and losing extra money. Try it.

Final real-life words

Similar to my advice to root for your opponents at poker, there’s an even more powerful trick in real life.

Root for your friends to succeed. Most people don’t. They’re envious or jealous of their friends outshining them. So, they secretly hope friends don’t get far ahead of them in life.

But that’s wrong. You should want your friends to succeed. If they do, you might be given advantages unavailable to others. If your enemies succeed, beware! Root for your friends.— MC

SHOWDOWN NOTES:

AMY, BOB, CAL, DEB: We play against these same opponents each day. The three-letter names were chosen because they substitute for players A (Amy), B (Bob), C (Cal), and D (Deb).

PLAYER PERSONALITIES (for table talk):

Amy. 28 years old. Asian. Politically very liberal. A little shy. Married. Two daughters, aged 3 and 5. Doesn’t swear. Pretty.

Bob. 53 years old. Caucasian. Politically a bit left of center. Divorced. Has crush on Amy. Pretty crude sometimes. Attractive.

Cal. 40 years old. African-American. Politically right of center. Business oriented. Married. Has son in college. Never gets upset. Body builder in great shape.

Deb. 35 years old. Caucasian. Politically conservative, but kind of libertarian. Outspoken. Married. No children. Sometimes likes to be shocking. Gorgeous.

Mike Caro. See link to my bio on the Poker1 home page. After that, it gets worse. You never know what I’m going to say or do — and neither do I.

(Note: Personalities above may be modified before Poker1 officially opens. After that, they’re pretty much trapped in time, never aging or evolving — except possibly for me.)

% CHANCE: The percentages given beneath each players cards are determined by simulation of 1,000,000 deals (5,000,000 individual hands), using Mike Caro’s Poker Probe software. They are rounded to the nearest whole percent, so it’s possible that some could have been very near the mid point and rounded up, when they should have been rounded down, and vice versa. In some cases, the percentages may not add to exactly 100 percent, because of the rounding.

→ Jump up to anatomy of today’s hand

→ Jump up to today’s $5 million showdown

→ Choose a previous random hand




Published by

Mike Caro

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Known as the “Mad Genius of Poker,” Mike Caro is generally regarded as today's foremost authority on poker strategy, psychology, and statistics. He is the founder of Mike Caro University of Poker, Gaming, and Life Strategy (MCU). See full bio → HERE.

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  1. Suppose the final card were the A♠, making the final board 8♠ Q♣ 8♥ 4♣ A♠. Bob and Carol still each have two pair (queens and eights), but both of them are now entitled to play the final ace as their fifth card, making their hands both two pair, queens and eights, with an ace kicker. Bob’s king no longer plays, because the ace on the board plays as the fifth card in both hands, and a hand is only composed of the best five cards. They therefore tie and split the pot. However, had the last card been a jack or lower (except an eight or a queen which would make a full house, or a ten which would give Carol a higher second pair), Bob’s king would have stayed in game and he would have won.

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