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Apr 30, 1997, 3:00:00 AM4/30/97

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I just lost a match to some kid from NYC in the Limited Jackpot,

quarter finals. The match was to 17 and the winner got $4800 with the

finals then worth $11000+ to the winner. I got notta.

The kid's name was Abe Mosseri. He was good, but lacked tournament and

match experience. When I doubled, he told me that at the club he

played at in NYC the position was nearly a beaver. If you use Jelly's

evaluation function, you get 50.0 wins for each side, so he would

almost be right. If you roll the position out using level 5, things

look better for me. Cubeless I win 51.7% and get 6.4% gammons vs. 1.5%

gammons for Abe.

So by now you're dying to see the position, so here it is:

| | | X | | O | | | | X | X | X | X | X |

| | | | | O | | | | X | X | X | X | X |

| | | | | | | | | | | X | X | X |

home boards >

| | | X | | | O | | | O | O | O | O | O |

| | | | | | | | | O | O | O | O | O |

| | | | | | | | | | | | O | O | |2|

Here are the rest of the facts:

Abe is X and he leads 10-6 in the 17 point match. I am O and I have

the cube on 2. It is my roll. Abe has 61 pips to go and I have 74. My

doubling window opens at 45.6% (.456). His take point is .277. So I

passed the window test. But its not often you should double toward

the short end of the window. So let's look at what is likely to

happen.In a non contact race with these pips, I only win 31%. However,

there is contact. He has 2 blots and I have 16 shots. I let Jellyfish

play 1296 games on level 5, and left the settlement value at .550.

If I hold the cube I win 57.6% and we both get 1.3% gammons for a

positive equity of .153

If I double he's not going to get to redouble me even when I miss.His

redouble window to 8 doesn't open until he is an 83.6% favorite. So I

gave Jellyfish him the cube and rolled it out again using my take

point (9.8%) to figure the settlement value, I used .804 (his 90.2%-

my 9.8%). What I got was 50.3% wins for me with 6.9% gammons vs. 1.0%

gammons for him. My equity is .066. If you multiply that by 2 (cause

the cube is twice as high) you can compare .132 to the equity of not

doubling = .153. Looks like its not a double by 2%.

However, let's look at what happens in this position:

By not doubling, If I hit and don't get hit back, I lose my market by

a mile but not quite enough to play for the gammon, though in all

cases I have a single or double shot at the other blot. If I roll 6-6,

5-5 or 4-4, those 3 rolls even out to an even race. If I miss, he

can't double back unless he makes a big mistake, and I'm likely to get

at least 1 more indirect shot, maybe 2 and maybe another direct shot.

If I do hit a shot on my first roll, I have to give him a few returns

unless I roll 1-1 or 2-1. I'm almost certain to have a direct shot at

another checker if I don't get hit back. How would Jellyfish play

this? Would he minimize returns and double if missed? I tried hitting

with a 2 and playing a 6 from the 17 point to the 11 point leaving 4

return hits, but leaving me 22 shots at the 2nd checker if he fans.

Jellyfish thinks this is a double, pass, but I would roll on for the

gammon, of which Jellyfish thinks I get 14% if I play on.

So I think I can play this position better than Jellyfish. And the

complications give my opponent a chance to make a mistake. What if he

redoubles when he is only 75 or 80%?

And what if I pull off the gammon on 4 and take the lead in the match

14-10? That might have a devestating effect on the opponent,

especially since the dice had been all his the whole match.

So the way I saw it, the cube was nearly dead, and if I hit, I would

hate to own the cube still when I was shooting at the 2nd man.

Oh, you want to know what actually happened? I rolled 3-1, my worst,

and he rolled 6-6, his best. I rolled another crap number, he doubled

and I passed. (my equity in the game was down to 3%). So much for a

dead cube!

ZZyzx

"Me, indecisive? I'm not so sure about that."

Apr 30, 1997, 3:00:00 AM4/30/97

to

For anyone (like me) who found Harry's position impossible to read, here

is a hopefully more readable reconstruction:

+13-14-15-16-17-18-+---+19-20-21-22-23-24-+

| O X | | O O O O O |

| X | | O O O O O |

| | | O O O |

| | | |

| | | |

| | | |

| | | |

| | | |

| | | X X |

| | | X X X X X |

| O X | | X X X X X |[2]

+12-11-10--9--8--7-+---+-6--5--4--3--2--1-+

May 2, 1997, 3:00:00 AM5/2/97

to

zzy...@earthlink.net wrote:

+13-14-15-16-17-18-+---+19-20-21-22-23-24-+

| O X | | O O O O O |

| X | | O O O O O |

| | | O O O |

| | | |

| | | |

| | | |

| | | |

| | | |

| | | X X |

| | | X X X X X |

| O X | | X X X X X |[2]

+12-11-10--9--8--7-+---+-6--5--4--3--2--1-+

: Here are the rest of the facts:

: Abe is X and he leads 10-6 in the 17 point match. I am O and I have

: the cube on 2. It is my roll. Abe has 61 pips to go and I have 74. My

: doubling window opens at 45.6% (.456). His take point is .277. So I

: passed the window test. But its not often you should double toward

: the short end of the window. So let's look at what is likely to

: happen.In a non contact race with these pips, I only win 31%. However,

: there is contact. He has 2 blots and I have 16 shots. I let Jellyfish

: play 1296 games on level 5, and left the settlement value at .550.

: If I hold the cube I win 57.6% and we both get 1.3% gammons for a

: positive equity of .153

This is a very complex problem, due to the potential of doubling later if

you hold the cube. Here is how I would work it out at the table, using

as much simplifying assumptions as possible.

First: Using Neil's numbers (which give a close approximation of my

match equity table):

6-14: 10% equity

6-12: 20% equity

8-10: 39% equity

10-10: 50% equity

So if it were a now or never situation you would be getting 11 to 10 odds

on the double. However it isn't a now or never situation -- if you hold

the cube, you may get to double later and win some games which might

have been lost if you had to play them to conclusion.

First simplifying assumption: I assume that O will never redouble to 8

(since he can't redouble except as a huge favorite, this isn't far off).

Let's suppose that X hits a shot. If he doesn't double, I assume he

always wins the game, since unless O rolls a joker X will be able to

claim with the cube next turn. This doesn't take O's jokers into

account, but they are somewhat counterbalanced by the potential of X

playing for, and getting, a gammon when O flunks.

If X does double and hits a shot, he has to play to conclusion. I

estimate that X will win 88% of the time when this happens (actually I

think it is a bit lower, but to compensate X will win a few gammons).

Let's suppose that X misses. He is a clear underdog, but has some racing

and some hitting chances. Also, he will clearly win more often if he

hangs onto the cube, since he may get an efficient double later and not

have to play to conclusion a game he might lose. I will guess that X

will win 35% of the time if he let's the cube go, and 40% of the time if

he hangs onto the cube.

So, what does all this mean? Roughly speaking, it looks like about 1/8

of the games X would win if he hangs onto the cube will turn into losses

if he doubles.

How does this figure into the match equities? If X loses a game he would

have won if he hadn't doubled, this costs him 29% equity (difference

between 39% and 10%). Thus, of the games X would have won if he hadn't

doubled, he gains 11% 7/8 of the time and costs 29% 1/8 of the time.

This comes to an average gain of about 6%. As we have seen, X loses 10%

if he doubles and is wrong. Thus, when we take the cube value into

account it looks like X is actually giving 10 to 6 odds with his

redouble. He clearly isn't close to being worth this in this position.

So, if you accept my estimates, the redouble is incorrect. Of course my

estimates may well be quite wrong, and different estimates might lead to

a different conclusion.

Kit

May 9, 1997, 3:00:00 AM5/9/97

to

>zzy...@earthlink.net wrote:

>

> +13-14-15-16-17-18-+---+19-20-21-22-23-24-+

> | O X | | O O O O O | score:

> | X | | O O O O O | X 11-away

> | | | O O O | O 7-away

> | | | |

> | | | | X on roll.

> | | | | Cube decisions?

> | | | |

> | | | |

> | | | X X |

> | | | X X X X X |

> | O X | | X X X X X |[2]

> +12-11-10--9--8--7-+---+-6--5--4--3--2--1-+

>

This is a very interesting, instructive, and potentially controversial

position. The match score weighs heavily, and market losers abound.

My news server rolled off the original post before I got a chance

to reply. But I seem to remember several things, not all of which are

obviously true. Something like:

1) O is a young, cocky New Yorker;

2) X is unlucky;

3) O says this is a money beaver;

4) X thinks s/he plays better than Jellyfish.

I think I'll stick to the position at hand (but will comment on

point 3, also). Kit did an "over the table" analysis and concluded that

X should hang onto the cube for at least one more shake. With pencil,

paper, and Jellyfish, I come to a different conclusion.

Here is the JF v2.01 level-6 cubeless rollout result:

total g+bg bg

X wins 52.0 6.5 0.2

O wins 48.0 1.6 0.0

1296 trials (equivalent to >32000 at level 5). X's cubeless money

equity is +0.090 and the standard deviation is 0.005 (in equity units).

According to Rick Janowski's semi-continuous money cube model, at these

gammon fractions O's beaver point is 45%, so this would be a money beaver,

but that isn't very relevant, since this position occurred in a match with

a skewed score and the trailer already owning a 2-cube.

Let's take a look at the the drop/take decision first:

decision and outcome O's resulting O's match

score winning chances

O passes -7, -9 0.61

-------------------------------------------------------

O takes and wins simple -3, -11 0.90

O takes and loses simple -7, -7 0.50 }

} = 0.47

O takes and loses gammon -7, -3 0.25 }

By taking, O risks 61 - 47 = 14% to gain 90 - 61 = 29%. So O's take

point is 14 / (14 + 29) = 33% ASSUMING NO CUBE OWNERSHIP EQUITY.

If O takes and turns the game around, where is X's subsequent drop/take

line? Since the corresponding 8-cube, if accepted, could put O over the

top, X would certainly reship to 16, so the game would then be for the

match. Dropping the 8-cube would leave X with a 10% chance in the match

(complement of 90% number above--score of 11-away, 3-away) so that would

be X's drop/take line, which is 90% from O's point of view. Thus WITH

A PERFECTLY EFFICIENT CUBE O's current take point is lowered by 10% from

33% to 30%. Applying the 70% rule (go 70% from 33% down to 30%) to

approximate REAL CUBE EFFICEINCY gives us O's take point--31%.

Clearly O has a take in this position. Does X have a double? We

first look at X's doubling window opening point (also known as the last

roll doubling point--assuming cube now or never).

X loses score X's MWC X wins score X's MWC

X never simple: -11,-5 19% } simple: -9,-7 39% }

doubles } 19% } 40%

gammon: -11,-3 10% } gammon: -7,-7 50% }

X doubles simple: -11,-3 10% } simple: -7,-7 50% }

now (O can't } 10% } 53%

redouble) gammon: LOSE 0% } gammon: -3,-7 75% }

(NOTE: final percentages are proration of simple and gammon wins, which

don't affect the numbers when O wins since O captures very few gammons.)

X risks falling from 19% to 10% by doubling, but stands to go from 40%

to 53% if the gamble works. So his/her doubling window opens at

(19 - 10) / [ (19 - 10) + (53 - 40) ] = 41%

Clearly X would have a "last roll double" (X is in the doubling window)

but, is the double correct? Are there market losers? Hit followed by wiff

(16/36 * 25/36 = 31%) are certainly BIG market losers (JF level-7 evaluation

says X will win 85-90% of these). This argues rather strongly for a double.

Can we find other evidence? Yes, by using JF level-5 CUBEFUL rollouts.

Here, though, we must CAREFULLY choose the settlement limit. (For those

unfamiliar, JF will allow a player to cash if above the settlement limit

and on roll, with minor "too good to double--play for gammon" situations

which shouldn't be particularly relevent here).

If X doesn't double and then misses the shots, we can assume that

there will be no gammons (not 100% true, but pretty close) in which case

O's drop point becomes about 26% (settlement limit is 1 - 2*0.26 = 0.48).

(The motivated reader should calculate this drop/take point.) Note that

if X hits and O fans, s/he will have a cash, so this settlement

limit will work for that case as well. If X DOES double then O will cash

a 4-cube at 90%, so the settlement limit in that case is 0.80. Here is

what JF v2.01 level-5 CUBEFUL rollouts give for these two situations:

Case 1: X owns cube and can cash at settlement limit = 0.48. (Cube remains

on 2 for all cases.)

outcome branching X's MWC product

fraction

X wins simple 0.570 0.39 0.222

X wins gammon 0.012 0.50 0.006

O wins simple 0.401 0.19 0.076

O wins gammon 0.017 0.10 0.002

------------------------------------------------

totals 1.000 0.306 (= X's MWC)

Case 2: O owns 4-cube and can cash at settlement limit = 0.80.

outcome branching X's MWC product

fraction

X wins simple 0.441 0.50 0.220

X wins gammon 0.059 0.74 0.044

X wins bg 0.002 1.00 0.002

O wins simple 0.489 0.10 0.049

O wins gammon 0.009 0 0

------------------------------------------------

totals 1.000 0.315 (= X's MWC)

(Note that even with these very conservative cube handling restrictions,

O is almost even at money play owning the cube. This is further evidence

that this is a money beaver.)

Thus level-5 cubeful rollouts favor doubling now, giving X about

1% more match winning chances than by holding. Did we make assumptions

that may have skewed the outcome? Jellyfish cubeful rollouts have a

couple weaknesses. 1) The cube owner is forced to lose his/her market.

2) The decision to cash or play on for gammon ways heavily toward cashing.

Both of these simplifications hurt the "hold" case, meaning that the

above 0.306 number should be a bit higher. In addition, forcing O to

hang onto the 4-cube until the game is a lock also means that the 0.315

number should be slightly smaller. All of this argues for an even closer

decision than was just indicated.

On the other hand, with the cube on 4, X should play more aggressively

for gammons than at money play. (risk::gain is 8::5 instead of 10::5 at

money play.) Thus JF, which makes it's decisions for money play, is

actually not playing optimum strategy. With the cube on 2, however, the

ratio is 20::11, and thus closer to money play. This fact says that the

0.315 MWC (cube on 4) should be a bit higher.

Finally, what if O misplays the cube? It is conceivable that some

O's will pass the 4-cube, suffering from gammon-phobia (2 blots). Also,

even if O takes, some may wait too long to redouble (although it's hard

to lose much here, since 90% is O's cash point). O may also misjudge

the position if X waits to cube (and possibly gives O a more pressurized

choice).

My conclusion is that X should double, but it is very close.

Chuck

bo...@bigbang.astro.indiana.edu

c_ray on FIBS

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