Random deal for 2♦ 5♦ (2013-11-26, pre-opening)

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 often are posted soon after being dealt.
So, please let me know if you notice 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: 5-2 of same suits

Expected win rate2 vs. a random hand (heads up): 38% (50% is average)

Expected win rate2 vs. eight random hands (nine-handed): 10.6% (11.11% is average)

Odds against being dealt a hand in this category3: 330.5 to 1

MCU4 ranking against few opponents (limit): 152 of 169

MCU4 ranking against many opponents (limit): 136 of 169

MCU4 composite ranking (limit / all situations): 165 of 169

COPS5 units6 won or lost (limit / nine-handed): -0.20

COPS5 units6 won or lost (no-limit / nine-handed): -0.16

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
(final strength)
Chance of finishing
with this outcome
Heads-up win-loss
with this outcome
Straight flush 0.11% 100%
Four of a kind 0.13% 88%
Full house 2.22% 90%
Flush 6.48% 93%
Straight 5.37% 91%
Three of a kind 4.33% 65%
Two pair 22.0% 55%
One pair 42.2% No data1
No pair 17.2% 1%

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.


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.

→ 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.


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 ↓
16% chance 13% chance 15% chance 20% chance 37% chance

(Note: A 20 percent chance is average at all stages. Chances are rounded to the nearest percent and don’t always total exactly 100.)

Starting hand comments

There’s a lot to learn from this matchup.

I’d wager that I could show these cards to 100 players, even pros, and very few would estimate that Deb’s chances would be as high as they are. I mean, we’re talking about ten-five off-suit and here it is with the best chance of winning by a mile.

Deb even sees her five duplicated in our hand, making it harder for her to pair. The key to her surprising dominance is that, in this rare grouping, her ten is the highest rank present. Also working in Deb’s favor is the entanglement of ranks. Three players have doubly duplicated ranks, including us. Cal is the only player besides Deb to have only one rank copied — and he is rewarded with a 20 percent chance, enough for second place.

Bob has heart flush hopes, but he’ll need to see exactly three hearts on the board, not four or Deb will beat him with her ten.

And despite the fact that our hand is suited and in straight flush range, we’re only in third place by a whisper. If this hand can’t even come close to the 20 percent average against this sorry assortment of miserable hands, it’s no wonder why it costs so much money in real games when players get inspired and barge into pots with it.

Starting hand table talk (while awaiting the flop)

Not even a whisper today.

Let’s see the flop…

↑ FLOP ↑

↓ Our hand ↓ ↓ Amy ↓ ↓ Bob ↓ ↓ Cal ↓ ↓ Deb ↓
2% chance 5% chance 8% chance 68% chance 17% chance

Flop comments

We fell from 16 percent to two percent. We can’t even win with two running fives, because Deb would have us outkicked, or with two running deuces, because Bob would conquer us. We’d have to catch a five and a deuce to win with two pair or make an unlikely straight, if both final cards fit perfectly. And even then, only A-4 would give us the whole pot.

Cal has suddenly jumped so high that he has more than a two-thirds chance of winning. And yet, he only made a pair of sevens.

Flop table talk (while awaiting the turn)

DEB: What are you reading, Bob?

BOB: Just the weather reports from around the world. These idiots who don’t believe in global warming should see this. It’s almost December and it was 90 degrees Fahrenheit in Sydney, Australia.

CAL: It’s summer in Australia, Bob. They’re in the southern hemisphere. Right, Mike?

MIKE CARO: Well, actually, it’s winter in Australia, just like it is everywhere on earth. It’s just that winter is the warm season there. Summer is cold.

AMY: Mike, when you say summer is cold, you’re being a bit insensitive to Bob. We all want to save the planet, and it’s obvious we’ve got to do something about rising temperatures, no matter how weird things are in Australia.

BOB: You know what else is hot, Amy? It’s sitting in the seat next to me. And I don’t mean Cal.

DEB: Oh, for god sake, Bob. Give it a rest. She’s never going out with you. And global warming is a myth, as far as I’m concerned. Can we just deal some cards?

CAL: Wobbly science is what it is. Let’s ask Mike.

MIKE CARO: Coincidentally, I’m going to upload an entry regarding climate change soon to Poker1. It’s about pre-Columbian Aztec human sacrifice.

CAL: Huh?

AMY: What?

DEB: Huh?

BOB: Deal.

Show us the turn card…

↑ FLOP ↑                 ↑ TURN ↑

↓ Our hand ↓ ↓ Amy ↓ ↓ Bob ↓ ↓ Cal ↓ ↓ Deb ↓
12% chance 5% chance 18% chance 61% chance 4% chance

Turn comments

That gave Bob a lifeline, as he can now catch a flush. Cal remains firmly in the lead, though.

As for us, we’ve come from last place to third and now have an open-end straight draw. Unfortunately, only an ace will win the entire pot for us with a wheel — another name for a five-high straight. If we hit a six on the high side, we’ll tie Deb with a seven-high straight. And whether it’s an ace or a six, it better not be a heart or Bob makes a flush.

Number of winning river cards: 3 of 38 remaining (3 other cards will tie)

Turn table talk (while awaiting the river)

No one speaks now.

We’re ready to ride the river…

↑ FLOP ↑                 ↑ TURN ↑    ↑ RIVER ↑

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

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

Results after 10 days

  Us Amy Bob Cal Deb
Wins 1 0 3 2 4
Result -$5,000,000 -$10,000,000 +$5,000,000 Even +$10,000,000
Days since
last win
3 0 4 1

Final poker words

Sometimes you hold poker hands that aren’t what they seem to be. Today’s race illustrates the point.

If it weren’t a showdown situation, would Deb have looked at her 10-5 unsuited and thought that it was the best hand by a huge margin? Would anyone have liked his or her hand? Nope.

And yet Deb’s hand was ideal for the circumstance. It didn’t win, but it had a moment of glory.

Final real-life words

In life, too, you don’t always need obvious strength to have a compelling advantage. Always ask yourself whether everyone else who’s interacting might be in worse shape than you are.

Sometimes you’ll see opportunities you never thought you had. And you would have let them go to waste, had you not bothered to look. MC


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.


2 thoughts on “Random deal for 2♦ 5♦ (2013-11-26, pre-opening)”

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  1. Your concept is not logical for a real game, in other words, the computer is not folding hands that should be folded. One example, the first person to get a flush on the turn should always bet very strongly, my opinion. I am thinking if a player get a flush on the turn the chance of another player also making a flush is slim, I think. The player with the flush can still win the hand if opponent does also make a flush on the river. The first player to make a flush should worry about other player making a full or quad. Therefor, for player with the flush on the turn should go all in or five to nine bet.

    1. There is no betting in this example. It’s just a statistical analysis of projected outcomes. Also, I doubt that betting as large as you recommend after making a flush on the turn would be the most profitable choice in typical situations. However, your comment is appreciated.

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