Calculating takepoint, considering gammons

[appleorange...@gmail.com]

GNU Backgammon Position ID: mGeHA0DGTsMBAw
Match ID : MBngADAAKAAE
+12-11-10--9--8--7-------6--5--4--3--2--1-+ O: GammonBot_IV
| X O O | | O O O | 3 points
| X O | | O O O |
| X | | O |
| | | |
| | | |
^| |BAR| |
| | | |
| | | X |
| O X | | X |
| O X X | | X O X | Cube offered at 2
| O X X | X | X O X | 5 points
+13-14-15-16-17-18------19-20-21-22-23-24-+ X: You

MATCH to 7 points

According to equity tables and the takepoint formula, my takepoint is 20% if I'm winning 2away 4away. This doesn't take gammons into account:

Pass, score is 2away 3away, 60% equity
Take and lose, 2away 2away, 50% equity
Take and win, 0away 4away, 100% equity
risk=10%, gain=40% Takepoint=r/r+g=10/10+40=20%

In this position I accepted the double, not thinking about the cost of gammons. Of course, I got gammoned and lost the match! GnuBG says it was a "Very Bad" mistake (-0.302) to have taken the cube. It must be because of its gammon chances.

I wish GnuBG would just tell me what my takepoint is. I'm having a hard time figuring out what the difference in risk is when you account for gammons. There must be a simple formula?

For this position, a rollout using 2-ply player settings in GnuBG 1.00 says I have a 38.2% chance to win the game, but my opponent has a 24.9% of getting a gammon.

If I take and lose, 75.1% of the time the score will be 2away 2away-or 50% equity. The other 24.9% of the time I lose the match-0% equity.

Am I correct that my equity for take and lose is actually (75.1% * 50%) added to (24.9% * 0%)=37.55%, giving a risk of 22.45%, and that my takepoint is actually 35.95%, or am I not "getting" it? I must not be getting it, because 35.95% is LOWER than the 38.2% GnuBG gives me to win.

What is my Takepoint?

What is the formula for takepoint, taking gammons into account?

Is there a way to get Gnubg, Snowie, or Extremegammon to simply tell me what my takepoint is in any given position/score?




--------------------------------------------------------------------------------
Cube analysis
Rollout cubeless equity +0.443 (Money: +0.404)

Cubeful equities:
1. Double, pass +1.000
2. Double, take +1.302 ( +0.302)
3. No double +0.908 ( -0.092)
Proper cube action: Double, pass

Rollout details:
Centered 1-cube:
0.618 0.237 0.004 - 0.382 0.069 0.004 CL +0.443 CF +0.908
[0.001 0.001 0.000 - 0.001 0.003 0.001 CL 0.005 CF 0.005]
Player You owns 2-cube:
0.618 0.249 0.009 - 0.382 0.092 0.008 CL +1.302 CF +1.302
[0.002 0.002 0.001 - 0.002 0.006 0.002 CL 0.010 CF 0.010]
Full cubeful rollout with var.redn.
1296 games, Mersenne Twister dice gen. with seed 681429115 and quasi-random dice
Play: world class 2-ply cubeful prune [world class]
keep the first 0 0-ply moves and up to 8 more moves within equity 0.16
Skip pruning for 1-ply moves.
Cube: 2-ply cubeful prune [world class]

[Tim Chow]

On Monday, June 17, 2013 8:46:39 PM UTC-4, appleorange...@gmail.com wrote:
> What is the formula for takepoint, taking gammons into account?

Do you mean ignoring recube vig and backgammons? Suppose your gammon value is V and your opponent's gammon value is v, and you win G gammons and your opponent wins g gammons. Then you can take if you win at least

t - G*V + g*v

games, where t is your raw takepoint.

> Is there a way to get Gnubg, Snowie, or Extremegammon to simply tell me
> what my takepoint is in any given position/score?

I don't think so. In eXtreme Gammon you can select Analyze -> Cube information and it will give you live and dead gammon-adjusted takepoints, but you still have to guess how much recube vig you have.

---
Tim Chow

[appleorange...@gmail.com]

Thanks for answering the second two questions....I see you're gonna make me try to answer the first, What is my takepoint?, on my own 8^). It seems strange that with all the info these bots can tell us, the wouldn't simply tell us the takepoint as well.

> Do you mean ignoring recube vig and backgammons? Suppose your gammon value is V and your opponent's gammon value is v, and you win G gammons and your opponent wins g gammons. Then you can take if you win at least
>
> t - G*V + g*v
> games, where t is your raw takepoint.
>

If I take in this situation, gammons and backgammons are meaningless to me, backgammons are meaningless to opponent, and there will be no recubing...So, using your formula, and a gammon value found on a Phil Simborg chart:

Take point = 20% - 9.2%*0 + 24.9%*1 = -4.9%...?

Assuming you meant to ADD to the raw takepoint it would be 44.9%.
Is this the correct takepoint for this score, with these gammon chances?

Thanks

[Tim Chow]

On Tuesday, June 18, 2013 7:37:52 PM UTC-4, appleorange...@gmail.com wrote:
> It seems strange that with all the info these bots can tell us

> the wouldn't simply tell us the takepoint as well.

When there's no recube vig, eXtreme Gammon does tell you the takepoint. Do you own eXtreme Gammon? Did you look at the cube information that I pointed you to in my last message?

The way the bots work, there's no way for them to calculate recube vig reliably without a rollout.

However, I do agree with you that if you *do* do a rollout, then the bots ought to make the recube information available to us. GNU Backgammon does, sort of, if you do a cube decision rollout and click on "View Statistics," but the information is hard to interpret. The other bots don't do it at all, because the backgammon community for some reason doesn't seem to demand it.

> Take point = 20% - 9.2%*0 + 24.9%*1 = -4.9%...?
>
> Assuming you meant to ADD to the raw takepoint it would be 44.9%.

I meant exactly what I said. Look again carefully at what you yourself typed. You plugged the correct numbers into my formula but then you misread your own (correct) plus sign as a minus sign and that's why you incorrectly got -4.9% instead of 44.9%.

> Is this the correct takepoint for this score, with these gammon chances?

Yes.

---
Tim Chow