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Multiple-player jam/fold w/44
I have spent too much time over the last week playing 1¢ hyper-turbo 990-player NLHE SNGs on Stars. They are somewhat interesting due to the multiple player preflop shoving.

The average hand shown down is almost exactly 75th percentile (by quantity, on the ProPokerTools scale).

Average winning hand is 78.49 percentile.
Average losing hand is 72.42 percentile.

44 performs very badly, winning 15% of the time. My parser tells me that there are an average of 2.4 players per showdown, which seems small to me. I'd expect 44 to win > 32% in these circumstances. I'm going to take another look at my parser---it may be screwed up, especially with the 2.4 pph figure.

I'm having a lot of fun with this--I haven't examined a hold em game in 5 years. If anybody has a bunch of stats or hand histories on these 1¢ SNGs, I'd enjoy hearing from you.

Swingo
As we all know, Swingo is the game for the 21st century.

As always, trying to make a rough map of unknown territory. Both charts depict the same data. Exposed cards are chosen randomly.

Hoffer quote
"You can discover what your enemy fears most by observing the means he uses to frighten you."

The above is a quotation from Eric Hoffer. I assume that I read it years ago and internalized it, eventually forgetting where it came from.

It's a good reason not to let slowrollers or other angle-shooters affect one's play at the poker table. To the detached observer, they are merely indicating what they fear.

Current Music: Paul Butterfield

Courchevel Tourney

I made it half way through, went on monkey tilt, crashed and burned.

Good game. Would have been better w/ 4 cards.

An aside: Same hands vs. opponent with top 20% of hands.
Here are some more ProPokerTools sims, with the same scenarios as the previous post, except the opponent is playing the top 20% of his hands.

We run Ts 8c 7s 6c with a board card of 7c against a random hand and get 70.03.

Vs. top 20% of hands: 64.15

And we run Ts 8c 7s 6c with a board card of 9c against a random hand and get 58.38.

Vs. top 20% of hands: 52.23

This is similar to what I got. Not let's add a second board card that pairs our hand:

Ts 8c 7s 6c with board of 7c, Th (2 pair) == 74.14.

Vs. top 20% of hands: 67.84

Ts 8c 7s 6c with board of 9c, 7h (pair and str8 draw) == 74.95! ZOUNDS! We've caught up.

Vs. top 20% of hands: 70.33

Let's give the key card a pairing T instead of a 7. Ts 8c 7s 6c with board of 9c, Th == 67.14.

Vs. top 20% of hands: 57.57

Now lets make the 'key' card off suit: Ts 8c 7s 6c with board of 9h, 7h == 67.82.

Vs. top 20% of hands: 62.32

Key Kard Kouchevel; a 4-card hand
I has been many years now that T876 double suited has been on my mind. Let's see how it plays out as a courchevel hand by examining Ts 8c 7s 6c.

The first thing I notice about Ts8c7s6c is that it has a "key card," a black 9. Why is a black nine key? It fills in the straight and in enables a flush, natch.

So heads up, what is the best flip card for Ts8c7s6c? Not a black nine, instead the 7c.

Here are the top fourteen flips, as per heads up sims of 100k.

7c       0.70238999999999996,
8s       0.70179000000000002,
6s       0.69030000000000002,
Tc       0.67323500000000003,
7d       0.63666,
7h       0.63663499999999995,
8h       0.63504000000000005,
8d       0.63325500000000001,
6h       0.62278999999999995,
6d       0.62105999999999995,
Th       0.60155999999999998,
Td       0.60128499999999996,
9s        0.58603000000000005,
9c        0.58023499999999995,

The top four flips are pairing cards that also enable a flush draw. The next eight flips are the pairing cards that are off-suit. Note that they are in the same order: 7, 8, 6, T. Apparently, having the *top* pair isn't the most powerful flip ... something else is at work here.

And then, after all the pairs are accounted for, come the 'key' cards.

Let's consult our old friend, ProPokerTools, and do some checking.

We run Ts 8c 7s 6c with a board card of 7c against a random hand and get 70.03.

And we run Ts 8c 7s 6c with a board card of 9c against a random hand and get 58.38.

This is similar to what I got. Not let's add a second board card that pairs our hand:

Ts 8c 7s 6c with board of 7c, Th (2 pair) == 74.14.
Ts 8c 7s 6c with board of 9s, 7h (pair and str8 draw) == 74.95! ZOUNDS! We've caught up.

Now for some simple math...

After the flip, there are 47 unknown cards, 35 of which don't pair us. So the odds of hitting a pair on the 2-card flop is

1 - c(35,2)/c(47,2) = ~.45.

So if we do hit a black nine, we got a 45% chance of having a +EV hand turn into a real player. (I know, I know, I'm not there yet, but I may actually be close to generating some useful information.)

Let's run some more sims...

Let's give the key card a pairing T instead of a 7. Ts 8c 7s 6c with board of 9s, Th == 67.14.
Not as good, and it confirms that pairing the Ten isn't so hot.

Now lets make the 'key' card off suit: Ts 8c 7s 6c with board of 9h, 7h == 67.82.

This would seem to confirm that having a semblance of a flush draw is nice.

To come:

Playing against a better range of hands.
Drawing to Draws, isn't that what poker's all about?
What's the deal with Tens, anyway?

Gettin' to the green line, a coupla HU hands from the left end.
The first chart in the previous post is for HU 5-card courchevel. The green topmost line is for the win% of the highest rated flip card.

Starting from the left, the first three plotted hands (with straight win%) are,

5c 4d 3c 2d 2h, (.386),
Tc 8d 3c 2d 2h, (.439),
7c 4d 3c 3d 2h, (.454).

As straight 5-card omaha hands (orange line), all of them are losers. But with play predicated on flip card selection, they may be winners. At the top of the chart, the green line plots the showdown win% with the very best flip card appearing on the board. The green line shows a nice little spike over the course of the first three hands, going from .608 to .615 to .812.

7c 4d 3c 3d 2h

What are these magic flip cards? Well for our high performer, 7c 4d 3c 3d 2h, there are ten flip cards that produce a > .50% showdown win rate. They are, 3s, 3h, 7d, 4c, 5c, 5d, 2d, 2c, 6d, 6c.

And these ten cards seem to be as they should. The first two, 3s and 3h, provide a set of treys. Both score in the .81 range.

The third card, the 7d, makes a pair of sevens and also enables a flush since the hand is double suited in clubs and diamonds. Its win% is down to .57 -- a pretty good drop.

The remaining seven flips are all flush-enabling clubs and diamonds that either makes small pairs, or enable a straight draw. The 2c made the list with a showdown win% of .52.

(Curious as to the flush-making power of flip cards, I changed the suitedness of the hand to 7c 4d 3h 3d 2c. This would allow for the 3c as a flip card which would both make a set and enable a flush. I was somewhat disappointed when the 3c as a flip card came in as .817, as compared to .810 for the 3s. I had expected at least a .02 improvement, but this may be because of the brevity of the sim. I may run it again for more iterations.)

And what's the lowest-performing flip for 7c 4d 3c 3d 2h?

9 of spades, at .332, but the 9 thru Q of bith spades and hearts are all in the same ball park.

Tc 8d 3c 2d 2h

What are the best flip cards for Tc 8d 3c 2d 2h? Since spiking a set did such good thing for a hand containing a pair of treys, I suspected a similar fate for a hand containing a pair of deuces. Alas! it was not to be.

There were nine flips with > .50 showdown win %s: Td, 8c, 2c, 3d, th, 8h, 8s, 9c.

The 2c came in third at .588, behind Td (pair of tens and flush draw) at .615, and 8c (pair of eights and flush draw) at .598.

The 2s missed the cut at .495, which now seems too *great* a drop for merely missing a flush draw, but the limited number of iterations of these first-go-through sims, 10k, probably explains a lot. In fact, until more extensive run are completed, these results shouldn't be considered as less than .05 accurate.

But it is interesting that a set of deuces doesn't carry much weight in 5-card courchevel, lagging behing a pair of tens and a pair of eights in winning potential.

And our biggest loser of a flip? King of spades at .316.

To be continued.

Gettin' Started

Current Mood: Twisting

Live session win streaks
I was reading Basketball on Paper, by Dean Oliver. In it, he talks about the concept of a player having a "hot hand," and offers some statistical tools for evaluating whether a "hot hand" really exists.

I've always thought that winning streaks existed in poker. I've always thought that winning sessions and losing sessions came in bunches. I further thought that if I booked a loss, I might be tilted for my next play, and therefore more likely to lose. I also thought that winning play begets winning play, and the longer I win, the more likely I am to continue winning. Alas none of the above is true.

In my never-ending, and largely futile, effort to organize my computer files, I have come across playing diaries from the 1980s and 1990s. These account for 1959 sessions. These are largely flop games and TD and SD draw games. Around 60% are pot limit, 30% limit, 10% no limit. I was playing a lot of stud back then, but stud games don't appear in this info.

Of the 1959 sessions, 1079 were winners, or 55%. 55% seems low to me, but is close to the prediction made by Chen and Ankenman in The Mathematics of Poker. 880 (45%) were losers. If wins and losses were evenly distributed, I would expect a loss to be followed by a loss 45% or 396 times. As it turns out, losses were followed by losses 359 times, or 37% of the time. Dunno what this means. I think I'll t-test it.

Chip abacus; tracking stats in live games
I'm going to post this here because I get asked about it every so often, and now I can just give people the link...

Chip abacus

This is fairly simple and I'll describe it step by step. Suppose I'm in a 10-handed hold em game and I want to track the number of players seeing the flop. It would be easy--all I'd have to do is have two Stacks of chips. Every time a hand was dealt, I'd put a chip in Stack A, and every time we saw a flop, I'd put chips in Stack B equal to the number of players seeing the flop. After a 100 hands, I would have 100 chips in Stack A, and, let's say, 340 chips in Stack B. So I am playing a game where an average of 3.4 players see each flop.

But all those chips would be cumbersome, so let's streamline the process. I know I'm at a 10-handed game, so instead of marking each hand with a chip, I'm going to mark each ten hands with a chip every time the button is on the #2 seat. If player 7 walks and misses a hand, I note it and wait until the button is on the #3 seat to add a chip to Stack A. So now when I get to a hundred hands, Stack A will have ten chips in (actually, it is more likely it will have two 5$ chips, since I color up).

As far as Stack B goes, I'm going to eyeball the game and estimate that maybe 3 people are seeing flop every hand, and set 3 as a benchmark. If four players see the flop on the first hand, I will only put 1 chip on Stack B since I am one over my estimate. If on the second hand five players see the flop, I add 2 chips to Stack B. If on the third hand no players see the flop, I remove three chips from Stack B, leaving none.

At the end of the same 100 hands, Stack A will have ten chips, and Stack B will have forty, but the results are the same. Stack A represents 100 hands. Stack B represents 100*3+40=340 players seeing the flop.

Going back to the game, after the third hand, we had no chips in Stack B. Suppose that no players saw the flop on hand four. We have to remove 3 chips from Stack B, but there are none there. What I usually do is have a marker chip for each stack. If the game is played with reds and whites, I'll use a red marker chip for B. After the first hand I put one white under the red. After hand 2, I put 2 more whites under the red. After hand 3, I remove the whites. After hand 4, I put 3 whites ON TOP of the red. If five players see the flop on hand 5, I remove two whites. And so it goes until I'm back in positive numbers.

Using marker chips is also handy because I often place Stacks on top of each other, and they keep the piles delineated.

If I want to track the average pot size, I use the same system. One chip in Pile A for each round. First, I estimate the average pot size. If it is $100, and the first pot is $120, I add $20 to Stack B. The bigger the game, the more rounding I use. Perhaps in this case I might add just one chip representing $25 to stack B.

Let's say I want to track each player seeing the flop. I'll start with a stack of ten red chips, numbered from top to bottom 1 through 10. If on the first hand, Seats #1, #3, #4, and #5 see the flop, I'll put a white chip under red chip #s 1, 3, 4 and 5. I color up the counting chips in a way that keeps the players clearly separate. It's nice when games are played with a large variety of chip colors as it helps in coloring up and keeping categories straight.

Almost anything can be tracked this way: Bluffing frequencies in razz, rake, buy-ins by player, opening standards, etc., etc. etc.

Notes:

I adapted/stole this system from John Fox.

After you use this system for a while, you'll find that it teaches you to keep the tracked info in your head, and you'll need it less.

Others constantly tell me that I have dirty stacks. Yes, I do.

I once used the system to track how much a dealer was stealing from a game. Later, the house man told me that he thought the dealer was swiping about $100 a night. My response: “$187.”

Current Mood: Running good

Architectural question
Public buildings often have inscriptions above their entryways. Is there a technical name for these inscriptions?

PS: I'm thinking of running a contest to suggest an inscription for the as-yet-to-be-built George W. Bush Presidential Library.

PPS: "Mission Accomplished" is too easy a shot.

Multi-card omaha high nutness
Test post. Graph may have problems. Operator may have hangover.

I am just playing with uploading graphics. Chart shows the "Nutness" of winning hands for showdown sims of 4- 5- and 6-card omaha with 2 to 7 players. Although O8 boards only allow 10 degrees of the nuts, for high hands I captured the top 20.

Interesting is the spike in frequency for winners with the eight-nut high. This spike doesn't disappear until it is seven handed with 6-card hands. I suspect it is due to the transition from flushes to straights on flush enabled boards, but frankly, I don't really have a clue.

I don't think I have any omaha sims with intelligent agents, but this spike might be fun to investigate.

Hope to have some better graphs up as soon as I figure out wth I'm doing.

Happy New Year!

Current Mood: groggy

Big Mitt; nutness of winning lows
Here's some stuff I found while rummaging through an old hard drive. Ten or fifteen years ago 5-card omaha, played NL or PL, was the premier big-money game in certain parts of the States.

Below are some comparisons of the nutness of winning lows in 4-, 5-, and 6-card omaha games with an eight qualifier. (I'll post the high nuttness soon.)

Current Mood: optimistic
Current Music: some french chick

Gary Snyder
P 211

I suspect that primary peoples know that their myths are somehow "made up." They do not take them literally and at the same time they hold the stories very dear. Only upon being invaded by history and whipsawed by alien values do a people begin to declare that their myths are "literally true."

Current Mood: testing
Current Music: Temptations

New Years Resolution - part 1
Several situations allow for the deployment of a designated heads-up strategy in poker:

    •    Tournament games with accelerating blind and ante structures that have played down to two players.

    •    Games with restricted seating, usually online games, that have only two players.

    •    Live full ring games that are just starting up, or are winding down, that have two players, or few enough players of a type to allow heads-up play.

    •    Live heads-up matches, often the result of challenges. These challenges are often played quasi-tournament-style as 'stacks' or 'freeze outs'.

My favorite way to play heads-up is after a full ring game has played down to two, or a few, players. Generally, at such time, the remaining players are either stuck or are compulsive gamblers. Also, by the time a game gets to this state, I have observed my opponent's playing styles while at the same time had the opportunity to exhibit a style of play that will mislead them as to how I play heads-up or shorthanded.

Another opportunity to play shorthanded presents itself when games are starting up. During a slow period, a card room may be willing to start a game with just a few players. Sometimes waiting players will propose that the game be played with reduced blinds, or reduced antes and bring-ins. These suggestions can be vetoed, thus discouraging tight players from joining and leaving a small cadre of gamblers who *may* provide opportunities for heads-up play. The downside to this type of game is the limited opportunity to evaluate my opponents, and the limited opportunity to establish an image that will allow heads-up situations. Still, starting up a game may provide opportunities for heads-up play.

My second favorite heads-up scenario is the challenge match. I get to play these fairly frequently -- I think because I look old and extinguished. I usually reach an agreement on how much money to lock up, then say something like, "Since I was challenged, I should get to pick the game. But to be fair, I'll nominate two, and let you pick the one you like." Usually the kids who want to play me heads up are young internet players, and this may their first hint that we won't be playing hold 'em.

What makes for a good head-up format?

Current Music: Live at Reykjavik

Fan-Boy post
Here are some animated graphs by Michael Ogawa and Kwan-Liu Ma of Vidi at U.C. Davis:

Python Developmental History:

http://www.vimeo.com/1093745

And Stargate:

http://vidi.cs.ucdavis.edu/research/videos/stargate

A357
A more conventional selection by the full ring player:

HU O8 -- Why I love it

Current Mood: Fatalistic
Current Music: IZ

Name that spike!
Here are some charts of winning hand distributions for two heads-up matches and a ten-handed match. Hands are charted by their ranking (1= straight flush, 7462 = 75432). 100k showdown sims. Note the weird spike. The spike denotes the same hand (#1600) or group of hands on all three charts. Also note the blue and orange color scheme in honor of the Mets acquisition of Santana in the off-season. Not only will we be getting 20+ strikeouts per game, but some amazing guitar solos as well.

This is all old data, I've been curious about the distribution of winning hands, and this is the stuff I had on my hard drive. I may get completely sidetracked and post some data for a wider variety of games.

Here is the same data, but with the tops of the charts chopped off. I wanted to look at the majority of the data, but saw no reason to use a log scale.

Now to figure out how to weight the hand occurrences. I've been thinking about the linearity and distribution of poker hands for several decades, and think I may be near an elementary understanding.

Current Mood: watchful
Current Music: Sonny Boy II

Wrong again
I had an epiphany while riding my bicycle yesterday. As with so many of my brilliant flashes of insight, it turned out to be wrong.

When I started running omaha sims a few years back, I didn't have the computing power or knowhow to run massive examinations of all 16k+ distinct omaha hands, so I came up with a system of simming 1365 double-suited hands, then simming 1365 rainbow hands with the same ranks, then assuming that I had the vast majority of omaha hands bracketed.

Lately I've been playing with second-best and true-inversion games, including lomaha, a true-inversion game based on omaha. Without giving it much thought, I'd assume that I would look at rainbow hands, and then double-suited hands, and have the universe of lomaha hands surrounded.

The insight I had yesterday was this couldn't possibly work, that having a lomaha hand be double-suited would make it so powerful that it's sim results wouldn't correlate to its rainbow brethren. This turned out to be wrong, probably because a double suited hand makes a flush only ~12% of the time. Here are some winning %s for lomaha hands, sorted on the lomaha rainbows, with the same hands double suited, along with the same hands played in omaha high.

Just glancing at it, the difference between rainbow and DS seems the same for lomaha and OH.

I think I'll capture some more info as to what final hands these starting hands make, and what they win and lose with. I also think I'll look at some 10-handed showdown sims...the L DS line seems to flatten a bit towards the winning end.

Current Mood: Beery
Current Music: Joe Jackson