In this sgf, I've attempted to follow Bill's logic and show how starting the ko is the best option for black. I've stuck to Bill's premises: there are no ko threats, there are a few 10 point moves on the board, and otherwise, the remaining moves will diminish in value. Comments appreciated.

[sgf-full]http://www.lifein19x19.com/forum/download/file.php?id=441[/sgf-full]

_________________
Patience, grasshopper.

Thanks, daal. It is not easy to illustrate this on the whole board. (And your comments about plays canceling out are unclear.)

Here is an illustrative example with a small environment of small endgame plays.

[sgf-full](;AP[GOWrite:2.2.21]FF[4]SZ[19]CA[ISO8859-1]ST[2]GM[1]PW[ ]C[Suppose that the rest of the board besides the two bottom corners has been played out, leaving only dame, and no ko threats. The ko is on the left, OC. On the right are plays that gain 2 points, 1.5 points, 1 point, and 0.75 point. White to play.]AB[qs][qr][qq][qp][qo][qn][qm][ql][rl][pl][ol][nl][nn][on][pn][pp][op][np][nr][or][pr][bq][cq][dq][cr][er][es][ds][ro][so][rn][sp]AW[om][pm][oo][pq][ml][mk][nk][ok][pk][qk][rk][sk][mm][mn][mo][mp][mq][mr][ms][bp][cp][dp][eq][fq][fr][aq][br][rq][rr][sl][rp][sm][rs]PB[ ]FG[259:]PM[2]GN[ ]
(
;W[ar]C[The largest play on the board, but a mistake.]
;B[nm]
;W[no]
;B[nq]
;W[ns]
;CR[bq][cq][dq][cr][dr][er][es][ds][cs][bs][as][om][pm][oq][pq][ps][rp][rq][rr][rs][sq][sr][ss]C[In the marked regions Black has 19 points and White has 18 points, a net of 1 point for Black.]B[os]
)
(
;W[nm]C[White should let Black start the ko.]
(
;C[But Black does not. A mistake. Since the largest play aside from the ko gains 1.5 points, we can estimate the cost of waiting until the end to play the ko as 1.5 points. OC, it will be an integer.]B[no]
;W[nq]
;B[oq]
;W[ns]
;B[os]
;W[sn]
;C[By Japanese rules Black will lose a point if she does not force White to win the ko before the end of play. Black would be dead in the corner without White having to add a stone.]B[ar]
;W[as]
;B[bs]
;W[cs]
;B[rm]
;W[dr]CR[bq][cq][dq][cr][ar][bs][ds][es][er][oo][po][pq][ps][rp][rq][rr][rs][sq][sr][ss]C[In the marked regions Black has 17 points and White has 18 points, a net of 1 point for White. ]
)
(
;C[Correct. Black makes the ko, forcing White to win it now.]B[ar]
;W[as]
;B[bs]
;W[cs]
;B[no]
;W[dr]
;B[nq]
;W[ns]
;CR[bq][cq][dq][cr][ar][bs][ds][es][er][oo][po][oq][pq][ps][rp][rq][rr][rs][sq][sr][ss]C[In the marked regions each player has 18 points, for a net of 0. Waiting to start the ko cost Black 1 point. Preventing the ko cost White 1 point.]B[os]
)

)

)[/sgf-full]

Note that each player's mistake gets punished.

_________________
The Adkins Principle:
At some point, doesn't thinking have to go on?
— Winona Adkins

Visualize whirled peas.

Everything with love. Stay safe.

Beautiful example, thank you!

De nada.

And thanks to you guys. I usually talk about this abstractly. Leading me around to a simple example has really helped.

_________________
The Adkins Principle:
At some point, doesn't thinking have to go on?
— Winona Adkins

Visualize whirled peas.

Everything with love. Stay safe.

I'm finding this discussion interesting, but confusing. Could someone illustrate it by means of a demonstration game, (perhaps on 7x7 to keep things simple), to show how it would be good to start a ko as soon as possible when one is likely to lose the ko?
I mean in the sense of showing the difference in points between starting a ko that will be lost versus not starting that ko?

Thanks in advance, Niek

Oops.. nevermind, I overlooked the example provided later on in this discussion, which is what I had in mind.