By Jeff Hwang

Most every gambler is familiar with the term

Far more confusing is how the concept of house advantage relates to multi-stage poker games involving multiple wagers, and sometimes multiple initial forced bets. In these games, there are two basic measures of house advantage:

As noted, the house advantage on the Pass Line in craps is 1.41%. But let's say the casino offers 3x-4x-5x odds (largely standard on the Las Vegas Strip); if you bet the full 3x-4x-5x odds, you will average 3.77 units wagered per Pass Line bet, and the house advantage is 1.41% ÷ 3.77 units, or 0.37% per unit wagered -- which is also 0.37% of

In Three Card Poker, the player places an ante wager, and is dealt three down cards, at which point the player can either bet 1x the ante or fold. Under optimal play, the player will play Q-6-4 or better, which happens on 67.4% of hands. This is enough to recover all but 3.37% of the ante, which is the base unit house advantage. If the player antes for $10, the house expects to win 3.37% x $10 = 33.7¢ per hand.

But because the player bets an additional unit on 67.4% of hands, the player bets 1.67 units per hand on average. Dividing the 3.37% house advantage by the 1.67 units bet per hand, we get a house advantage of 2.01% per unit wagered, which is what the Wizard of Odds refers to as the

Element of Risk = House Advantage ÷ Average Bet Per Hand (Units)

Most every gambler is familiar with the term

**house advantage**and how it relates to traditional single-bet games like baccarat, blackjack, roulette, and craps. In craps, for example, the house advantage on the Pass Line bet is 1.41%; if you bet $10 on the Pass Line, the casino will make 1.41% x $10 = 14.1¢ on average. Similarly, the house advantage on the Banker bet in baccarat is 1.06%; for every $10 wager, the house expects to make 10.6¢.Far more confusing is how the concept of house advantage relates to multi-stage poker games involving multiple wagers, and sometimes multiple initial forced bets. In these games, there are two basic measures of house advantage:

**House advantage.**This is house advantage expressed as a percentage of the initial ante wager.**Element of risk (adj. house advantage)*.**Coined by Michael Shackleford a.k.a. Wizard of Odds, this is simply the house advantage per unit wagered, and is calculated as the house advantage divided by the average bet per hand.

As noted, the house advantage on the Pass Line in craps is 1.41%. But let's say the casino offers 3x-4x-5x odds (largely standard on the Las Vegas Strip); if you bet the full 3x-4x-5x odds, you will average 3.77 units wagered per Pass Line bet, and the house advantage is 1.41% ÷ 3.77 units, or 0.37% per unit wagered -- which is also 0.37% of

*all money wagered*.In Three Card Poker, the player places an ante wager, and is dealt three down cards, at which point the player can either bet 1x the ante or fold. Under optimal play, the player will play Q-6-4 or better, which happens on 67.4% of hands. This is enough to recover all but 3.37% of the ante, which is the base unit house advantage. If the player antes for $10, the house expects to win 3.37% x $10 = 33.7¢ per hand.

But because the player bets an additional unit on 67.4% of hands, the player bets 1.67 units per hand on average. Dividing the 3.37% house advantage by the 1.67 units bet per hand, we get a house advantage of 2.01% per unit wagered, which is what the Wizard of Odds refers to as the

**element of risk**.Element of Risk = House Advantage ÷ Average Bet Per Hand (Units)

House Advantage and Element of Risk

GameCraps - Pass Line with 3x,4x, 5x Odds Ultimate Texas Hold’em Baccarat - Banker Crazy 4 Poker Four Card Poker Mississippi Stud High Card Flush Three Card Poker Pai Gow Poker (Commission-Free) Caribbean Stud | House Advantage1.41% 2.19% 1.06% 3.42% 2.79% 4.91% 2.64% 3.37% 2.51% 5.22% | Average Bet Per Hand3.77 Units 4.15 Units 1.00 Units 3.14 Units 2.14 Units 3.59 Units 1.71 Units 1.67 Units 1.00 Units 2.04 Units | Element of Risk0.37% 0.53% 1.06% 1.09% 1.30% 1.37% 1.54% 2.01% 2.51% 2.56% |

**Source: Wizard of Odds**

It should be noted that the house advantage is expressed as a percentage of the initial ante

In Crazy 4 Poker, for example, the player starts with

The average bet per hand in Crazy 4 Poker is 3.14 units. This results in a house advantage of 1.09% per unit wagered – a.k.a. the element of risk.

The simplest way to think about element of risk is to look at craps with odds.

Let's say you're playing $5 craps with 3x-4x-5x odds on the pass line. If you only bet $5 on the Pass Line but never take odds, the house advantage is 1.41%. This will wager will cost you $5 x 1.41% or about 7 cents.

But let's say you instead bet $5 on the pass line and always take the full 3x-4x-5x odds. In this case, you will average 3.77 units or $18.85 per pass line wager, and the house advantage is 0.37% of the total 3.77 unit or $18.85 average wager. And in this case, these wagers will cost you 0.37% of $18.85, or about 7 cents -- the same 7 cents as before.

Here's what this means. If you're a flat $5 bettor, are risk adverse and want to bet the minimum possible, then element of risk does not help you -- you are stuck betting $5 on the Pass Line at 1.41%. But if you are a bigger bettor and are willing to bet an average of $18.85 per Pass Line wager, then you are

What this really means as far as what the target house advantage and target element of risk of a given game should be is a more complicated question. At minimum, we know that the player can bet the Pass Line with 3x-4x-5x odds at 0.37% with no skill, and that the player can bet the Banker bet in baccarat at 1.06% with zero skill and no additional wagering. And if we are going to develop games requiring skill, the 0.37% and 1.06% numbers are the ones we need to beat in order to properly compensate the player for developing the skills required to play such games.

*only*, and**all initial wagers, whether forced or otherwise.***not*In Crazy 4 Poker, for example, the player starts with

*two*initial wagers – an Ante and a Super Bonus bet. In this case, the house advantage is expressed as a percentage of the Ante bet, and*not*both bets combined. So let’s say a player sits down at a $10-minimum Crazy 4 Poker table, and bets the minimum, which requires both a $10 Ante bet and a $10 Super Bonus bet. The house advantage in Crazy 4 Poker is 3.42%, representing 3.42% of the $10 Ante, and not the $20 total initial wager. Thus the casino expects to win 3.42% x $10 = 34.2¢ per hand when the player starts with two $10 initial forced bets.The average bet per hand in Crazy 4 Poker is 3.14 units. This results in a house advantage of 1.09% per unit wagered – a.k.a. the element of risk.

**What's the Right Way to Think About Element of Risk?**The simplest way to think about element of risk is to look at craps with odds.

Let's say you're playing $5 craps with 3x-4x-5x odds on the pass line. If you only bet $5 on the Pass Line but never take odds, the house advantage is 1.41%. This will wager will cost you $5 x 1.41% or about 7 cents.

But let's say you instead bet $5 on the pass line and always take the full 3x-4x-5x odds. In this case, you will average 3.77 units or $18.85 per pass line wager, and the house advantage is 0.37% of the total 3.77 unit or $18.85 average wager. And in this case, these wagers will cost you 0.37% of $18.85, or about 7 cents -- the same 7 cents as before.

Here's what this means. If you're a flat $5 bettor, are risk adverse and want to bet the minimum possible, then element of risk does not help you -- you are stuck betting $5 on the Pass Line at 1.41%. But if you are a bigger bettor and are willing to bet an average of $18.85 per Pass Line wager, then you are

*far better off*betting $5 and taking the full 3x-4x-5x odds, as you are now wagering $18.85 at 0.37%, which is far better (3.77x better in fact) than simply putting $18.85 on the Pass Line with no odds at 1.41%.**What Does This Mean as Far as Target House Advantage and Element of Risk?**What this really means as far as what the target house advantage and target element of risk of a given game should be is a more complicated question. At minimum, we know that the player can bet the Pass Line with 3x-4x-5x odds at 0.37% with no skill, and that the player can bet the Banker bet in baccarat at 1.06% with zero skill and no additional wagering. And if we are going to develop games requiring skill, the 0.37% and 1.06% numbers are the ones we need to beat in order to properly compensate the player for developing the skills required to play such games.

**Next:**Qualifiers***Note:**The term element of risk is widely used in the industry, and Shackleford deserves full credit for the concept. However, the term element of risk sounds more abstract than it is, and unless you’re in the industry and know exactly what it means, it’s not obvious that the term is related to house advantage, when in fact the measures are directly related. In fact, few expert gamblers know what element of risk is, largely because few expert gamblers study unbeatable games. As a consequence, my preference is to present the measure as adj. house advantage.*Jeff Hwang**is President and CEO of High Variance Games LLC. Jeff is also the best-selling author of Pot-Limit Omaha Poker: The Big Play Strategy and the three-volume Advanced Pot-Limit Omaha series.*