# Match to Five Points, Game 1 Round 2

Checksum: 6+10+12 + 9 + 9 + 9 + 5 + 7 + 4 + 3 + (3*10) = 104

Hero: Redouble to 4

Villain: Take

Actual play (Mar 26, score = 474): ih, ij (Qd)

SpiderGM Comments:  An unexpected double from Hero. I will have plenty to say about this in the post-mortem!

Actual play (score = 472): di,id (9d)

SpiderGM Comments:  Bart has enumerated the subsequent play for the thirteen different ranks and somehow came up with the illegal “ih” 😉 At least this is trivial to fix

Actual play (Mar 27, score = 470): ei, ed, ie, id, ed (Qs)

Spider GM Comments: Villain would have re-doubled to 8 if Hero didn’t get the empty column, but now it’s getting interesting.

Actual play (Mar 28, score = 462): bc, jb, he, hj, eh (6s) bd (4d)

Villain doubles to 8

Actual play (Mar 29, score = 450): di,ed (7h)

Spider GM Comments: In the context of a 5-point match I guess there’s no turning back for both sides …

Actual play (Mar 30, score = 448): ie, bi (3d)

Actual play (trivial): bi (7d)

Spider GM comments: Bart/BUG didn’t mess around with column 3 and surely no reason to mess with it now.

Actual play (Mar 31, score = 445): eb, gb, ci

Spider GM comments: Oh well. So much for getting six good cards in a row.

Final position of Round 2: summary and next round coming soon to a place near u

## 36 thoughts on “Match to Five Points, Game 1 Round 2”

1. Bart Wright says:

Score 474

In line with earlier thinking, DOUBLE! See detailed explanation at the bottom. If villain declines, then the game is over. If as we expect, villain accepts, then play on as follows.

ih, ij. I think it’s the only turnover we can get at this time. As for the future, the basics are pretty obvious.

As for what comes up…
K — grumble
Q — ih
J — ij
T — dj, ij
9H — ei, ie
other 9 — grumble
8 — grumble
7 — ie
6 — grumble
5 — ab, ai, dj, aj
4 — grumble
3 — bc, ib
2 — ic
A — ib

Whether there are tweaks to do ahead of a couple of those moves — I haven’t thought it through really carefully. Motivation to be really careful isn’t the highest right here. Looking only at ranks, that’s 4 grumbles and 8 turnovers, and the 9s are split.

Why double? As noted in an earlier post reply, player starts the entire “play to 5 points” in a desperate situation. (It was not “best of 5”, as I erroneously said in that earlier post, but “best of 9”). When I run a simulation with the very generous value of 35% win rate of any single game, then winning a “best of 9” is 17%. If we assumed 30%, it goes down to 10%.

Our situation is far from hopeless in this one game — I’ll say 13% — and if we win, then the score is 4-0 and we can win the whole thing by winning one more game and have 4 chances to decline doubles or just lose along the way (or is villain prohibited from doubling when we have 4 points? Not sure.) My simulation says 88% chance of winning if games are a simple 1 point apiece. Given the win estimate for this one game at 13%, then the other 87% of the time our situation will become practically hopeless when we lose this game (simulation says half a percent, I’ll round to zero) but consider what happens if we play on. If we lose, the score is 2-0 against us and again our situation is very nearly hopeless. Simulation says 5.5%.

Should the villain accept the double? Simulation suggests that playing on the match with the villain behind 2-0, chances of player winning are .47.

Chances of winning match if we don’t double — .87 * .055 = .0478
Chances of winning match if we do double and accepted — .13 * .88 = .114
Chances of winning match if we double and villain declined — .47.

So we should make the double and the villain should accept it.

Should the villain have doubled before?

Let’s suppose that the villain bases their overall strategy on my hypothesis that the more games that are played, the better villain’s chances of winning. So the villain never doubles, the good guys always double immediately (can they double before they even see the opening deal?), and we are in effect in a “best of 5” situation.

Simulation suggests the good guys will win 24% of the time. Note that with no doubling at all (best of 9) it was 17%.

So back to whether the villain should have doubled. It depends critically on what they thought our win chances were at that time (of course). Let’s say they thought our chances of winning were 20%, and villain knows that the good guys will double back immediately.

Simulation suggests that in a match to 3, where the chance of good guys winning the first game are .20 but the others are .35, good guys win .05799 of the time. That’s what happens if villain doesn’t double.

If villain doubles and it’s redoubled at the .20 mark, simulation shows good guys win .105 of the time.

That could be turned into an equation asking what chances of winning for the good guys should be an “indifference point”. But I’m arguing it is below .20. I’m too tired to do that now. 😦

This could all be generalized and done much better, and maybe I’ve made big mistakes…

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1. Hi Bart,

>or is villain prohibited from doubling when we have 4 points? Not sure

This is where the Crawford Rule comes in. The Crawford Rule is universally applied in serious Backgammon tournaments and there is no reason to deviate just because we are playing a completely different game 😊

The Crawford Rule says if the leader is 1 point away from victory then the next game is played without the doubling cube. If the trailer wins that game then the trailer is allowed to double immediately in all subsequent games. Note that the trailer always has trivial cube decisions but the leader does not.

I think the purpose of this rule is to avoid the farcical situation where neither player has an incentive to win a single game if the score is 3-3 in a 5-point match. OTOH if the cube were dead for every subsequent game then it’s too much of a handicap for the trailer. Hence the Crawford Rule is a reasonable compromise.

>can they double before they even see the opening deal?

Not allowed. In Backgammon we have a similar rule: doubling is not permitted before the opening roll.

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2. Blockchain has been updated and Villain’s plans for world domination have been put on hold for the time being

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2. I too think that we need to offer the D-cube back. The odds of the Heroes playing Microsoft Solitaire Collection Random straight-up and arriving at nine games played and still be batting above .500 are slim, so a short game is our best bet.

ih, ij

It would take me too long to proceed with 13 possible scenarios therefore I will go with Esteemed Scholar Bart’s plans for continuation.

PS. Master Chi-Yuen, I tried to post earlier but it does not show up anywhere. If this doesn’t go through I will e-mail you.

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1. Well, that posted just fine, Rod Serling time is upon me.

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2. Blockchain has been updated and Villain’s plans for world domination have been put on hold for the time being

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3. Position 470

We can proceed with getting a void in Col 9 and a TurnOver in Col 6.

Should that fail to produce wonderful results, we can also gain a TurnOver in Col 2.

For our Void/TurnOver:

.ei, ed, ie, id, ed, eh(super)

No Help? .bc, db(super) gives a second Turnover.

I would not be surprised if Esteemed Scholar Bart can improve on this simple rendition with his superior skills.

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4. Bart Wright says:

Score 470

ei, ed, ie, id, ed, gets space
eh(super), uncover
bc, bd(super), uncover

We’re certainly hoping the uncovers are something interesting, but if not:
Cleanup: cd, cd, c(1)-d(2), c(3)-d(2),
controversial: aj, da, c(3)-d(1), jd (allows uncovering c more easily)
one of those uncovered cards gets put in space, but could also be c.

In terms of the grumble index, we are at .20, meaning 4/5 of this many cards would be LESS evenly distributed. That’s good (if not a large factor). But it does mean that we don’t have any “We’re missing 3 xs!” There’s potential to sort out our board just by shuffling things around, if we can get to them.

————-
That was all pre-bug. We’re perfectly aligned! Our only difference is what I assume must be a typo/braino: Last move is bd, not db. And I go on to speculate about the future beyond what is needed.

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1. Esteemed Scholar Bart thank you for correcting my db’s.

At the time of my post I did not do a continuation, but prompted the fact that up until now you have carried the extra credit work load (and without looking at what you proposed), came up with almost the same. I erred by covering the Spade Duce with the Spade Ace, a play that should be saved for later.

This would be a fine time to go on a run of Six Straight Helpful TurnOvers

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1. Blockchain has been updated and we have fulfilled 1/6 of the required Six Straight Helpful TurnOvers.

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2. Blockchain has been updated and we have fulfilled 1/6 of the required Six Straight Helpful TurnOvers.

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5. Bart Wright says:

462

Looks like we can still get a turnover in b along with continuing to dig in column e. E has one fewer card, and we really could use another space, so let’s go there first.

Got to be careful to sort out club/spade royalty before the uncover in e:

bc, jb, he, hj, eh.

If nothing interesting, continue as we were going to before, but the 2 is already out of the way so now it can be written in one step:

bd.

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6. What great things could we do?

We can take a TurnOver in Col’s 2, 5 & Ten

For now, disregard Col Ten as it involves filling a void with a King.

I’d surely like to straighten out Col 7 by moving the KQ of Hearts to Col 9, ready to accept the J-Ten of Hearts from Col 8 in the future, and then regain our void in Col 7. But we would need to give up a Two and our only 8, and giving up the 8 would cost us a Turnover so NoCanDo right now. But I want to get to this as soon as it makes sense.

So I would opt for a TurnOver in Col 5 whilst playing with the Dark Royalty a wee bit.

Gain Access to the Club 4 and Club King: bc, jb

Spade J to the Spade Q: he(super)

Club Q to the Club K: hj

Spade Q to the Spade K: eh(super) = TurnOver = Club 8

Follow up with TurnOver in Col 2: bd(super)

Time to post this dribble and see if Esteemed Scholar Bart has commented.

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7. I’m not seeing much here. If we attack Col 3 for a TurnOver we gain a lot of organization in the lower card ranks, but expose two aces and also lose an Atomic Turnover in Col 5……..NoCanDo

I am still not ready to move the Club K-Q into a void so early in the play.

So the simple: . .ei

If no help, cover the Club Deuce with the Club One.. gd

And possible cover the Dia. Deuce with the Heart Ace?.. ac

Wait a minute, on my final Look-See-Before-Posting I realize that there are very few cards that can really help and a Five is one of them, but with the simple ei a Five is both a blessing and a curse as we immediately gum up our only Atomic Void.

Perhaps swap out Sixes?.. di, ed might be much better

Yes, I like it, now a Five or Black Seven gives us two turnovers and leaves Col 9 Atomic Void-ish.

Final: . di,ed

If no help: . gd and ac

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8. Bart Wright says:

Score 450

Accept the double. I can see why the villain would double in the mindset of “Ah, c’mon, you’re gonna LOSE, man!” but if our situation improves dramatically (however unlikely), villain would still have a decent shot of winning the match going into the next game trailing by 4-0 — unless my whole analysis in my lengthy reply not long ago is wrong. I should think we would only decline a later double if there was essentially NO arrangement of the remaining cards that would allow us to win.

cb, cb, b(2)-c(1), b(2)-c(3), de, cd, cd to uncover
If nothing useful, bi, filling space to uncover. I suppose we might for some reason prefer ci, putting in the space what we just revealed, but I figure master/villain will stop if they so perceive.

If our first turnover is no good, I’d prefer ei, to uncover in the column with fewer cards, but I don’t think our cards let us at that point to have an atomic thing in e to put in the space.

I do get indigestion at uncovering TWO more aces, leaving us with five exposed, but we need turnovers, and we do get to reduce a lot of disorder in the low spades and diamonds. What precious resources did we give up in revealing those two aces? A 4 — two more receivng 4s lurk under other aces right at the surface. Our 6. Not good, but we do have the chances of converting a receiving 8 into a receiving 6 by way of column g if we were to get an 8 and then a 5. A 2 — at least we still have one more receiving 2.

The alternative would be a simple “ei” at this point to keep those aces covered and just get one turnover. There are two more deals, but deals often make things worse, so I think uncovering those aces is worth it. We need some very good luck here no matter what. That’s been true for some time.

Above is what I had before reading the wisdom of the grasshopper.

He is strongly against the “reveal two aces” plan. We see the same downsides but weight them differently. I agree that his “di,ed” variant is better than the simple “ei” I considered and that was his first reaction.

Where I disagree with him more strongly is in putting those aces on the 2s. Under the one ace is a receiving queen — but we already have one of those in J. Under the other two are receiving 4s — and we already have one in column b. If we include the column c ace — which is more accessible than it looks, there are four aces potentially looking for homes, and two homes. I’d suggest leaving all possibilities open for future work.

On a little further thought, I’ll switch to prefer the bug’s plan on the major decision for a reason he suggests. We really need another empty column possibility, and it’s column e. One turnover there is arguably worth two turnovers in columns b and c.

So we reached a consensus on that one, and only differ in whether to put the aces on the 2s. I forget what method the GM has in store at present for resolving that disagreement. If I had to choose one of the two I would move the ace of clubs. We are a jack and an 8 away from a club suit, and getting that ace in on the plan now has some advantage.

Final joint answer of Barticus and BugIMus:

“di,ed”

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1. Let’s just do . di,ed . and see what the card is. If no help we can then pontificate on what to do or not to do with the Aces. This will slow things down, but I prefer to not be hasty at this point in the hand.

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1. I forgot to accept the Double.

Going into the next hand down 0-4 does not look inviting. And I still feel the short game is in our best interests.

We are not in the greatest of shape, but “It ain’t over ’till it’s over”

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2. Blockchain updated. At least we get the empty column back.

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2. Blockchain updated. At least we get the empty column back.

NOTE: When voting, I use a random number generator as tie-break when Bart/Bug disagree on the best play. So far this wasn’t necessary, but that may be a function of the game state rot13(fhpxvat) thus leaving very few reasonable options in the first place 😊

I have no problem with slowing the game down. Now that the double is accepted, the match is guaranteed to last only one game anyways 😊

I agree things are not in great shape, but in previous hands I’ve also seen Team Good come back from worse 😊

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1. Master Chi-Yuen, I am going to ask Esteemed Scholar Bart to comment on my insanity before we move on. Please allow us time for a Huddle-Up

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9. Bart Wright says:

Score 448

If we could put the 7 from column e in the space that would be my favorite but I don’t see a way to do that. We should “ie” to return things to what they were, except now there’s a face-up 7 under the 6 in column e.

One option is a simple “bi”. But now I return to the fairly complicated plan I had initially favored last time. Yes, expose two more aces, but get an extra turnover. If nothing useful comes up, continue with “bi”.

ie to regain space, then
cb, cb, b(2)-c(1), b(2)-c(3), de, cd, cd to uncover

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1. Esteemed Scholar Bart, your attacking Col 3 looks much better to me now.

I would like to hear your thoughts on my crazy ideas below before agreeing with you on this course of action.

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10. Well, there is the obvious, “ie, bi”

That makes me feel like I am just puttering along behind a bad hand which is leading me to 0-8.

Lets just do “ie” and mull over what is possible.

We can still gain a Turnover in Col 10. And I still don’t like it.

We can still gain a TurnOver in Col 3 and keep our void, giving us two turnovers. This looks lots better now than it did a card ago.

But I like “.ie, fc, fd(super), bi = TurnOver”

This makes Col 2 AtomicTurnover (if no King is lurking)…Col 6 AlmostAtomicTurnOver…Col 7 AtomicTurnover…and Col 9 AtomicVoid.

I give a nod to this rather than attacking Col 3 and uncovering all the aces.

If I was playing this hand by myself and was sure Master Chi-Yuen would never find out, I would give strong consideration to not even taking a TurnOver and returning the Clu 6 & Friends to Col 9 instead of “bi” and taking the draw with four Atomics.

Now, here is the fun part of this game.

I prefer making Col 7 Atomic and taking one TurnOver rather then attacking Col 3 with two TurnOvers.

From there, I would probably move further from center and forgo the Turnover, achieving Four Atomics. “.ie, fc, fd(super), ei = No TurnOver and a probable rap on the knuckles with the slide-rule thing”

BUT !!! I am having trouble justifying not taking a TurnOver in the face of Two Sure Thing Turnovers by attacking Col 3, which was my first rejection.

So if I was playing this just for myself, I would close it down and come back tomorrow and see how I felt.

I’ll do the next best thing,

“.ie, fc, fd(super), bi = TurnOver”

And see if Esteemed Scholar Bart has posted and if I want to change.

I need to dust off my dictionary and see if this still fits into the realm of “Fun”

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11. Bart Wright says:

The GM didn’t make any provision for the good guys to huddle and achieve a consensus, since of course that might prove impossible in a reasonable amount of time if both of us were even moderately stubborn (or principled, or whatever).

I can almost see the GM giving me the hairy eyeball for attacking column 3. I imagine him saying that while indeed we have an extra 6 and an extra 2 now, lots of things can change after a deal when you get 10 cards at once, and while exposing a single ace might be worth it, exposing two is… cause to go back to the beginners class. It’s not as if we were on the verge of removing spades or diamonds, which might be a reason to sort them out.

So since I am so ambivalent about attacking column 3, I’ll sign on to “bi” for the turnover. The opinion of one’s peers is a legitimate source of information in making tough decisions too, right?

I’m less happy about fc, fd. It’s true that it makes that column atomic, and we are expecting 8s (with 7 of them not yet seen). However, all else being equal we would much prefer to use an 8 for column 5 than 6. Column 7 is also interesting, in that if we have a space (and a 2) we can convert a receiving 8 into a receiving 6. Yes, we have an extra 2, but we also have 4 aces already on the board looking for homes (column 3 ace is closer than it looks) so I’d rather not use a two up.

So, at the risk of making GM’s random number generator feel unappreciatd, as I have made my case I will sign on to doing “fc, fd” or omitting it as you see fit. Your call!

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1. Esteemed Scholar Bart, Thank you for your thoughts………right up to the last two words!!!

This position looks simple enough, but gave us pause to think.

So it is “Keep Da’ Deuce vs. AtomicTurnover………I got the ball and everyone is watching me.

I give only a slight edge to AtomicTurnover and have a much stronger appreciation of Esteemed Scholar Bart’s superior playing skills.

Youth wins out again, “ie, bi” ………..right back where we started a few thousand words ago.

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12. I’m not seeing much here, shift the Club 6 to Col 2 and follow that up with the Club Ace

.eb, gb

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13. Bart Wright says:

Score 445

I didn’t try an independent evaluation before reading bug’s.

eb — fine, I’d do that too. Make the pile with fewest cards atomic.

I’m ambivalent about gb… Using up a precious ace, but in this case it could help remove clubs… except the 7 of clubs is buried in that same pile. But I’ll go along with it.

But also we need “ci”, right?

Final answer: eb, gb, ci.

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1. Round 2 is officially complete. Summary and next round coming soon to a place near u

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1. Round 2 is officially complete. Summary and next round coming soon to a place near u

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