Quiz : First Six Wins

[Hardy_whv]

Yes, hardy, this sums up to 59%=36/61 ...

Sure it is. I said so 3 days ago  


Hardy    

[nabla]

Yes, there is a mistake, you are turning the cube after the roll instead of before it. Assuming you own the cube (even if it's on 1) and double, and opponent doubles too, then you don't double anymore, the game starts with double/take so the cube is already on 2 when you roll. So you get:

2*(396/1296)-4*(275/1296)+ 4*(625/1296)*(11/61) = 0.11

which is less than the 0.18 cubeless equity, so I still believe it's a no double!

You are absolutely correct, my mistake. This means that the strategy of doubling once commits oneself into doubling at every turn and creating mayhem. Given that, I also would not double !
It seems to be one of those situations where a good guy will not be the first one to double, but will reply to every double from his opponent with a retaliation double of his own, otherwise he would allow the "bad guy" to gain equity. It is still somewhat paradoxical.

Sure Hardy ! I just wanted to point out that I had already said the *why* of the 59%.

[gumpi]

so, now its time for my unqualified comments:

first: dorbelÃ,´s right.

second: "It comes from the formula 1-p=25/36*p (the winning probability for the second player is the probability that he survives the first roll, times the winning probability for the first player), giving p=36/61" is also right.

third: the DP in moneyplay in gammonless positions is fix, (exept last roll positions) when the game still has a way to go can be generated from point of last take (22% in money): initial double 3 pips ahead: 72%, redouble 2 pips: 74%.. nicely fixed in comparison to this weird floating DPs and TPs at various Matchscores .

a position where the first six mostly wins is for examle: you own a single cheker behind your opponents five prime, heÃ,´s closed out in your six-point prime. your winning is about 60% with no gammons. now suppose your sixpoint breaks in the next roll or two (because of missing).... than... with white on roll his winningpercentage is about 60% to roll the first six..... his doubling point comes when you break the five point also and have a stripped four point... and its still a take... also the bots believe in that.

so... thats it, i Ã,´ll go and have a beer, cherrs!

[socksey]

This all means that if you want to become a really good backgammon player, you must become a mathematician?      

socksey



I never drink water because of the disgusting things that fish do in it. - W.C. Fields

[spielberg]

This all means that if you want to become a really good backgammon player, you must become a mathematician?      

socksey

No sox - you don't have to understand (for example) how match equity tables/take points/gammon values are calculated - you just(!) have to know their values.

[gumpi]

not really ..

the "first six wins" was an introduction in Walter trice "backgammon bootcamp" and was the introduction for your winning percentage and doubling points in prime positions like the one i described before.

[Zorba]

A few corrections:

The (initial) doubling point (DP) in money games with no gammons is 50%.

The cashpoint (CP) is 100% minus opponent's takepoint (TP). It depends directly on how much use your opponent gets out of owning the cube, also known as livelinessWith a dead cube, the TP is 25% so the CP is 75%. With a fully live cube, the TP is 20% and the CP is 80%. For most positions, a TP of 22% is assumed so the CP is 78%.

Now, the range from your DP to your CP is called the doubling window or market window, so for money, that would be something like 50%-78% most of the time.

It can be correct to double at any place in this market window, but not necessarily so. That depends on the volatility of the position, or more precisely, the marketlosers and their size.

The "first six wins" position has a very high volatility; plenty of big marketlosers. Therefore, it can be correct to double with even less than 70% or 65% winning chances.

In long races, this is different since volatility is lower. Therefore you can wait for higher GWC before you double, thereby making more efficient doubles.

[socksey]

This is giving me a headache!     Or was that, 'not tonight, I have a headache?'!   

socksey



"If you walk backwards, you'll find out that you can go forwards and people won't know if you're coming or going." - Casel Stengal, former Baseball player

[spielberg]

Oh excellent - I get to correct Zorba:

With a fully live cube, the TP is 20% and the CP is 80%. For most positions, a TP of 22% is assumed so the CP is 78%.

Lowest possible TP is 18.75%. Consider cash game, 1 man each on both 6 points - perfectly efficient cube on both sides!

[gumpi]

thats right, with both on the sixpoint you get a 18,75 take point because of your redouble vig. i m mostly interested in getting calculated things like that in my head without bots or match equity tables. in situatins like this 2 roll position i calculate like this: i need to have 324/1296 to take, i Ã,´ve got 9 fans and 27 winners (exactly those 18,75), thats less than 324 cubeless. the redouble vig i calculate with kleinmanns "double the difference from 18" so 27-18 is 9 *2 is 18 plus 8 is 36 winners *9 fans... is exactly 324.. easy to calculate in my head, even after one or two beers.

cheers