Craps hardways system

Yes, I know what you're going to say, and yes, I agree that all systems have their flaws.

I will even point out the flaws in this system. But it is an interesting system that I'd thought I'd share.

Watch a typical craps player and if he's betting the hard ways, he will press his bet if it hits. While I agree that dice have no memory, after a hit seems to me to be the ideal time to REDUCE the bet. And that is the basis of this system.


To keep things simple, I'll only discuss a single hard way bet.

Bet $1 on a hard 6. If an easy 6 or 7 is rolled, replace the bet and increase it $1. If the hard 6 is rolled, take it down (and restart at $1). If anything else is rolled, do nothing.

For example, put up $1. Eventually you hit an easy 6 or 7. Replace it with $2. Another loss for a total lost of $3. Put up $3. Another loss for a total lost of $6. Put up $4. Hit a hard 6. Win $36, plus take down the $4 bet. (Win if Hit column shows this $40 total). Subtract the $6 previously invested and lost, and the $4 bet itself, for a net profit of $30.

Ignoring rolls that are neither 6 or 7, there is a 10/11 chance that the roll is not a hard six - i.e. 90.9%. That two rolls of 6 or 7 are both not a hard 6 is (10/11)^2, or 82.6%, etc. This is shown in the 'Loss Expectation' column in the chart.

Bet	Invested	Win if Hit	Net	Loss Expectation
1	1	10	9	0.9090909091
2	3	20	17	0.8264462810
3	6	30	24	0.7513148009
4	10	40	30	0.6830134554
5	15	50	35	0.6209213231
6	21	60	39	0.5644739301
7	28	70	42	0.5131581182
8	36	80	44	0.4665073802
9	45	90	45	0.4240976184
10	55	100	45	0.3855432894
11	66	110	44	0.3504938995
12	78	120	42	0.3186308177
13	91	130	39	0.2896643797
14	105	140	35	0.2633312543
15	120	150	30	0.2393920494
16	136	160	24	0.2176291358
17	153	170	17	0.1978446689
18	171	180	9	0.1798587899
19	190	190	0	0.1635079908
20	210	200	-10	0.1486436280
21	231	210	-21	0.1351305709
22	253	220	-33	0.1228459736
23	276	230	-46	0.1116781578
24	300	240	-60	0.1015255980
25	325	250	-75	0.0922959982
26	351	260	-91	0.0839054529

It's interesting to me that row 11, which is the statistical point in which you should hit the hard 6, is at the peak of the net profit. (Side note: Is that the correct way to phrase that?)


FYI: Come out rolls don't matter. Since there's a 1/36 chance of a hard six, and 10/36 chance of an easy 6 or a 7 on EVERY roll, having hard ways off for a come out doesn't affect the statistics, probability or payoffs.


The bad side of this system:


As you can see, if there are 19 losses, even if it's followed by a win, you're still $10 in the hole. And there's a 16.3% chance of that, OR WORSE, happening.

Suffer 22 losses, and you're in the hole so far that even hitting a win at level 23, You'd need another win, at level 9, just to break even. (OK, You're actually still $1 short.)


It's also damn boring.

Since most dice rolls will result in no resolution, it's too time consuming - except on a virtual craps table.

I tested this system a few times on the Wizard of Odds craps table. With a roll every couple seconds, I was able to quickly simulate several hours of live play. Every time, as expected, I was down quite a bit before I started to climb out of the hole, but was always ahead after 10 minutes.

In a real-world casino test, it's easy to forget where you are. You need a helpful / friendly stickman. I tried it at a table that had only two players. The dealers were intrigued by my theory. The stick helped me by telling me how much was there on a loss, so I could simply pay to keep it (and press $1) rather than clearing the loss and resetting the bet. I think I got lucky because I never went more than 13 levels deep, and had a hit both the 6 and 8 right about the time I wanted to leave.


After the real-world test, I told my wife about this system. She was skeptical but intrigued and said we should test it with our poker chips and regular dice on our dining room table.

We set up two $500 bankrolls, and played the hard 6 and 8 separately.

The hard 6 bankroll never got lower than $350, and ended up close to $400 ahead when we stopped. At the same time, the hard 8 bankroll needed to take out several markers as it missed a whopping eighty-seven times!


Bottom line: As interguing as this system is, I'll never do it again.

But I thought I'd share.

Statistically speaking, this is a stinker.

The HA on the hard 6 and 8 is 9.0909%. And the hard 6 and 8 will be resolved every 36 / 11 rolls.

So, you have to ask the question, how often does the martingaling result in a net loss of units?

After the 19th consecutive loss, you begin to lose units because the amount you Martingale no longer covers the cost. The odds of losing 20 or more times in a row is .9090909 ^ 20 = 14.86%, which is no small number.

So, I simulated a $500 bankroll using your system, and did 1,000 rolls of the dice with "ruin" happening when the total was greater than a $500 loss. I completed this over 100 trials for a total of 100,000 dice rolls. Your biggest win would be $976.

You would be in ruin on 59 of those trials. Your net loss over the 100 trials would be $16,621 (an average loss of $166/trial). Without any ruin in effect, you would lose $25,831 (an average loss of $258/trial).

Martingaling doesn't work.

Quote: boymimbo

Statistically speaking, this is a stinker.

The HA on the hard 6 and 8 is 9.0909%. And the hard 6 and 8 will be resolved every 36 / 11 rolls.

So, you have to ask the question, how often does the martingaling result in a net loss of units?

After the 19th consecutive loss, you begin to lose units because the amount you Martingale no longer covers the cost. The odds of losing 20 or more times in a row is .9090909 ^ 20 = 14.86%, which is no small number.

So, I simulated a $500 bankroll using your system, and did 1,000 rolls of the dice with "ruin" happening when the total was greater than a $500 loss. I completed this over 100 trials for a total of 100,000 dice rolls. Your biggest win would be $976.

You would be in ruin on 59 of those trials. Your net loss over the 100 trials would be $16,621 (an average loss of $166/trial). Without any ruin in effect, you would lose $25,831 (an average loss of $258/trial).

Martingaling doesn't work.

This *does* seem very Martingale. The attraction of the Martingale is always that in your gut it seems unlikely that you could be unlucky enough, except on rare occasion, to have a big string of losses in a row. However, the facts show that a long string of losses in a row are quite likely nearly every "session".

Quote: DJTeddyBear

It's interesting to me that row 11, which is the statistical point in which you should hit the hard 6, is at the peak of the net profit. (Side note: Is that the correct way to phrase that?)

I'd say you're half right.

On average the hard 6 should take 7.27 bets to hit. This number is the solution to (10/11)^x = 1/2. After 10 bets the probability of at least one hard 6 hitting is 61.4% and after 11 bets it is nearly 65%. You don't get to 90% certainty of winning until the 25th bet! (24.16 bets, actually. Of course this includes all instances of winning more than once.)

It is easy to see why the net win goes down after the 10th bet. For each new bet after the 10th, the unit increment (the total risked) goes up by more than the incremental win ($10).

I must be an idiot and missing something, because your chart looks like a hard 6 or 8 pays 10 to 1.

Quote: playpianoking

I must be an idiot and missing something, because your chart looks like a hard 6 or 8 pays 10 to 1.

Probably missing the "take it down" when the hardway hits.

Quote: 7outlineaway

Quote: DJTeddyBear

It's interesting to me that row 11, which is the statistical point in which you should hit the hard 6, is at the peak of the net profit. (Side note: Is that the correct way to phrase that?)

I'd say you're half right.

On average the hard 6 should take 7.27 bets to hit....

You're talking about probabilities. I was talking statistically.

STATISTICALLY, out of every 11 rolls of 6 or 7, one is a hard 6.

When talking about probabilities, look at my Loss Expectation column. You're right. There's a 50% chance of hitting a hard 6 after the 7th roll of a 6 or 7, and a 10% chance of still not hitting a hard 6 after the 25th roll of 6 or 7.

Quote: seattledice

Quote: playpianoking

I must be an idiot and missing something, because your chart looks like a hard 6 or 8 pays 10 to 1.

Probably missing the "take it down" when the hardway hits.

Yep.

When it hits, take it down (and optionally, restart at $1).


The "Take It Down" concept is how I came up with this in the first place. It always amazes me to see people pressing their hardways right after it hits.

Oh, sure, the dice have no memory, so a back-to-back is possible. But is that really a reasonable expectation?


when you're playing an even money game such as the 1:1 bets on Roulette, it makes sense to press the bets when you're winning. Tap into that emotion that says you're on a hot streak. Drop back to the minimum after a loss.

But when playing long shots like the hard ways, the thing to do is to press it when you're losing, since a losing streak is the normal and expected outcome. Then drop back to start after a win.