Bet method based on mini-games

[beretta28]

Sorry,I miscalculated.Your table is perfect.I'm not stronger than a computer......

In fact all my comments or doubts were based on the fact that I'm in Europe and I know and play only roulette,one zero,partage rule.
That's why your tables seemed to me a bit strange,mainly bankroll 10 units win goal + 1 unit.

In the book of Dubins and Savage(How to play ,if you must),that take into consideration only European roulette,partage rule,the best strategy for 10 units to 11 units is "to play the minimum amount of units on EC,that allows to reach the goal in the lowest number of spins,that is:
1 unit,if lose 2 units,if lose 4 units,if lose 3 units.If lose again,game over.If win last 3 units bet,than bet 5 units and so on with the same principle that Dubins and Savage call "the brave and risky strategy" or something like that.
What I don't understand is that playing this way the % of success is 89,9406,exactly the same % you mention with NO partage rule in your EC version.(!!!)

[beretta28]

Sorry,I miscalculated.Your table is perfect.I'm not stronger than a computer......

In fact all my comments or doubts were based on the fact that I'm in Europe and I know and play only roulette,one zero,partage rule.
That's why your tables seemed to me a bit strange,mainly bankroll 10 units win goal + 1 unit.

In the book of Dubins and Savage(How to play ,if you must),that take into consideration only European roulette,partage rule,the best strategy for 10 units to 11 units is "to play the minimum amount of units on EC,that allows to reach the goal in the lowest number of spins,that is:
1 unit,if lose 2 units,if lose 4 units,if lose 3 units.If lose again,game over.If win last 3 units bet,than bet 5 units and so on with the same principle that Dubins and Savage call "the brave and risky strategy" or something like that.
What I don't understand is that playing this way the % of success,according to the book and my calculations and experience, is 89,9406,exactly the same % you mention with NO partage rule in your EC version.(!!!)

[mr.ore]

To make thinks clear, my software policy generator cannot use partage rule right now. I still wonder if with big bankrolls and targets it would always prefer even chance, just because there is lower house edge. In theory we should only use the options with lowest house edge, but I have seen in some article someone combined two worse bets on craps and obtained better probability than with don't pass, so who knows.

Look there: link:://wtwii.wordpress.com/2006/08/24/debunking-a-craps-system/

More interesting is a case (which can also be called a system) in which playing two bets simultaneously in a certain manner results in a lower house advantage. A place bet on the six or on the eight is well known for having a vig of 1.52% (calculated as ((5/11)*7+(6/11)*(-6))/6). However, when you play a place bet on the eight simultaneously and meticulously put both bets up at the same time and remove them both when either wins, the house advantage is only 1.04% (calculated as ((10/16)*7+(6/16)*(-12))/12)!

Anything but Seven

Another similar case occurs with the so-called Mensa Anything But Seven system. You place a one-roll bet for $22 ($6 each on the place 6 and 8, $5 on the field, and $5 on the place 5). The house advantage on this bet (verified here - link:://wizardofodds.com/askthewizard/109) is only 1.136%, less than any of the individual bets placed separately.

[mr.ore]

By the way, what happens with imprison rule, if zero(es) hits, bets are frozen, and next spin another zero hits? Are they lost or imprisoned again, until something other than zero(es) hits? On win they are returned if I remember correctly, right?

[beretta28]

They are imprisoned again and again....
That's why is better to ask the dealer to give half bet back,at the first zero!

[mr.ore]

Does imprison affects also dozens and columns? They are also outside bets.

[beretta28]

I heard also something like that,concerning roulette,but I didn't found anything about that.
I know that is only valable if you play a low number of spins(how many?who knows?) and if the ratio win goal/bankroll is a certain % that I don't know too,but also very low.
I'm wondering if is not called "Parrondo paradox".
That's why I 'm so interested in your tables.I thought that was what I've been looking for several months.
I'm still wondering why % of 89,9406 for EC Marty is the same in your tables(NO partage option,you said-sure?-) and in Dubin and  Savage book(partage option taken into account)

Your example for craps is very interesting.
Unluckily I don't know craps very well(in Europe it doesn'exist partically)

[beretta28]

NO,partage rule exists only for EC.
Dozens and colums are like lines,streets,squares and so on...no partage option!

[mr.ore]

Maybe they did not use that rule, maybe the difference is so negligible, that it is not visible in a few first digits of computed probability number.

[beretta28]

An additional point for roulette is:
-if 1000 players play at least 20000 spins on EC and 1000 players play 20000 spins on an given straight number,both flat bet,at the end of 20 thousand spins ZERO  EC players  will have a positive balance(all losers),but at least 5 players of straight number will still earn money.
That's why EC are not the best bet in certain situations of BKR,wingoal,etc

[mr.ore]

It is obvious, singles have higher variance. After 20000 spins with en prison rule, you have no chance to be positive flat betting. On a number, the chance exists, maybe even on american roulette.

For a nearly optimal play strategy, just do a progression on a single, or with lower targets make a parachute. Nearly optimal strategy is to win at least your target bankroll size in one hit with as few units as possible. If there are more possibilities, just select the one which is as near your target as possible, it's the one which wins minimal amount of units. You can also cap your target bankroll size to force probability stay near optimal strategy. It is that simple.

[beretta28]

Yes,the problem is that the 995 losing players on straight numbers,lose a huge amount of money,much more than each EC players.

The nearly optimal strategy you mention is what I play in Montecarlo Casino.
My win goal is very low(no greed),15% at the most of my bankroll.
Progression:1,2,4,8,10,12,14,16,18,20:105 units(Marty 4 terms and D'Alembert 6 terms).
Risk of ruin/bankruptcy 1,2% or 1 every 83 attacks
(you are expert in Computers,can you check these % as risk of ruin?Thanks)
I don't trust in bet selection:IMHO it doesn't exist.
An alternative is "the bold strategy".
Parachute is dangerous,but I use it just for fun when 15% of bkr is achieved.
I must study your tables and reflect on them.......
If some good ideas i ÃÆ'Ã,¬ll write to you again.

[mr.ore]

If you have 105 units for your progression, then your target = 105*1.15=120 units. You can try this strategy instead, start on a line with bankroll 105. It is should be very near optimal method.

bankroll	bet	W	L	Pwin
0	no bet	-	-	0.0000%
1	1 unit on 35:1	36	0	0.7902%
2	2 unit(s) on 35:1	72	0	1.5918%
3	3 unit(s) on 35:1	108	0	2.4124%
4	3 unit(s) on 35:1	109	1	3.2048%
5	3 unit(s) on 35:1	110	2	4.0083%
6	3 unit(s) on 35:1	111	3	4.8302%
7	3 unit(s) on 35:1	112	4	5.6249%
8	1 unit on 2:1	10	7	6.4303%
9	3 unit(s) on 35:1	114	6	7.2539%
10	10 unit(s) on 11:1	120	0	8.1081%
11	1 unit on 35:1	46	10	8.9005%
12	2 unit(s) on 35:1	82	10	9.7058%
13	3 unit(s) on 35:1	118	10	10.5402%
14	3 unit(s) on 35:1	119	11	11.3362%
15	3 unit(s) on 35:1	120	12	12.1462%
16	6 unit(s) on 17:1	118	10	12.9722%
17	6 unit(s) on 17:1	119	11	13.7719%
18	6 unit(s) on 17:1	120	12	14.5866%
19	9 unit(s) on 11:1	118	10	15.4042%
20	20 unit(s) on 5:1	120	0	16.2162%
21	9 unit(s) on 11:1	120	12	17.0270%
22	12 unit(s) on 8:1	118	10	17.8363%
23	12 unit(s) on 8:1	119	11	18.6433%
24	12 unit(s) on 8:1	120	12	19.4674%
25	1 unit on 35:1	60	24	20.2644%
26	2 unit(s) on 35:1	96	24	21.0763%
27	8 unit(s) on 11:1	115	19	21.8901%
28	8 unit(s) on 11:1	116	20	22.7085%
29	8 unit(s) on 11:1	117	21	23.5258%
30	18 unit(s) on 5:1	120	12	24.3481%
31	11 unit(s) on 8:1	119	20	25.1681%
32	8 unit(s) on 11:1	120	24	25.9970%
33	1 unit on 35:1	68	32	26.7966%
34	2 unit(s) on 35:1	104	32	27.6140%
35	5 unit(s) on 17:1	120	30	28.4374%
36	1 unit on 35:1	71	35	29.2381%
37	2 unit(s) on 35:1	107	35	30.0578%
38	7 unit(s) on 11:1	115	31	30.8623%
39	7 unit(s) on 11:1	116	32	31.6963%
40	16 unit(s) on 5:1	120	24	32.5267%
41	1 unit on 35:1	76	40	33.3294%
42	7 unit(s) on 11:1	119	35	34.1604%
43	7 unit(s) on 11:1	120	36	34.9755%
44	2 unit(s) on 35:1	114	42	35.7914%
45	15 unit(s) on 5:1	120	30	36.6160%
46	2 unit(s) on 35:1	116	44	37.4264%
47	2 unit(s) on 35:1	117	45	38.2528%
48	9 unit(s) on 8:1	120	39	39.0805%
49	2 unit(s) on 35:1	119	47	39.8952%
50	2 unit(s) on 35:1	120	48	40.7269%
51	4 unit(s) on 17:1	119	47	41.5376%
52	4 unit(s) on 17:1	120	48	42.3734%
53	1 unit on 35:1	88	52	43.1811%
54	6 unit(s) on 11:1	120	48	44.0199%
55	13 unit(s) on 5:1	120	42	44.8371%
56	8 unit(s) on 8:1	120	48	45.6664%
57	1 unit on 35:1	92	56	46.4756%
58	1 unit on 35:1	93	57	47.2857%
59	3 unit(s) on 17:1	110	56	48.1169%
60	12 unit(s) on 5:1	120	48	48.9593%
61	1 unit on 35:1	96	60	49.7712%
62	7 unit(s) on 8:1	118	55	50.5946%
63	7 unit(s) on 8:1	119	56	51.4345%
64	7 unit(s) on 8:1	120	57	52.2620%
65	11 unit(s) on 5:1	120	54	53.0977%
66	1 unit on 35:1	101	65	53.9128%
67	3 unit(s) on 17:1	118	64	54.7394%
68	3 unit(s) on 17:1	119	65	55.5801%
69	3 unit(s) on 17:1	120	66	56.4040%
70	10 unit(s) on 5:1	120	60	57.2362%
71	6 unit(s) on 8:1	119	65	58.0624%
72	6 unit(s) on 8:1	120	66	58.8952%
73	1 unit on 35:1	108	72	59.7159%
74	4 unit(s) on 11:1	118	70	60.5490%
75	9 unit(s) on 5:1	120	66	61.3864%
76	4 unit(s) on 11:1	120	72	62.2280%
77	1 unit on 35:1	112	76	63.0529%
78	1 unit on 35:1	113	77	63.8789%
79	5 unit(s) on 8:1	119	74	64.7081%
80	5 unit(s) on 8:1	120	75	65.5608%
81	1 unit on 35:1	116	80	66.3913%
82	1 unit on 35:1	117	81	67.2234%
83	1 unit on 35:1	118	82	68.0577%
84	1 unit on 35:1	119	83	68.8946%
85	7 unit(s) on 5:1	120	78	69.7363%
86	2 unit(s) on 17:1	120	84	70.5759%
87	3 unit(s) on 11:1	120	84	71.4166%
88	4 unit(s) on 8:1	120	84	72.2573%
89	1 unit on 17:1	106	88	73.0831%
90	6 unit(s) on 5:1	120	84	73.9387%
91	1 unit on 17:1	108	90	74.7669%
92	2 unit(s) on 11:1	114	90	75.6063%
93	3 unit(s) on 8:1	117	90	76.4511%
94	13 unit(s) on 2:1	120	81	77.2914%
95	5 unit(s) on 5:1	120	90	78.1648%
96	1 unit on 17:1	113	95	79.0000%
97	2 unit(s) on 11:1	119	95	79.8559%
98	2 unit(s) on 11:1	120	96	80.7027%
99	4 unit(s) on 5:1	119	95	81.5469%
100	4 unit(s) on 5:1	120	96	82.4054%
101	1 unit on 17:1	118	100	83.2534%
102	1 unit on 17:1	119	101	84.1057%
103	1 unit on 17:1	120	102	84.9649%
104	2 unit(s) on 8:1	120	102	85.8240%
105	3 unit(s) on 5:1	120	102	86.6832%
106	1 unit on 11:1	117	105	87.5342%
107	1 unit on 11:1	118	106	88.3904%
108	6 unit(s) on 2:1	120	102	89.2606%
109	1 unit on 11:1	120	108	90.1314%
110	2 unit(s) on 5:1	120	108	91.0021%
111	1 unit on 8:1	119	110	91.8691%
112	1 unit on 8:1	120	111	92.7481%
113	1 unit on 5:1	118	112	93.6150%
114	3 unit(s) on 2:1	120	111	94.5061%
115	1 unit on 5:1	120	114	95.3970%
116	2 unit(s) on 2:1	120	114	96.2879%
117	3 unit(s) on 1:1	120	114	97.1788%
118	1 unit on 2:1	120	117	98.0938%
119	1 unit on 1:1	120	118	99.0211%
120	no bet	-	-	100.0000%

[mr.ore]

From my tests I would say, that it is better to use the table as a positive progression, and start with lower bankroll and make sessions from that, there can be some nice upswings, but also long times of no win, of course. If you start with 105 units, it tanks too often in my opinion, wins are small and cannot make up for losing ones. I have seen several loses killing it and only maybe two or three wins in between. On the other way, several times it survived 10000 spins and in the end returned to positive. Other times the 10000 spins window was just a losing graph. Be warned, it can fluctuate very much. But probability of ONE win is maximised, price is that you either win 15 units or lose all 105, nothing in between.

[beretta28]

Thanks
You are probably right for my progression.
My experience is  that also positive progressions are a slow way to the agony and death.
It's a matter of time!
Guetting ,Pluscuop,Maxxpro,D'Alencon tested as positive progressions hundreds times.
Small losses very frequent,big wins every now and then that don't offset previous losses.
But I agree negative progression are kamikaze behaviours.
IÃÆ'Ã,¬ll try your table,that is dangerous too,I'm afraid.

I don't Know a more solid progression of  a Marty eleven terms(the maximum possible in Montecarlo,1023 units!):Risk of ruin 1/1524 attacks,but exposed to house edge on high terms!!

Headache......