• Mike Caro   Exit

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How it works:

Once a week or so, I deal 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 regularly 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

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→ Jump down to today’s $5 million showdown

→ Choose a previous random hand

Anatomy of today’s hold ’em hand

Category¹: 8-6 of mixed suits

Expected win rate² vs. a random hand (heads up): 43% (50% is average)

Expected win rate² vs. eight random hands (nine-handed): 9% (11.11% is average)

Odds against being dealt a hand in this category³: 109.5 to 1

MCU⁴ ranking against few opponents (limit): 133 of 169

MCU⁴ ranking against many opponents (limit): 129 of 169

MCU⁴ composite ranking (limit / all situations): 130 of 169

COPS⁵ units⁶ won or lost (limit / nine-handed): -0.19

COPS⁵ units⁶ won or lost (no-limit / nine-handed): -0.15

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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.

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Distribution chart of outcomes7
Outcome (final strength)	Chance of finishing with this outcome	Heads-up win-loss with this outcome
Straight flush	0.02%	98%
Four of a kind	0.12%	88%
Full house	2.24%	93%
Flush	1.97%	77%
Straight	7.77%	93%
Three of a kind	4.34%	66%
Two pair	22.3%	63%
One pair	43.4%	No data1
No pair	17.7%	8%
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 hands tie, a portion of a win is credited. (Usually 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.

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→ Jump up to anatomy of today’s hand

→ Choose a previous random hand

Today’s $5 million showdown

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— Introduction —

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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…

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Today’s starting hands…

↓ Our hand ↓	↓ Amy ↓	↓ Bob ↓	↓ Cal ↓	↓ Deb ↓
22% chance	12% chance	20% chance	9% chance	37% chance

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

Starting hand comments

A couple things might strike you as odd about the chances for our five starting hands.

At first glance, it would probably surprise most players that our hand has a better than average chance of winning — average being 20 percent. In fact, we’re in second place. Notice that Amy and Cal each have a king, harming their chances of connecting.

The reason Amy’s K-2 is better than Cal;s K-4 is that Deb also holds a four and, if another one hits the board, she will be in a superior situation with an ace kicker.

Perhaps the most puzzling to many is that our 8-6 off-suit has a better chance than Bob’s 7-6 suited. I’m guessing most people would instinctively pick Bob’s hand, if given a choice. But some things are working against Bob. There are three of his diamonds in opposing hands. And sometimes, he can make a straight and lose to our higher straight, if he pairs sevens.

Deb is clearly in the lead with A-4 suited. But maybe we’ll catch up.

Starting hand table talk (while awaiting the flop)

BOB: I notice that you anted my million dollars for me. That’s a nice thing to do.

MIKE CARO: It’s the money you won on New England last night. I bet Denver, remember? We agreed yesterday, while waiting for the turn card.

BOB: Actually, I forgot all about it. Thanks for being so honest.

Let’s see the flop…

↑ FLOP ↑

↓ Our hand ↓	↓ Amy ↓	↓ Bob ↓	↓ Cal ↓	↓ Deb ↓
35% chance	14% chance	3% chance	1% chance	47% chance

Flop comments

Two spades hit the board, giving Deb four parts of a flush. We paired our high card. And even though it’s only a pair of eights, it might hold up if we can keep Deb from catching a spade.

Amy paired deuces and has jumped a little, from a 12 percent chance to 14. Bob and Cal’s chances are pitiful.

Flop table talk (while awaiting the turn)

AMY: While we’re waiting, I have this neighbor down the block who’s becoming a problem for me.

DEB: Share with us! I love it when you open up.

BOB: Is this going to be another chick sensitivity moment?

AMY: She’s lonely since her husband died. So, she keeps asking me over and phoning me for long talks. It’s taking too much of my time away from the kids and work. And I have to drive here to play this showdown every day.

AMY: I’m going to have to hurt her feelings and tell her that we’re not that good of friends and that I’d rather she didn’t bother me so often. But I dread doing it, because her life is sad enough already.

CAL: Ask Mike what to do. He always knows.

DEB: Good idea. What should Amy do, Mike?

MIKE CARO: Amy, I want you to listen to me. You’re a very sensitive person, and that’s often a good thing. In this case, there’s a better solution that you should try first.

MIKE CARO: Instead of admonishing the lonely woman for being too pesty, apologize.

AMY: Apologize?

MIKE CARO: Yes, say something like, “I’m sorry I haven’t had enough time for you lately. My days are getting busier and busier. Everyone thinks I’m being rude by ignoring them.” That accomplishes three things: (1) It doesn’t hurt her feelings; (2) You politely put her on notice that her time with you will diminish; and (3) You say that she isn’t alone — that you’re slighting others, too, and you feel badly about it — especially in her case.

MIKE CARO: Hopefully, she’ll tell you not to apologize and that she understands how hectic things must be in your life. If so, you won’t have to use any Plan B.

MIKE CARO: You should frequently look for opportunities to use similar life tactics. Make people who might otherwise be personally offended think that it’s not just happening to them. It’s happening to everyone. And you’re upset by it. Often that person will try to make you feel better.

AMY: That’s brilliant, as always! Thank you so much.

DEB: I think I’ll try that technique.

CAL: Me too.

BOB: Whatever.

Show us the turn card…

↑ FLOP ↑                 ↑ TURN ↑

↓ Our hand ↓	↓ Amy ↓	↓ Bob ↓	↓ Cal ↓	↓ Deb ↓
45% chance	11% chance	16% chance	0% chance	29% chance

Turn comments

Oh-oh. Now we not only have to worry about Deb connecting for a flush on the river, we have to withstand Bob’s newly found open-end straight try.

We’re in first place, but we would expect to win only 45 percent of the time. So, even now, we need to be lucky.

Amy can still win with four cards, by catching a king or a deuce. But Cal can only watch..

Number of winning river cards: 17 of 38 remaining

Turn table talk (while awaiting the river)

The silence signals the suspense.

We’re ready to ride the river…

↑ FLOP ↑                 ↑ TURN ↑    ↑ RIVER ↑

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

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

Results after 9 days

	Us	Amy	Bob	Cal	Deb
Wins	1	0	2	2	4
Result	-$4,000,000	-$9,000,000	+$1,000,000	+$1,000,000	+$11,000,000
Days since last win	2	—	1	3	0

Final poker words

Some players get upset when this happens. But it was more likely to happen than not. We had the best hand and lost. But a best hand usually loses. This is easy to understand when you consider that the player who had the best chance originally, the player who had the best chance after the flop, and the player who had the best chance after the turn — well, those usually aren’t the same player. And, if they’re not, some “best chance” is destined to lose.

Notice that when Deb hit her flush, Bob simultaneously hit his straight. If this hadn’t been a showdown, in which he already knew what Deb’s cards were, he would have liked the river.

After nine attempts, we’ve only won once, and Amy remains winless.

Final real-life words

So, let’s talk about Amy’s misery. I’m about to share something that could surprise you.

Although Amy is now feeling as if fate has singled her out for monumental torture, her winless streak isn’t so unusual.

Mathematically, losing nine of nine five-handed showdowns will happen 13.4 percent of the time. That means the real-life equivalent is that one in seven or eight people who surround you are having bad fortune like Amy’s right now! And, if it isn’t you, be prepared. Your turn is always around the corner.

The secret is to expect Amy’s luck to happen to you many times every month, but to realize that great breaks can occur at any moment. Your job is to make the best decisions whether luck is good or bad. It’s someone else’s job to decide who gets lucky. — 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

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