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Equity Bets

Posted By: Albert Steg
Date: Monday, 21 September 2015, at 9:26 p.m.

Over the past winter I had been planning to share a relatively recent Boston-area tradition that I came up with while playing one of my may long sessions with Herb ‘The Propmeister’ Gurland. True to his name, Herb had gotten the best of me in virtually every prop we had played out, even though subsequent XG rollouts had confirmed I had been on ‘the right side’ of half of them. Obviously, you’ve gotta know how to play ‘em.

Somewhere along the line it occurred to me that since the ‘bot settled the matter at the end of the day, we could just use the rollout result itself to award a settlement commensurate with the size of the “rightness” of the correct player by making a $100-per-point ($1 per .01) bet on the difference between the competing plays. This turns out to feel like “just the right size bet” if you’re playing for $10’s. And of course, if you feel more strongly about a position, you can bet $2 per .01 or $5 per .01.

For a play that’s a measly .02 better than the opponent’s play, you get a measly $2.00. For a huge error, say .36, you pay a whopping $36.00 that's appropriate to that degree of wrongness. For example, in the position below when Herb played the 6 out and lifted the blot in his home board, I offered to bet it was better to step up to the 22-pt. XG agreed with me, by .034. I was right, but he wasn't enormously wrong. $3.00 is just what I deserve.

White is Albert

score: 0
pip: 107
Unlimited Game
Jacoby Beaver
pip: 78
score: 0

Blue is Herb
Blue to play 62

1.XG Roller++24/16eq: -0.521
30.87% (G:4.83% B:0.02%)
69.13% (G:27.17% B:1.62%)
2.XG Roller++22/16 5/3eq: -0.555 (-0.034)
24.77% (G:3.04% B:0.01%)
75.23% (G:15.78% B:0.44%)
3.2-ply22/14eq: -0.753 (-0.232)
20.55% (G:3.56% B:0.01%)
79.45% (G:25.84% B:1.38%)
4.1-ply22/16 4/2eq: -1.228 (-0.707)
10.58% (G:0.96% B:0.01%)
89.42% (G:44.17% B:4.55%)
5.1-ply22/16 3/1eq: -1.231 (-0.710)
10.63% (G:0.92% B:0.01%)
89.37% (G:44.53% B:4.49%)

eXtreme Gammon Version: 2.10

As we went along making these occasional bets, we did run into some unanticipated cubing situations where it wasn’t clear what the $ settlement should be. For instance in the position below I held off redoubling as Blue, and after I cashed a roll or two later Herb offered to bet this had been a cube. I took him up on it and, yikes! it’s a huge pass (okay, okay -- and yes, the full rollout yields an even bigger pass).

White is Herb

score: 0
pip: 85
Unlimited Game
Jacoby Beaver
pip: 121
score: 0

Blue is Albert
Blue on roll, cube action?

Analyzed in XG Roller++ No redouble Redouble/Take
Player Winning Chances: 75.95% (G:26.47% B:0.70%) 76.23% (G:26.46% B:0.70%)
Opponent Winning Chances: 24.05% (G:7.55% B:0.10%) 23.77% (G:7.56% B:0.09%)
Cubeless Equities +0.714 +1.440
Cubeful Equities
No redouble:+0.866 (-0.134)
Redouble/Take:+1.271 (+0.271)
Best Cube action: Redouble / Pass

eXtreme Gammon Version: 2.10

. . . but the question arose whether Herb should collect a full $27 (re-double/take vs. no redouble), since he also thought it was a take at the time. A $13 payment seemed fair since we were both wrong about the excess improper take vig, but on the other hand it seemed he did deserve the full $27 since over the board, or if we had played it out as an actual prop, he would have enjoyed the fruits of that error by virtue of my playing out Double/Take. vs No Double. Similar confusion can arise in cases where you bet Double/No Double and it turns out to be a Beaver.

For awhile we tried expressing a “full cube decision” where you had to specify the complete action, as in BG quizzes, but this led to other unwanted complexities, and we knocked around the question with other locals in our chouette circle, looking for an approach as simple as possible and also assigning an appropriate level of penalty for wrongness. We’ve come around to what seems now the right solution, which is that each bettor has his action evaluated against an ideal opponent, which is of course XG, and that you have to accept the fullest consequence implied by your action. So if you bet ‘Double’ and it turns out a beaver, you have to pay the larger, beavered value of the position, even if your opponent didn’t say it was a beaver. And in the position above, I should have paid the larger $27 because my position clearly implied I thought ‘Take'.

Of course, you hope these peculiar situations shouldn't come up real often — and they don’t — but it’s good to have a policy in place when they do.

If this is already a common practice elsewhere, sorry, I didn’t mean to appropriate what may be an obvious practice as a Boston invention — but I haven’t heard other people at tournaments betting this way (It’s typically “$20 that’s a drop!”) and it really is a fun and equitable way of betting on disagreements now that the ‘bots have largely eliminated ‘propping’ positions. I hope others might find it as lively and educational a practice as we have.

At first I was calling these “Bot Bets” — but Alex Zamanian coined the more apt “Equity Bet,” which better captures the proportional aspect of the settlement figure.


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