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    STICKMAN'S STANCE - MONTHLY ARTICLES BY STICKMAN
Craps Training

The Iron Cross

Over the years there has been a lot of talk about a betting system called the Iron Cross. The attraction to this betting system is straight-forward – you will get paid whenever any number rolls, except for the seven. Imagine, when the 4 hits, you get paid - when the 5 hits - you get paid, when the 6, 8, 9, or 10 hits – you get paid. Even when craps numbers hit – you get paid. You make money on the 2, 3, 11, and 12. If you do the math, you know there are only(?) 6 ways to make the 7 out of 36 possibilities, so 30 out of 36 combinations result in a win.

The Iron Cross bet consists of place bets on the 5, 6, and 8 and a field bet. The field bet wins if you throw a 2, 3, 4, 9, 10, 11 or 12. When the field bet loses, one of the place bets wins giving the player a small profit – except of course if a 7 appears. When that happens the player loses all the bets.

I can recall many times when I had a pass line bet with odds and placed the 6 and 8 and threw number after number without collecting anything. The Iron Cross bet will definitely eliminate that situation. The only time you will not win money is when you throw the 7.

Sounds like an ideal situation, doesn’t it?

And it would be, were it not for the fact that when you throw the 7, you lose all your bets.

The question, then, is how good (or bad) a bet is the Iron Cross. Is winning better than 83 percent of your bets a good deal?

Let’s assume we are playing a random game. Conventional wisdom states that hedge bets cause you to lose more money. If you ordinarily bet $6 on the 6 and 8, you have $12 at the mercy of a 1.52 percent house edge. Multiplying the two you are destined to lose about 18 cents on the $12. Now, if you add a place bet on the 5 for $5, you add 4 percent of it or 20 cents. Add still another bet on the field for $5 and you add 5.56 percent of it or another 27.8 cents. You have more money at risk with higher house edges so you will lose more money – period.

But what if you ordinarily bet $12 on the 6 and 8 for a total of $24 wagered and you would rather bet $22 on the Iron Cross? Your bets would be $6 each on the 6 and 8 and $5 each on the 5 and field. Here you are betting slightly less money and getting many more wins than before. What is the house edge (there will be a house edge, not a player edge) and what can you expect to lose per dollar bet?

This much we know:

  • The 6 and 8 have a 1.52 percent house edge working on $24.
  • The 5 has a 4 percent house edge working on $5.
  • The field bet has a 5.56 percent house edge working on $5.

Intuitively, the edge on the total bet of $22 should be between 1.52 and 5.56 percent. So let’s calculate the exact edge. I want to acknowledge Dan Pronovost, the creator of the Smart Craps software, for his assistance in the following calculations.

Suggestion: If you are only interested in the answer and not the mathematical proof, you can skip ahead to "The Result".

The Math:

Alright, if you are still with me, here comes the technical stuff.

First, what do we mean by house edge? The simple to understand definition is:

Sum of all profit (or loss)
-----------------------------------
Sum of all bets made

Next, we need to come up with a way to apply this to the Iron Cross betting scheme. For this exercise we are using a $30 6 and 8, a $25 5 and a $25 field bet. Let's look at the problem on a per roll basis:

Roll

Occurrences

Roll Frequency

Profit per roll

Pro-rated. Profit

2

1

2.78%

$50.00

$1.39

3

2

5.56%

$25.00

$1.39

4

3

8.33%

$25.00

$2.08

5

4

11.11%

$10.00

$1.11

6

5

13.89%

$10.00

$1.39

7

6

16.67%

-($110.00)

($18.33)

8

5

13.89%

$10.00

$1.39

9

4

11.11%

$25.00

$2.78

10

3

8.33%

$25.00

$2.08

11

2

5.56%

$25.00

$1.39

12

1

2.78%

$50.00

$1.39

Total:

36

100.00%

($1.94)

A win on the 2 and 12, is paid 2 to 1 on the field bet so our net profit is $50 (2 times the $25 bet). On a 6, we lose the $25 field bet, but get back $35 on the placed 6, netting $10. On a 3, we win the field bet at even money ($25).

We now know the profit for each roll. But each roll occurs in a different proportion, so let's multiply by the 'Roll Frequency' column to yield the 'Pro-rated profit' column above. Then, we can sum this up to yield the average net loss per roll of $1.94.

Remember, however, that in order to be counted as a win in the amount in the "Profit per Roll" column, we need to take the bet down. For example, we have a $25 field bet and a 3 is rolled. If we simply collect the $25 and leave the field bet up, we do not have a $25 profit, we are even on that $25 bet. What we are doing in reality is collecting our winnings – and bet – and then replacing the bet. The ‘New Bets After Roll’ column in the following table details these amounts.

Roll

Occurrences

Roll Frequency

New bets after roll

Pro-rated bets/roll

2

1

2.78%

$25.00

$0.69

3

2

5.56%

$25.00

$1.39

4

3

8.33%

$25.00

$2.08

5

4

11.11%

$50.00

$5.56

6

5

13.89%

$55.00

$7.64

7

6

16.67%

$110.00

$18.33

8

5

13.89%

$55.00

$7.64

9

4

11.11%

$25.00

$2.78

10

3

8.33%

$25.00

$2.08

11

2

5.56%

$25.00

$1.39

12

1

2.78%

$25.00

$0.69

Total:

36

100.00%

$50.28

And once again, we need to pro-rate the new bets based on the roll's frequency, yielding the 'Pro-rated bets/roll'. Summing these up, we get an average of $50.28 in new bets every roll.

So back to the edge equation – the net loss per roll is $1.94, and the average "New bets per roll" is $50.28. Divide these two, and we get an actual casino edge of 3.87% over the player.

The Simulation

Using Smart Craps and script betting, the Iron Cross betting scheme can be modeled. After 10 millions execution rounds, the empirical edge is -3.831340%, which is sufficiently close to the mathematical edge we computed above.

A Check and Audit…

Not sure this approach makes sense? Let's use the same approach to analyze a $30 6 place bet (1.52% house edge):

Roll

Roll Frequency

Profit per roll

Pro-rated. Profit

New bets after roll

Pro-rated bets/roll

2

2.78%

$0.00

$0.00

$0.00

$0.00

3

5.56%

$0.00

$0.00

$0.00

$0.00

4

8.33%

$0.00

$0.00

$0.00

$0.00

5

11.11%

$0.00

$0.00

$0.00

$0.00

6

13.89%

$35.00

$4.86

$30.00

$4.17

7

16.67%

($30.00)

($5.00)

$30.00

$5.00

8

13.89%

$0.00

$0.00

$0.00

$0.00

9

11.11%

$0.00

$0.00

$0.00

$0.00

10

8.33%

$0.00

$0.00

$0.00

$0.00

11

5.56%

$0.00

$0.00

$0.00

$0.00

12

2.78%

$0.00

$0.00

$0.00

$0.00

Total:

100.00%

($0.14)

$9.17

Using the totals from above, -$0.14 / 9.17 = 1.52%… just like all the experts say.

The Results:

If you came directly here and bypassed the proof above, you either completely trust me, or you get lost easily in math and charts and tables. Either way, the results are accurate.

We surmised early on that the house edge for the Iron Cross bet would be between 1.52 percent and 5.56 percent – and we were right. Betting one unit ($25 in the proof) on the Iron Cross, carries a 3.87 percent house edge when both the 2 and 12 pay double in the field bet. Let’s check the answer to the original question. Is it better to bet $12 each on the 6 and 8, or $22 on the Iron Cross?

  • 6 and 8: $24 * 1.52% = about 36˝ cents lost.
  • Iron Cross: $22 * 3.87% = about 85 cents lost – even though less money is at risk.

Even though you are getting paid on 30 out of 36 rolls, the "tax" on those winnings amounts to about 2 ˝ times as much money. This is not a good bet. No matter how tempting is may be prudent players will avoid it.

In the next installment on the Iron Cross I will look at what happens when you vary the amounts bet on the individual components of the Iron Cross. I will also show the effect on the house edge of varying degrees of dice control and various betting combinations. The results should prove interesting to you.

 

Until then remember:

"Nothing is foolproof to a sufficiently talented fool."

Stickman



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