Random deal for 3♥ K♣ (2013-11-19, 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

Anatomy of today’s hold ’em hand

Category1: K-3 of mixed suits

Expected win rate2 vs. a random hand (heads up): 51% (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): 60 of 169

MCU4 ranking against many opponents (limit): 108 of 169

MCU4 composite ranking (limit / all situations): 90 of 169

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

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

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
Chance of winning
with this outcome
Straight flush 0.01% 97%
Four of a kind 0.13% 97%
Full house 2.23% 94%
Flush 1.96% 81%
Straight 2.34% 88%
Three of a kind 4.47% 79%
Two pair 22.7% 72%
One pair 46.2% No data1
No pair 20.0% 22%

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”).


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

Today’s $5 million showdown

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

You can treat it two ways: (1) as a substitute for astrology, signaling the kind of luck you can expect today; or (2) as amusement, like I do. Your choice.

Remember that — similar to real life — you only need to be lucky once in five days to break even. So, let’s ante $1 million and see what happens…

Today’s starting hands…

↓ Our hand ↓ ↓ Amy ↓ ↓ Bob ↓ ↓ Cal ↓ ↓ Deb ↓
24% chance 25% chance 14% chance 4% chance 34% chance

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

Starting hand comments

Notice that the chances add to 101 percent. That possibility is explained in the showdown notes at the bottom. What’s happening is that the chances are being rounded to the nearest percentage. In this case, we were 23.54 (became 24), Amy was 25.00, Bob was 13.52 (became 14), Cal was 3.84 (became 4) and Deb was 34.18 (became 34).

Now let’s talk about the hands. We have already theoretically made money! That’s because we have a 24 percent chance of winning, and we only need 20 percent to have a fair share (one in five). This means we should be able to find a buyer willing to take a risk on the outcome. If that’s you, raise your hand.

Nobody has a pair and nobody is suited. Only Amy has adjacent ranks, providing her with greater straight hopes than anyone else.

We hold the second-highest rank (a king). Our three is mirrored by Cal, but if a pair of threes wins, our kicker will rule. In fact, Cal’s eight is also outkicked, putting him in sad 4 percent territory. Deb’s ace is supreme, as a single ace always is in such situations.

Let’s see the flop…

↑ FLOP ↑

↓ Our hand ↓ ↓ Amy ↓ ↓ Bob ↓ ↓ Cal ↓ ↓ Deb ↓
4% chance 1% chance 1% chance 1% chance 93% chance

Flop comments

This is what a paired ace can often do to the rest of the players! The good news is that we’re in second place, still having about one chance in 25 of winning. To do that, we’ll need to see the board fill in with J-10 for an ace-high straight, with 5-4 for a five-high straight (which would only tie Cal), K-3 for two pair, K-K, or 3-3.

It isn’t pretty, but three players are in even worse situations.

Show us the turn card…

↑ FLOP ↑               ↑ TURN ↑

↓ Our hand ↓ ↓ Amy ↓ ↓ Bob ↓ ↓ Cal ↓ ↓ Deb ↓
24% chance 25% chance 14% chance 4% chance 34% chance

Turn comments

The turn provided us with a opportunity to make a low straight. All we need is to see a four as the river card. Unfortunately, that will only give us half a win, because we’ll split with Cal. So, we have a 5.26 percent chance of making our straight, but our chances — which actually reflect our share of the money — are only half that good.

But it’s even worse! There are two fours held in opposing hands.

At this point, Deb is the only player who can win the whole pot. Amy has no shot whatsoever. Cal can tie me, if we make straights. And Bob can tie Deb, if they make straights.

Obviously, we’re in better shape than Bob or Cal. How much better? Well, there’s not a card in the deck that can help either gentleman. They’re toast. So, it’s just our hand against the ladies. Good luck to us!

Number of winning river cards: 3

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

Our pre-opening results so far: -$2,000,000 in 2 days.

Final poker words

Two days, two million dollars lost. If you’re a typical worker in the middle class, this could turn into a problem if bad luck continues for another couple weeks.

Deb has now won both days and is $8,000,000 ahead. Each other player (including us) is down $2,000,000.

Final real-life words

Cheer up! It’s not like your pet goldfish died.

Tomorrow the sun will shine somewhere. — 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).

% 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.

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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