Game 5, move 2 : Bltzxz 6-2

[diane]

Blitzxz, white to move 6-2

4NvBASSYc8wBMA:MAGrACAAGAAA

[blitzxz]

First of all I wouldn't have doubled even though I was not given chance. But it can't be awfully far away. Because of the score I'm eager to double when ever there is even slightest chance for gammon.

The move is tricky. In normal score or gammon save I would move 24/16 without thinking at all, but in this score I really want to hit. But it just doesn't look very balanced move. There is not very good chance that my blitzing plan will work and it looks like I might get stuck behind the prime if I don't move my back checkers. But any way I move 11/3*. Safe playing just doesn't suit to my mind set right now. If the forum doesn't hit me and doesn't anchor to high point, I will want to consider doubling.

[diane]

Doubling is a good point - and always difficult to manage from my end of things.

If you can keep an eye on the forums move threads - once the voting has closed [1 day], you can see the move picked by the forum - it would help me if you could post your cube action on that thread for me to pick up when I come to move the match along.

I guess the same could apply top the forum - if any player feels they might like to cube after you have posted your move, that would be a good time to mention it.

[diane]

But it can't be awfully far away. Because of the score I'm eager to double when ever there is even slightest chance for gammon.

Well, we have some time to kill - how about we spend some of it running through where on earth this cube comes from.  I see people do it all the time, and I still do not get it.

I get the 2pt match cube.  I get why the Forum has the 'deep take', as donz always described it,  at this score.

But I dont get why someone 3 down would kill the cube early on.

I can never really put all this into 'bg speak', so I will do my best with the random thoughts that wander through my head...

Forum has the 'deep take', so why double early - I might as well wait a moment or two and see if gets a weeny bit better - as they will still take.

I would rather go to 2 away 2 away, than potentially chuck the whole match on a very slight advantage

hmm, those are my main thoughts...so - I shall sit back and wait for the real maths to start flying...or for the bemused replies...

[dorbel]

Thanks diane, let's sort this one out, because I know that many people will find it instructive. let's start with this.

I get why the Forum has the 'deep take', as donz always described it,  at this score.

A deep take is one where you can take with less than normal game winning chances. Leading 2-away, 3-away, one actually needs more than normal, 27% in games where there is no gammon. How is this calculated?
In any gambling situation, one needs to do a risk/gain analysis to see whether or not a bet is a winner or a loser.
In a backgammon game for money this is quite easy in a game where there is no chance of a gammon. If you pass, you lose a point. This is the baseline. If you take and lose, you lose 2 points. By taking, you RISK 1 extra point. Instead of being -1, you are -2.
If you take and win, you GAIN 3 points, because instead of being -1, you are +2. We can use this information to determine the winning chances that we need to make a take correct by doing a RISK/GAIN analysis and the formula is RISK/RISK + GAIN. In our backgammon game this is 1/1+3 =1/4 = 25%. In a backgammon money game, that is the winning chance that you need to make a take correct, in a game where there are no gammons. Note that this is the CUBELESS winning chance that you need. If the game still has a long way to go, then owning the cube will win you some games later so in practice we can take with a little less in games where the cube is said to be LIVE, sometimes with as little as 21.5% and in one unique position, 18.75%!

We can also apply this risk/gain analysis to cube decisions in matches. Let's look first at the score where we lead 2-away, 3-away. If we are doubled in a pure race, then if we pass we will be 2-away, 2-away, or 50% of course. If we take and lose, we will trail 1-away, 2-away Crawford. At that score, match equity tables show that our match winning chance will be 31.5%. (I have used Snowie's ME table here). Thus taking involves a RISK of 18.5%, the difference between passing (50%) and take/lose (31.5%).
If we take and win, we win the match and go to 100%, so our GAIN is 50%, the difference between pass (50%) and take/win (100%).
RISK/RISK+GAIN in this case 18.5/18.5 + 50 = 18.5/68.5 = 27%. We need 27% cubeless to take a gammonfree cube at this score, considerably more than usual.

Now let's address diane's original query, which is why should the trailer be doubling aggressively when there is some chance of a gammon? There are three factors in play. The first is that by doubling, the trailer kills the leader's gammon threat. With the cube on 2, the leader's gammons are now worthless. The second is that the trailer makes his own gammon threat stronger. An undoubled gammon takes him to Crawford, but a doubled gammon wins the match. The third is that doubling kills the cube, the leader can no longer use the cube if the game goes his way later.
To see why these factors skew the cube decision, imagine playing a money game, where after a double and take, you aren't allowed to redouble, you aren't allowed to win a gammon, but you can lose one! Not nice eh?

We can do a risk/gain analysis to decide when to double as well and if you really want to see some numbers, it is possible to factor in gammons too. However, take it from me, trailing 3-away, 2-away, the trailer wants to get frisky with the cube when there are gammons about and the leader wants to be wary of taking. Even when there are no gammons, the trailer will be doubling earlier than usual because as we have seen, the leader must pass earlier than usual and the trailer will be anxious to avoid losing his market. When there are gammons about and you are the favourite in the game, ship it in! Even if it is wrong, it won't be wrong by much. No need to overdo it though, you don't want to make the take trivially easy, just "not-quite-sure" is good enough.

[diane]

Thanks dorbel, but I confess, I am not finding that easy going.  At this point , I understand so little, that I am not sure how to ask for clarification.

I will swill it around in my head for a while, and see if I can get to a place of more understanding, or at least understanding what I dont understand. 

[dorbel]

Fair enough. I have encountered so many chapters like this and they just don't go in first time. They need several readings and of course in some cases they need re-writing. Try it bit by bit. Read down until you get to where it says 18.75%, which just explains how we do it in a money game. If you can get that bit weighed off, we can go onto the next bit. I'm quite happy to spend a lot of time on this, because I bet that 90% of fibsters don't have an entirely firm grasp on how this is done. If the way that I've put it isn't clear, I'll rewrite it until it is.

[ah_clem]

One salient point about this match score is that our take point is rather high.  34% according to this table of market windows http://www.bkgm.com/articles/mpd.html#market_window_table .  So, if blitzxz waits until he's 66% GWC, he's waited too long.  His doubling window is rather small, so there are more market losing sequences.  This means that it's correct to ship the cube much earlier than usual.

But that's not the whole story.  The way gammons play out is very different depending on the cube value.  Let's assume that we have a 40% GWC and that there are 20% gammon chances on both sides.  We can calculate our MWC as follows:

Spoiler

3-2 in match to 5
60% GWC for trailer  20% gammons on both sides

No Double

.2 win gammon -> 5-2 -> MWC = 1.
.2 win single -> 4-2 -> MWC = 0.75
.4 lose single -> 3-3 -> MwC = 0.5
.2 lose gammon -> 3-4 -> MWC = 0.3

MWC = .2(1) + .2(.75) + .4(.5) + .2(.3)
   = .2 + .15 + .2 + .06 = .61

Cube at 2

.2 win gammon -> 7-2 -> MWC = 1.
.2 win single -> 5-2 -> MWC = 1.
.4 lose single -> 3-4 -> MWC = .3
.2 lose gammon -> 3-6 -> MWC = 0.0

MWC = .2(1) + .2(1) + .4(.3) + .2(0)
   = .2 + .2 + .12 + 0 = .52

[close]

At most match scores pushing the cube at 60% GWC is premature. But here we see that double-take increases blitzxz's match equity from .39 to .48.  As Dorbel said, with the cube at 2, gammons become particularly valuable for the trailer, and worthless (marginally, vs a single point win) for the leader.

Of course, I can't do all this math over the board, and can't even accurately estimate gammon chances.  But the thing to remember at this match score as the trailer:

• Your doubling window is narrow, so cube earlier than normal
• If it looks gammonish, push the cube

Oh, and by the way, I'm one of the 90% that doesn't have a firm grasp on this.

[dorbel]

Oh, and by the way, I'm one of the 90% that doesn't have a firm grasp on this.

Then you won't mind me correcting a mistake I hope.

One salient point about this match score is that our take point is rather high.  34% according to this table of market windows http://www.bkgm.com/articles/mpd.html#market_window_table

Either you have misread the table or it is wildly wrong. The point of last take for the leader at this score, as demonstrated in my post, is 27%. 34% is just wrong.
I personally can't make head or tail of the figures that you have posted under a spoiler. This is because I don't ever think in terms of game equity. I know that there are people who do this, but I can't see the point. If you can work out what you need to do from an estimate of game winning chances and gammon chances, why convert them to equities? Anyway, if it works for you that's great. For me it doesn't.


In blitzx's original post that sparked this thread, he said

First of all I wouldn't have doubled even though I was not given chance. But it can't be awfully far away. Because of the score I'm eager to double when ever there is even slightest chance for gammon.

How far away is a cube in that position? It's very close. Doubling would be a tiny error. If we had played 13/8, 13/11 on our turn, a cube would be correct.

Clem tells us that he can't estimate gammon chances well over the board and can't do the math in his head either. But you don't need to! Is White a favourite? Yes. Have his gammon chances improved since the start of the game? A bit yes. That's all you need to know, ship it in! I wouldn't dream of trying to do a match equity calculation here. Waste of energy!

[ah_clem]

Either you have misread the table or it is wildly wrong. The point of last take for the leader at this score, as demonstrated in my post, is 27%. 34% is just wrong.

Your calculation is the gammonless take point. Tom Keith's table is based on 20% gammons on both sides.  Gammons  distort the decision making process at this match score quite a bit.  With 20% gammon chances, the 34% figure is correct.  Question:  would you take a cube at this match score with your opponent 67% to win and 20% to win gammon?

I personally can't make head or tail of the figures that you have posted under a spoiler.

Agree that my calculation was kind of cryptic.  Let's see if I can illuminate:

If we win a single point  with the cube in the center, the match score goes to 4-2
and we are 75% to win the match (using Kit's MET). If we win a gammon, the match
score goes to 5-2 and we have won (100%) .  We can do the same calculation if we
lose, and again with the cube at two.  We get the following outcomes - the final
number is our equity at the conclusion of this game after the various results:

Centered Cube
win single -> 4-2 -> MWC = 0.75
win gammon -> 5-2 -> MWC = 1.
lose single -> 3-3 -> MWC = 0.5
lose gammon -> 3-4 -> MWC = 0.3

Cube at 2
win gammon -> 7-2 -> MWC = 1.
win single -> 5-2 -> MWC = 1.
lose single -> 3-4 -> MWC = .3
lose gammon -> 3-6 -> MWC = 0.0

Note that  our opponent gains considerably more equity when he wins with the cube
at 2 vs centered. Our equity doesn't improve nearly as much.  IOW, he has little to lose and lots to gain by shipping the cube. Our gammons are neutralized, while his become very valuable.

An accurate risk vs reward calculation needs to incorporate the gammon possibilities; instead of doing risk vs reward, I simply calculated the equities directly assuming  60% GWC & 20% gammons by weighting each possible outcome by the assumed probability.  I got .61 for no double and .52 for a doubled/take.  Of course, double/pass gets us to .50.  At 67% GWC for the opponent, our equity is below 50%.

If you can't follow the calculations, I wouldn't sweat it. They're more of an exercise for me than anything else.