thecesspit
Joined: Apr 19, 2010
• Posts: 5936
March 18th, 2015 at 7:53:51 AM permalink
'Better' depends on you definition to compare two systems and what the goal is. Better for one goal can be worsevfor another.

Betting systems do vary. The other important factor is variance.

If you compare over infinite plays, yes all systems lose your bankroll. Not everyone plays until their bankroll is empty...
"Then you can admire the real gambler, who has neither eaten, slept, thought nor lived, he has so smarted under the scourge of his martingale, so suffered on the rack of his desire for a coup at trente-et-quarante" - Honore de Balzac, 1829
ThatDonGuy
Joined: Jun 22, 2011
• Posts: 4289
March 18th, 2015 at 7:53:57 AM permalink
Quote: Twirdman

None of them change the EV of the game as a proportion of amount bet which for gambling is all anyone ever talks about. They change the amount bet which can change the expected loss per hour but again none of them to any better then just flat betting table minimum so what does it really matter.

Because the EV is a fraction of the bet. The more money you bet, the more you are expected to lose.

If your stop point is, "I'll stop after betting a total amount X", then you're right; all systems are the same in that all of them are expected to lose the same fraction of X.

Example: even-money betting on a double-zero roulette wheel (probability of winning = 9/19).
You start with a bankroll of 2, and you want to double it before losing everything.
If you make a single bet of 2, you always end after betting a total of 2, your probability of success = 9/19.
On the other hand, if you stick to bets of 1:
81/361 of the time, your first two bets win, and you have reached your target.
100/361 of the time, your first two bets lose, and you have lost your bankroll.
The other 180/361 of the time, you win one and lose one, and are back to your starting point; repeat the process.
You might end up betting a total of 2, or 4, or 6, or 8, or any positive even number.
Your probability of success is 81 / (81 + 100) = 81/181 < 9/19.
JyBrd0403
Joined: Jan 25, 2010
• Posts: 548
March 19th, 2015 at 3:46:17 PM permalink
Quote: thecesspit

'Better' depends on you definition to compare two systems and what the goal is. Better for one goal can be worsevfor another.

Betting systems do vary. The other important factor is variance.

If you compare over infinite plays, yes all systems lose your bankroll. Not everyone plays until their bankroll is empty...

Yes, but if you were to compare the different systems based simply on 1 million trials. You should be able to "rank" the systems based on how much money each system lost after 1 million trials. Should be pretty straight forward, since they all produce different results.

Quote: ThatDonGuy

The 1-2-3-4-5 Martingale has an average bet of 1.85040487 in a 1% game, and 1.90068217 in double-zero roulette.

Yes, there's a generic solution for this as well: (1 - (N+1) qN + N qN+1) / (p (1 - qN))
I have a feeling this can be reduced further.
...and it can: N + 1 / p - N / (1 - qN)

Thanks for this Don.
Kavouras
Joined: Apr 22, 2014
• Posts: 52
March 19th, 2015 at 5:19:33 PM permalink
Quote: JyBrd0403

Yes, but if you were to compare the different systems based simply on 1 million trials. You should be able to "rank" the systems based on how much money each system lost after 1 million trials. Should be pretty straight forward, since they all produce different results.

It's pretty straightforward in the sense that in the "long run" (1 million spins can be considered long run I guess) all systems are expected to return to you 97,3% of what you bet.
So, without a specific (win) target, bankroll requirements and some sort of plan/strategy all systems are the same as throwing your chips on the table, if you plan to mindlessly play a progression over 1 million spins, without bankroll and table limitations.

1 million spin tests are useless. Because we already know the result.
http://www.Roulette30.com
ThatDonGuy
Joined: Jun 22, 2011
• Posts: 4289
March 19th, 2015 at 6:06:57 PM permalink
Quote: Kavouras

It's pretty straightforward in the sense that in the "long run" (1 million spins can be considered long run I guess) all systems are expected to return to you 97,3% of what you bet.

I think that's the point - what systems have what average bets? The lower the average bet, the longer your bankroll is expected to last.
mustangsally
Joined: Mar 29, 2011
• Posts: 2463
March 19th, 2015 at 6:58:23 PM permalink
Quote: Kavouras

It's pretty straightforward in the sense that in the "long run" (1 million spins can be considered long run I guess)

i say your guess is wrong
just wrong
Quote: Kavouras

all systems are expected to return to you 97,3% of what you bet.

exactly
key word = expected
in other words
expected = average
or in your opinion expected = ??
Quote: Kavouras

So, without a specific (win) target, bankroll requirements and some sort of plan/strategy all systems are the same as throwing your chips on the table, if you plan to mindlessly play a progression over 1 million spins, without bankroll and table limitations.

hahaha

Quote: Kavouras

1 million spin tests are useless. Because we already know the result.

a wrong one in me opinion

take 18/37 = p (p=probability of success)

after 1,000,00 spins and equal average bets (1 unit okay)

1 in 15,787 (on average) would be outside the range of 4SD or four standard deviations

so with 1 million players playing 1 million spins (happens every second i say)
i would expect more than a few would be outside of these ranges and NOT exactly or close to your 97,3%

0.976967429 to 0.968978517
and as a percentage
97.6967429% to 96.8978517%

and in real \$\$\$\$ lost
because gamblers do lose real money
that range = -23,032.57 to -31,021.48

not close to exactly -27,027.03
(all values are in units)

you may check my math as Excel did it for me

Sally says in Oh so many words

all opinions
except Excel wanted to do the math real bad!
I Heart Vi Hart
Kavouras
Joined: Apr 22, 2014
• Posts: 52
March 19th, 2015 at 6:59:59 PM permalink
Quote: ThatDonGuy

I think that's the point - what systems have what average bets? The lower the average bet, the longer your bankroll is expected to last.

Yes. And as we all know the lowest average bet is zero. Do not play at all :-)
http://www.Roulette30.com
JyBrd0403
Joined: Jan 25, 2010
• Posts: 548
March 19th, 2015 at 11:28:57 PM permalink
Quote: ThatDonGuy

I think that's the point - what systems have what average bets? The lower the average bet, the longer your bankroll is expected to last.

Yes, exactly my point, since they all have different average bets, which produce different results, it should be able to clearly "rank" which ones are better or worse, mathematically.

Just thinking about it. A Reverse D'Alembert or Reverse Martingale would both, I would assume, have lower average bet sizes than playing the normal way. So, there's two games that would rank higher than a regular D'Alembert or Marty. That's surprising, to me at least. I wouldn't have guessed that. Anyway, I think it would be interesting to see the different Systems ranked. That's all I'm saying.
ThatDonGuy
Joined: Jun 22, 2011
• Posts: 4289
March 20th, 2015 at 10:54:21 AM permalink
Quote: JyBrd0403

Just thinking about it. A Reverse D'Alembert or Reverse Martingale would both, I would assume, have lower average bet sizes than playing the normal way. So, there's two games that would rank higher than a regular D'Alembert or Marty. That's surprising, to me at least. I wouldn't have guessed that. Anyway, I think it would be interesting to see the different Systems ranked. That's all I'm saying.

What's "the normal way"? The obvious answer to "what's the best system" is, flat bet the minimum. By definition, a reverse anything system starts out with a higher bet than the minimum.

"The best system is not to play" reminds me of WarGames - speaking of which, ever hear the story of "WarGames: The Next Five Minutes"?
"Sir, our launch system has been deactivated."
"Incoming missiles - confirmed visually!"
"WOPR, what is happening?"
"You left one scenario out of Global Thermonuclear War - Soviets launch, USA doesn't; I win. I disabled your launching system. If Kirk is allowed to 'alter the conditions' of Kobayashi Maru, why can't I?"
Biggredd
Joined: Jan 20, 2014