Gammon Question #1: pips + position and the CUUUBE

[DcifrThs]

so pips refers to the # of moves it would take to get your pieces into your home.

it does not, however, take into acct the likelihood of being picked up and thus having 6*4=24 pips added to your total remaining pips.

(for example, if you have 103 pips and your opponent has 103 pips it's a dead even game according to the # of moves it would take both of you to get your pieces off the board. if you roll a 4+3 then you get 103-7=96 pips remaining)

now, the real point of all this is to explain the betting structure.

if both of you have the same position and the same # of pips (i.e. in the beginning of the game) and the same skill level, then doubling the bet (offering the cube to your opponent) is an exercise in coinf lipping.

now lets say you are even skill leveled and you roll double 6s for the first roll. now offering the cube is advantageous and your opponent may simple reject and resign.

the question i want to ask, is that ASSUMING your opponent is competant, is it EVER correct to accept the doubling cube when offered by your opponent?

Barron

[AlphaWice]

You are wrong about the coinflipping exercise. There is equity in being the sole-posessor of the cube. Look at "cubeful equity" in GNUBG.

If your opponent only offers the cube when it is +EV for him to do so, AND he always plays the most +EV moves when he rolls the dice, then obviously it is never okay to take the cube.

[Our House]

Think of it like you and your opponent are grains of sand in a funnel and the winner is the first one to make it to the bottom.

Now, the beginning (or first few rolls) of a backgammon game are like being at the top of the funnel. Either of you may have dodged some sand grains better than the other player, and although that person is the favorite, there are still many uncertainties ahead of you.

In match games, the score of the match is what determines cube acceptance. In single games, it's a matter of how far behind you are...weighed up against how much sand is still left in the funnel. Of course, the amount of the cube matters.

If it's early on in the game, and your equally skilled opponent throws you the cube after only one good roll, you should ALWAYS accept. Possession of the cube is HUGE. Likely, the lead will change hands a few time throughout the remainder of the game. When you own cube possession, you are the only one with the ability to end the game prematurely when you have the upper hand...thereby eliminating any chance for your opponent to luckbox against you.

Barron, I just woke up, so hopefully all of that just made sense. [img]/images/graemlins/wink.gif[/img]

[AlphaWice]

Generally, the biggest mistake of noobs to bg is that they greatly underestimate the % chance to win in a "way behind but I have blockers" situation.

[ChrisV]

Yes, it is often right to take doubles.

As Alphawice said, there is equity in possession of the cube, because the holder always has the option of raising the stakes. However, there is also danger in taking a double if there's a good chance you'll get gammoned. Let's pretend all that doesn't exist for a sec.

Suppose the game is currently being played for one point. If your opponent turns the cube, then you can pass, in which case your opponent's EV is one point. If you take, then your opponent's EV is (P winning)*2 - (P losing)*2. The point at which this breaks even, if you plug the numbers in, is (P winning) = 0.75. So in the absence of the factors mentioned last paragraph, it is correct for your opponent to turn the cube whenever he is greater than 50% to win, and for you to accept the double whenever he is less than 75% to win.

In other words your question is a bit like "In poker, is it ever right to call a bet when you are behind?". Yes, often.

[atrifix]

[ QUOTE ]
If your opponent only offers the cube when it is +EV for him to do so, AND he always plays the most +EV moves when he rolls the dice, then obviously it is never okay to take the cube.

[/ QUOTE ]

This is not true.

[RoundTower]

[ QUOTE ]
[ QUOTE ]
If your opponent only offers the cube when it is +EV for him to do so, AND he always plays the most +EV moves when he rolls the dice, then obviously it is never okay to take the cube.

[/ QUOTE ]

This is not true.

[/ QUOTE ]

[atrifix]

[ QUOTE ]
now lets say you are even skill leveled and you roll double 6s for the first roll. now offering the cube is advantageous and your opponent may simple reject and resign.

[/ QUOTE ]

If you roll double 6s on the first (second) roll, offering the cube is DISadvantageous. Your opponent can properly take and be about equal in the game.

[AlphaWice]

[ QUOTE ]
[ QUOTE ]
If your opponent only offers the cube when it is +EV for him to do so, AND he always plays the most +EV moves when he rolls the dice, then obviously it is never okay to take the cube.

[/ QUOTE ]

This is not true.

[/ QUOTE ]

How? By definition of expected value, this is true - we have defined the situation so that expected value is maximized by offering the cube. (By "offer cube when it is +EV", i mean "offer cube when it is more +EV than not offering", of course.)

[atrifix]

[ QUOTE ]
[ QUOTE ]
[ QUOTE ]
If your opponent only offers the cube when it is +EV for him to do so, AND he always plays the most +EV moves when he rolls the dice, then obviously it is never okay to take the cube.

[/ QUOTE ]

This is not true.

[/ QUOTE ]

How? By definition of expected value, this is true - we have defined the situation so that expected value is maximized by offering the cube. (By "offer cube when it is +EV", i mean "offer cube when it is more +EV than not offering", of course.)

[/ QUOTE ]

ChrisV answered this as well as I can. It is correct to take a double if you are better than a 3-1 underdog (although the other factors such as gammons and potential redoubling throw this number off a bit). But it can also be, and usually is, correct to double with less than a 3-1 advantage.

I don't think people are thinking about this analytically. The two important factors are that 1) there is value in holding the cube, and 2) by resigning you give up the game immediately, whereas by accepting you have a chance to win double (or quadruple, etc.) the stakes.