ThatDonGuy

Joined: Jun 22, 2011
• Posts: 4470
Thanks for this post from:
July 30th, 2020 at 11:58:47 AM permalink
Quote: OnceDear

For a zero edge game...
Probability of Success = (Starting Bankroll)/(Starting Bankroll + Target Profit)

For a low house edge game, it gives a decent probability estimation if you wager a modest proportion of bankroll on each wager, especially so with a progressive such as Marty or d'Alembert

I acknowledge that it's far more complex, and beyond me to derive an equation where there is a house edge.

Actually, for flat betting, there is a formula for the probability of reaching the target before losing the entire initial bankroll:

(1 - ((1-p)/p)^B) / (1 - ((1-p)/p)^(B+T))

where p is the probability of winning the initial bet (assuming p < 1/2), B is the initial bankroll (in terms of the number of bets), and T the target profit (again, in terms of the number of bets).

For p = 1/2, the probability = B / (B + T), as you state in your blog post.
USpapergames
Joined: Jun 23, 2020
• Posts: 687
July 30th, 2020 at 4:23:14 PM permalink
Can someone help me? I just want to post my own form questions but I don't know how.
Math is the only true form of knowledge
ThatDonGuy

Joined: Jun 22, 2011
• Posts: 4470
July 30th, 2020 at 5:40:15 PM permalink
Quote: USpapergames

Can someone help me? I just want to post my own form questions but I don't know how.

1. Click on "Forums" in the menu bar at the top of each page.
2. Scroll down until you see the list of topics - for example, this thread is in "Betting Systems" under "Gambling".
3. Click on the topic name to bring up that topic's page.
4. Click on the "New Thread" button at the top of the topic's page.
OnceDear
Joined: Jun 1, 2014
• Posts: 4619
July 30th, 2020 at 5:50:42 PM permalink
He sees the mobile view. such features seem hidden by the forum layout
Take care out there. Spare a thought for the newly poor who were happy in their world just a few days ago, but whose whole way of life just collapsed..
Wizard
Joined: Oct 14, 2009
• Posts: 22448
Thanks for this post from:
August 1st, 2020 at 4:37:40 PM permalink
My video on the d'Alembert is up for preview. Please enjoy. I welcome all comments. Please keep in mind I'm not making a Ken Burns documentary here.

Direct: youtu.be/ucvz-pDgv50
It's not whether you win or lose; it's whether or not you had a good bet.
lilredrooster
Joined: May 8, 2015
• Posts: 3171
August 4th, 2020 at 2:33:46 AM permalink
I like this progression
I'm not saying it's a long run winner
I mean for playing for fun
as far as I know it doesn't have a name
I think it's somewhat similar to what John Patrick (no I don't recommend him) calls 𝙪𝙥 𝙖𝙣𝙙 𝙥𝙪𝙡𝙡 but it is not the same

the progression is 4 bets and if you lose any one or win all you return to the beginning

assuming you win your first 3 bets the progression is:

𝐛𝐞𝐭 𝟏............𝐛𝐞𝐭 𝟑............. 𝐛𝐞𝐭 𝟐...................𝐛𝐞𝐭 𝟒

the worse thing (other than long losing runs) is if you lose your 2nd bet - 3 - which means in the first 2 bets you will lose 2 instead of breaking even if you flat bet

if you win the 2nd bet and lose the 3rd you will win 2 - whereas if you flat bet you would win only 1

if you win the 3rd bet but lose the 4th you will win 2 - which is the same as if you flat bet

if you win all 4 bets you will win 𝟏𝟎 𝐮𝐧𝐢𝐭𝐬...........................𝘵𝘩𝘢𝘯𝘬 𝘺𝘰𝘶 𝘑𝘦𝘴𝘶𝘴...................which means you've won 6 more than if you flat bet
Last edited by: lilredrooster on Aug 4, 2020
𝘱𝘢𝘵𝘳𝘪𝘰𝘵: 𝘵𝘩𝘦 𝘱𝘦𝘳𝘴𝘰𝘯 𝘸𝘩𝘰 𝘤𝘢𝘯 𝘩𝘰𝘭𝘭𝘦𝘳 𝘭𝘰𝘶𝘥𝘦𝘴𝘵 𝘸𝘪𝘵𝘩𝘰𝘶𝘵 𝘬𝘯𝘰𝘸𝘪𝘯𝘨 𝘸𝘩𝘢𝘵 𝘩𝘦 𝘪𝘴 𝘩𝘰𝘭𝘭𝘦𝘳𝘪𝘯𝘨 𝘢𝘣𝘰𝘶𝘵............. ᴍᴀʀᴋ ᴛᴡᴀɪɴ