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If you're a 60/40 fav in 1 game, how big a fav in 5 etc If you're a 60/40 fav in 1 game, how big a fav in 5 etc
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10-27-2010 , 01:35 AM
#1
Chicken Dinner
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stranger
Join Date: Nov 2009 Posts: 9
Hi.

I regularly play bad bg players for money. Some of these players will play for much bigger bucks than me put i am a bit of a bankroll nit.

If i'm a 60/40 fav against them in 1 game (hypothetical)...how many games would i need to be an 80 or 90% favourite?

Assumptions are each game is best of 1 with no bonus for gammons.

Cheers
Last edited by Chicken Dinner; 10-27-2010 at 01:43 AM.
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10-27-2010 , 02:58 AM
#2
Chicken Dinner
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stranger
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bump
If you're a 60/40 fav in 1 game, how big a fav in 5 etc Quote
10-27-2010 , 03:44 AM
#3
MordellWeil
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Join Date: May 2010 Posts: 33
Do you mean that you play a match without gammons and backgammons counting ? Is it without the cube ?

I think your opponent will have to be much weaker than you in order to be a 60/40 favourite in a single game.
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10-27-2010 , 09:08 AM
#4
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bschr04
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grinder
Join Date: Jul 2008 Posts: 454
under your conditions:

~80% fav = 17 game match. 1-BINOMDIST(8,17,0.6,TRUE)= .801
~90% fav = 39 game match. 1-BINOMDIST(19,39,0.6,TRUE)= .8979
If you're a 60/40 fav in 1 game, how big a fav in 5 etc Quote
10-27-2010 , 10:44 AM
#5
Alpha Fish
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Pooh-Bah
Join Date: Aug 2008 Posts: 3,832
Quote:
Originally Posted by bschr04
under your conditions:

~80% fav = 17 game match. 1-BINOMDIST(8,17,0.6,TRUE)= .801
~90% fav = 39 game match. 1-BINOMDIST(19,39,0.6,TRUE)= .8979
technically it won't be that simple since the match is not a series of unrelated 60% flips

FIBS formula puts a 400-point fav. at about 60/40 for a single game and 80/20 for a 9-point match, but that assumes gammons and cube which OP doesn't use for whatever reason, so the truth would probably be somewhere in the middle
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10-27-2010 , 11:14 AM
#6
Aaron W.
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Carpal \'Tunnel
Join Date: Sep 2002 Posts: 30,132
Quote:
Originally Posted by Alpha Fish
technically it won't be that simple since the match is not a series of unrelated 60% flips
I don't think this matters. Suppose you're playing a match to 7 points (with no gammons/no cube). Even though the match can be determined by the 7th game, there's no "harm" in playing 13 of them. It will not change the win/lose outcome. So you can basically view each trial as independent and run 13 of them every single time.

This type of idea was discussed at length in a slightly different context in SMP:

http://forumserver.twoplustwo.com/47...tennis-784882/
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10-27-2010 , 11:22 AM
#7
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Quote:
Originally Posted by bschr04
under your conditions:

~80% fav = 17 game match. 1-BINOMDIST(8,17,0.6,TRUE)= .801
~90% fav = 39 game match. 1-BINOMDIST(19,39,0.6,TRUE)= .8979
This is the same as a first to 9-point or 20-point match (without cube and gammons) correct?
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10-27-2010 , 11:49 AM
#8
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bschr04
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grinder
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Quote:
Originally Posted by mute
This is the same as a first to 9-point or 20-point match (without cube and gammons) correct?
Yep. OP will either be an 80 percent favorite in a race to 9 points or have an 80% chance of winning money in 17 unrelated games, depending on how you look at it. Ditto 90%, race to 20 match.

Im not sure why anyones game strategy would change based on the match score if gammons and cubes are out of play. There are only 2 possible payouts for each game, and your goal is to maximize your chance of getting the good one. So I am pretty comfortable modelling this as a series of independent/identical flips.
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10-27-2010 , 12:42 PM
#9
Alpha Fish
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Pooh-Bah
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Quote:
Originally Posted by bschr04
Yep. OP will either be an 80 percent favorite in a race to 9 points or have an 80% chance of winning money in 17 unrelated games, depending on how you look at it. Ditto 90%, race to 20 match.

Im not sure why anyones game strategy would change based on the match score if gammons and cubes are out of play. There are only 2 possible payouts for each game, and your goal is to maximize your chance of getting the good one. So I am pretty comfortable modelling this as a series of independent/identical flips.
you're right, I obviously didn't account for no gammon/cube rule
what's interesting is that FIBS formula gives practically the same answer for a roughly 60% single game winner
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