Marching Soldier

I was asked on my last live stream about the Marching Soldier craps strategy. Here is my interpretation of how it works on a table where you must pay the commission on the 10 in advance.

1. Make $5 place bet on the 4.
2. If step 1 wins, then take $14 win* plus $1 from your stack and make $15 place bet on the 5.
3. If step 2 wins, then make $36 place bet on the 6.
4. If step 3 wins, then make $78 place bet on the 8.
5. If step 4 wins, then bet $169 win plus $1 from your stack on the 9.
6. If step 5 wins, then you will have $408. Take $12 from your stack to pay the $20 commission on a $400 buy bet on the 10.
7. If step 6 wins, then take down the $1200.
8. If any bet loses, then you're done.

*: By "win" I include the original bet amount.

The part about adding $12 from your stack after a win on the 9 is an assumption of mine. I can't find any source that makes it clear what to do.

Here is my analysis.

Event	Pays	Probability	Expectected win
Immediate loss	-5	0.666667	-3.333333
Loss before 5	-6	0.200000	-1.200000
Loss before 6	-6	0.072727	-0.436364
Loss before 8	-6	0.033058	-0.198347
Loss before 9	-7	0.016529	-0.115702
Loss before 10	-19	0.007346	-0.139578
Win on 10	1181	0.003673	4.337925
Total		1.000000	-1.085399

I show the expected bet amount to be $5.49. Dividing the expected loss of $1.09 by the expected bet of $5.49 gives a house edge of 19.76%.

If the commission is paid only after a win on the 10, then I would pocket $8 after a win on the 9. A win on the 10 would have a return of $1180. Here is my analysis under if commission is paid on wins only on the 10.

Event	Pays	Probability	Expectected win
Immediate loss	-5	0.666667	-3.333333
Loss before 5	-6	0.200000	-1.200000
Loss before 6	-6	0.072727	-0.436364
Loss before 8	-6	0.033058	-0.198347
Loss before 9	-7	0.016529	-0.115702
Loss before 10	1	0.007346	0.007346
Win on 10	1188	0.003673	4.363636
Total		1.000000	-0.912764

The lower right cell shows an expected loss of $0.91.

Expected bet is $5.36 for a house edge of 17.03%.

The question for the poll is would you play the Marching Soldier? Multiple votes allowed.

I can see the parlay logic appeal. It reminds me of the 1 3 2 4 system where you try to snowball your winnings into a big payoff while minimizing risk to your starting bankroll. Still, the only reason I can see someone here doing it is to simply say that they did. It's the craps equivalent to joining the mile high club.

I think it is always worth saying no combination of negative expectation bets can result in positive expectation.

Normally I would say then that analysis is a waste of time, however, you decided to do so. I know you didn't think it would be +EV , so what caught your interest here?

Quote: Wizard

The lower right cell shows an expected loss of $0.91.

Expected bet is $5.36 for a house edge of 17.03%.

The question for the poll is would you play the Marching Soldier? Multiple votes allowed.
link to original post

(Quote truncated)

I just want to point out that the marching soldier combines a bunch of bets with a house edge far less than 17.03% and you end up with a Wiz calculation of a combined house edge of 17.03%. Makes sense to me as this is like a paroli.

But, many on this board denigrates ThomasK for stating that a martingale combines bets of a certain HE and leads to a combined bet with a lower HE.

There’s a contradiction in these positions.

Quote: unJon

I just want to point out that the marching soldier combines a bunch of bets with a house edge far less than 17.03% and you end up with a Wiz calculation of a combined house edge of 17.03%. Makes sense to me as this is like a paroli.

But, many on this board denigrates ThomasK for stating that a martingale combines bets of a certain HE and leads to a combined bet with a lower HE.

There’s a contradiction in these positions.
link to original post

It depends how you define the house edge involving parlays. I generally only count the original wager as money bet. The reason the house edge is so high is the same money is often bet multiple times.

Quote: Wizard

I was asked on my last live stream about the Marching Soldier craps strategy. Here is my interpretation of how it works on a table where you must pay the commission on the 10 in advance.

1. Make $5 place bet on the 4.
2. If step 1 wins, then take $14 win* plus $1 from your stack and make $15 place bet on the 5.
3. If step 2 wins, then make $36 place bet on the 6.
4. If step 3 wins, then make $78 place bet on the 8.
5. If step 4 wins, then bet $169 win plus $1 from your stack on the 9.
6. If step 5 wins, then you will have $408. Take $12 from your stack to pay the $20 commission on a $400 buy bet on the 10.
7. If step 6 wins, then take down the $1200.
8. If any bet loses, then you're done.

*: By "win" I include the original bet amount.

The part about adding $12 from your stack after a win on the 9 is an assumption of mine. I can't find any source that makes it clear what to do.

Here is my analysis.

Event	Pays	Probability	Expectected win
Immediate loss	-5	0.666667	-3.333333
Loss before 5	-6	0.200000	-1.200000
Loss before 6	-6	0.072727	-0.436364
Loss before 8	-6	0.033058	-0.198347
Loss before 9	-7	0.016529	-0.115702
Loss before 10	-19	0.007346	-0.139578
Win on 10	1181	0.003673	4.337925
Total		1.000000	-1.085399

I show the expected bet amount to be $5.49. Dividing the expected loss of $1.09 by the expected bet of $5.49 gives a house edge of 19.76%.

If the commission is paid only after a win on the 10, then I would pocket $8 after a win on the 9. A win on the 10 would have a return of $1180. Here is my analysis under if commission is paid on wins only on the 10.

Event	Pays	Probability	Expectected win
Immediate loss	-5	0.666667	-3.333333
Loss before 5	-6	0.200000	-1.200000
Loss before 6	-6	0.072727	-0.436364
Loss before 8	-6	0.033058	-0.198347
Loss before 9	-7	0.016529	-0.115702
Loss before 10	1	0.007346	0.007346
Win on 10	1188	0.003673	4.363636
Total		1.000000	-0.912764

The lower right cell shows an expected loss of $0.91.

Expected bet is $5.36 for a house edge of 17.03%.

The question for the poll is would you play the Marching Soldier? Multiple votes allowed.
link to original post

IMO this strategy is totally mis-leading. It does NOT take into account the number of rolls within the hand to complete the ultimate objective. Since the 7 appears on average every six rolls, the likelihood of the ultimate win is more remote than shown. While this calculation might have some merit, the reality of table play would not bear out these HE numbers.

tuttigym

Quote: tuttigym

IMO this strategy is totally mis-leading. It does NOT take into account the number of rolls within the hand to complete the ultimate objective. Since the 7 appears on average every six rolls, the likelihood of the ultimate win is more remote than shown. While this calculation might have some merit, the reality of table play would not bear out these HE numbers.
link to original post

I'm pretty sure the Wizard took that into account.

I’ve never been a sidebet person at craps but this does seem more fun than a $1 fire bet for a similar or lower house edge. Plus maybe you get credit for a bigger average bet on those occasions when you do get up to a $400 10.


Also, the probability of a win is 0.003673 on the chart. What does that convert to in term of “1 out of…” tries? More generally, what’s the formula for converting that?

If I had to brute force figure it out, I’m guessing I could do something like 1/3 x 2/3 x 5/6 x 5/6 x 2/3 x 1/3 and then reduce the fraction to 1 / something?

duplicate post

Number	Bet	Win	Total	Keep	Kept	Net if Lost
Four	5	9	14	4	4	-5
Five	10	14	24	0	4	-1
Six	24	28	52	4	8	-1
Eight	48	56	104	4	12	3
Nine	100	140	240	20	32	7
Ten	220	440	660	660	692	27

Number	Bet	Win	Total	Keep	Kept	Net if Lost
Four	10	18	28	3	3	-10
Five	25	35	60	6	9	-7
Six	54	63	117	3	12	-1
Eight	114	133	247	22	34	2
Nine	225	315	540	40	74	24
Ten	500	1000	1500	1500	1574	64

Number	Bet	Win	Total	Keep	Kept	Net if Lost
Four	15	27	42	7	7	-15
Five	35	49	84	6	13	-8
Six	78	91	169	19	32	-2
Eight	150	175	325	25	57	17
Nine	300	420	720	70	127	42
Ten	650	1300	1950	1950	2077	112

Number	Bet	Win	Total	Keep	Kept	Net if Lost
Four	25	50	75	10	10	-25
Five	65	91	156	6	16	-15
Six	150	175	325	25	41	-9
Eight	300	350	650	25	66	22
Nine	625	875	1500	200	266	78
Ten	1300	2600	3900	3900	4166	334

The number in bold is what you end up with if you take it down after all six hit.

Note that I didn't figure in the vig on the ten, (or four at the $25 table).

Quote: TinMan

Also, the probability of a win is 0.003673 on the chart. What does that convert to in term of “1 out of…” tries?
link to original post

Basic math: Reciprical.

1 / 0.003673 = 272.257

Quote: TinMan

I’ve never been a sidebet person at craps but this does seem more fun than a $1 fire bet for a similar or lower house edge. Plus maybe you get credit for a bigger average bet on those occasions when you do get up to a $400 10.


Also, the probability of a win is 0.003673 on the chart. What does that convert to in term of “1 out of…” tries? More generally, what’s the formula for converting that?

If I had to brute force figure it out, I’m guessing I could do something like 1/3 x 2/3 x 5/6 x 5/6 x 2/3 x 1/3 and then reduce the fraction to 1 / something?
link to original post

I agree with you, this seems like a silly fun "accomplish once" kind of thing if you plan on playing craps for years/decades. Just like hitting the ATS/firebet once and never betting it again. @Wiz my understanding of Marching Soldiers is you just parlay the wins along the board, you don't have to power press / half press at all. Just make the bets proper on 6 and 8.

Overall thought I don't think I'd ever play this at an actual table. This would be a purely min-bet Roll to Win table, or Bubble craps game kind of thing. I can't imagine ever making serious money off of this compared to just about any other weird craps strategy.

I'd like to nominate this strategy for being one of the worst craps strats to exist, however it's better than the "All-in field" "all-in Hardways" and "all-in bet the 7" type strategies. Its also worse than just split the sisters.

Quote: DJTeddyBear

Quote: tuttigym

IMO this strategy is totally mis-leading. It does NOT take into account the number of rolls within the hand to complete the ultimate objective. Since the 7 appears on average every six rolls, the likelihood of the ultimate win is more remote than shown. While this calculation might have some merit, the reality of table play would not bear out these HE numbers.
link to original post

I'm pretty sure the Wizard took that into account.
link to original post

Perhaps, but talk about guessing, there is no way to possibly quantify the rolls or 7's in the REALITY of play. One could do the simulation thing for billions of rolls and still not be nearly accurate.

One other thing for the truly "lucky," the feat could actually be accomplished in as few as six consecutive rolls. So, I am saying it is not impossible. Go for it.

What does a 17.03% HE mean exactly? Can the player only lose 17.03% of the time or 17.03% of his bankroll? What?

tuttigym

Quote: tuttigym

… What does a 17.03% HE mean exactly? Can the player only lose 17.03% of the time or 17.03% of his bankroll? What?

tuttigym
link to original post

Just like any other game. If you play it a billion times, you should end up with 17.03% less money.

Quote: DJTeddyBear

Quote: tuttigym

… What does a 17.03% HE mean exactly? Can the player only lose 17.03% of the time or 17.03% of his bankroll? What?

tuttigym
link to original post

Just like any other game. If you play it a billion times, you should end up with 17.03% less money.
link to original post

tuttigym rejects the central limit theorem. It’s not worth engaging.

If you think you can roll it, bet it, otherwise stay as far away from this system as possible.