blind games [0,1]

A study of blind play.

SB is one chip. BB is two chips. The three chips
will be considered the pot's chips. All fold to
the blinds. This study will restrict itself to
fixed limit. Each players' choices will be initially
limited. The choices will be expanded as the study
processes.

1. SB will raise, bet or check at his turn to act.
BB can call or fold.

1.1. Each player has a stack of four chips. SB
open raises any two, meaning SB raises 100% of the
time. This is the same as a forced raise. BB may
call or fold.
There are 6 chips in the pot on BB's turn to act.
BB is getting 6 to 2 for his call. BB should call
with a LHS of 25 or higher.















SB's expected value of the game.
In the red area of the chart SB wins the blinds.
In the blue area SB loses two additional chips.
In the white the blinds chop the pot.

red= 1/4 X 3 = .75
blue= 1/4 X 3/4 X -3 = -.5625
white= 3/4 X 3/4 X 1 = .5625
SB's EV = 0.75

BB's EV

red= 0
blue= 1/4 X 3/4 X 6 = 1.125
white= 3/4 X 3/4 X 2 = 1.125
BB's EV = 2.25

SB's net EV is 0.75 minus his one chip blind.
His net is minus 0.25
BB's net EV is 2.25 minus his two chips blind.
BB's net is plus 0.25.

Conclusion: SB going all in blind against a
thinking BB doesn't work.

1.2 Each player has a stack of six chips. SB
open raises any two, meaning SB opens 100% of the
time. BB always calls. On the flop SB bets his
remaining two chips. BB may call or fold.
This is the same as both blinds are four chips with
the action starting after the flop. SB has a forced
continuation bet. BB may call or fold.
There are 10 chips in the pot on BB's turn to act.
BB is getting 10 to 2 for his call. BB should call
with a LHS of 16.67 or higher.

SB's EV

red= 1/6 X 5 = 0.8333
blue= 1/6 X 5/6 X -5 = -0.69444
white= 5/6 X 5/6 X 1= 0.69444
SB's EV = 0.8333
SB's net EV is neg 0.16667.

1.3 Each player has a stack of six chips. SB
open raises any two, meaning SB opens 100% of the
time. BB may call or fold. On the flop SB bets
his remaining two chips. BB may call or fold.
There are 10 chips in the pot on BB's turn to act.
BB is getting 10 to 2 for his call. BB should call
with a LHS of 16.67 or higher.
In this game the LHS values remain static. When
BB call prf BB will call on the flop.

SB's EV

red= 1/4 X 3 = 0.75
blue= 1/4 X 3/4 X -5 = -15/16
white= 3/4 X 3/4 X 1 = 15/16
SB's EV = 0.75
SB's net EV is neg 0.25

Conclusion: BB does better by folding hands with
LHS of under 25 prf. *In holdem no starting two
has a LHS less than 32.

1.4 Each player has infinite chips. SB open raises
prf and bets every street. BB forced call prf. BB
may fold on flop and calldown all bets.
18 to 10 for the calldown. BB should call with a
LHS of 35.714 or higher.

SB's EV

red= .35714 X 3 = 1.0714
blue= .35714 X .64286 X -13 = -2.9847
white= .64286 X .64286 X 1 = 0.4133
SB's EV = -1.5
SB's net EV is neg 2.5

Conclusion. This is a very poor strategy for SB.
BB can easily exploit SB by playing passively.

1.5. Each player has infinite chips. SB open raises
prf and bets flop. BB forced call prf. BB may fold
on flop and calldown all bets. SB may bet or check
on the turn/river. The turn/river is an 8 chip bet.
SB bets over 35.714 LHS. BB callsdown with over
35.714 LHS.

SB's EV

red= .35714 X 3 = 1.0714
blue= .35714 X .64286 X -5 = -1.148
white= .64286 X .64286 X 1 = 0.4133
SB's EV = -0.3367
SB's net EV is neg 1.3367

This is a clear improvement over continuely betting
hopeless hands. Maybe micromanaging SB's betting
points will improve SB's EV.

1.6. Each player has infinite chips. SB open raises
prf and bets flop. BB forced call prf. BB may fold
on flop and calldown all bets. SB may bet or check
on the turn/river. The turn/river is an 8 chip bet.
SB bets over 73.193 LHS. BB callsdown with over
35.714 LHS.















SB's EV

red= .35714 X 3 = 1.0714
pink= .26573 X .28572 X 11 = 0.83517
blue= .35714 X .64286 X -5 = -1.148
blue= .28572 X .26573 X -5 = -0.3796
white= .26573 X .26573 X 1 = 0.0706
white= .28572 X .28572 X 1 = 0.0816
SB's EV = 0.5312
SB's net EV is neg 0.4688

Conclusion: SB's EV has gone from -2.5 to -0.4688.
The real solution must be somewhere inbetween.
Either way opening any two with a raise has negative
expectation against anyone who defends his blind.

Note: It's not absolutely clear that my logic is valid.
The LHS of a starting hand remains constant in the [0,1]
game. In holdem the LHS changes with the appearance of
each new board card. Also starting cards catch a piece of
the flop from 32 to 40% of the time. With two unpaired
starting cards missing the flop can make the LHS value
drop drastically.

character set test

0

LHS PrF Starting Hands

Column A is the two hole cards.
Column D is for the hand space of a 10% preflop raiser.
Column E is for the hand space of a 20% preflop raiser.

The entry of the cells is the LHS against that space.

"Golden Mean of Poker"

http://groups.google.com/group/rec.gambling.poker/search?
q=&start=10&scoring=d&enc_author=2IMEHhgAAABIfsVGFKjfS-
anNRwnEVTLMxB39KJNQ76SLnMRgR9a0A&filter=0&as_drrb=
b&as_mind=1&as_minm=1&as_miny=2003&as_maxd=
31&as_maxm=1&as_maxy=2003&


This is from the [0,1]game series by Chen/Jerrod on
RGP. r is from part 3.

r=.414

r is the "golden mean of poker".

Use the reciprocal of r. Bet if your hand has a
linear hand strength(LHS) of .586 against your
opponent's range of hands. Range of hands sounds
so awkward. Will use hand space instead of range
of hands.
Square r, cube r and quad r for .171, .071 and
.029. The corresponding LHS are .829, .929 and
.971. You should raise with a LHS of .829.
Reraise with .929 and cap with .971.
This assumes both you and your opp are rational.
Both are trying to win. Also assumes neither
will fold.

In practice this isn't necessarily true. Many
opps fail to adjust to new info. Against these
opps you can and should often rebet your same
values.

Tom Weideman Challenge

It's time to reexamine the Weideman Challenge. This
challenge is for the specific case where each of two
players ante one unit. Tom and Cal are each dealt a
card from the line interval [0,1]. Tom is allowed to
bet one unit or check. If Tom bets Cal may call or
fold. This is essentially the same as betting half
the pot.

Tom should bet any card .7 or higher. Tom should
bluff .1 or lower. Cal should call .4 or higher.
Tom has a +EV of 0.1 bets.

Let's example other cases. Betting the size of the
pot. Now Tom should bet less often. Cal should call
less often. For Tom, bet .78 and bluff .11. Cal
should call .53. Tom has a +EV of 0.056 bets.

In fixed limit the bets will be much smaller than the
pot. Instinctively I tend to value bet less. This
is wrong. Value bet more often. Cal will be forced
to call more often due to the size of the pot. Tom's
bluffing frequency relative to his betting frequency
will be lower.

Note: the uniform [0,1] games now use low values as
the best values. This is a flip-flop from the
previous high values as best.

Linear Hand Strength(LHS)

Linear Hand Strength: This is a measure which ranks
your hand in the range of possible hands.
Specifically, all possible hands are evaluated,
and ordered, and the measure of the hand is the
fraction of all hands which it beats or ties. By
convention, this measure is mapped to a value in
the range [0,1].

I wasn't aware that there was a term for ranking
hands. So from now on linear hand strength will
be used to rank hands. But zero to 100 will be
used instead of [0,1]. All the odds calculators
give results in percentages. I will also use the
term LHS for preflop, flop, turn and river.

For on the flop each hand type will be given a
general LHS value. The flop is three small cards.
Each possible two overs will be given a LHS value
against various range of hands. Normally it's
worth calling a continuation bet with 35% or
higher.

I have started to compile a file of these values
in Excel. When it gets organized in some readable
form, the table will be posted on this blog.

Shifting gears

When Doyle Brunson coined the term shifting gears it was a sophisticated play only known to experts. Today all advanced players know the term and many know when to use it. Tomorrow, in the future, this will be a intermediate concept.
Shifting gears is so basic. One changes speeds on a one-dimensional line. Hold'em is much too complex for best strategy to be one-dimensional. Shifting gears should be an integral part of an overall strategy.
Shifting gears only cover your range of preflop starting hands. This set of hands was always a function of many factors. These factors include number of players on the table, relative chip stack sizes, stack sizes in terms in big blinds, your starting position, have others all ready entered the pot, styles of the other players, etc. and etc. This would suggests a strong player is shifting gears from hand to hand. Sometimes during a hand.
Phil Ivey was asked of his strategy starting a new tourney.
Ivey replied that he had no preplanned strategy. He would
observe the table and adjust.
There isn't a fixed relationship between the weighting of
the importance of each variable affecting the opening of
hands. When your chip stack is large relative to the big
blind you may choose among many opening styles. If your
chip stack is very small you are restricted to jam or fold.
You should be shifting gears from hand to hand.