In a nutshell, element of risk is basically a marked-down or more player-favorable view of a game’s house edge.
On many games with raise features or multiple bets, any bets added to the main bet often provide a bit of a discount for the player increasing his action.
When a player increases his bet on a hand being played, by doubling (splitting and doubling down in blackjack), taking additional odds (pass and don't-pass lines in craps), or raising (Ultimate Texas Hold 'em), the overall house edge decreases on the new combined bet amount. Thus, the player experiences a more favorable scenario odds-wise, meaning the element of risk.
For example, in craps, a pass-line bet itself has a house edge of 1.41%, but adding two times odds (with its "no-house-edge" payout) reduces the house advantage to 0.47% on the combined pass-line and odds bet. These savings are passed on to you, should you pony up and win.
Same thing when playing Shuffle Master’s Ultimate Texas Hold ‘em. The player makes Ante and Blind bets to start, and can later make a Play bet that can be raised up to 3 times the size of the Ante bet. The house advantage is stated as a percentage of the Ante unit size only, or 2.185%. If a player bets $10 each on the Ante and Play, the house expects to make 21.85 cents per round.
However, because of the additional Blind and Raise bets, the average amount actually bet is 4.15 betting units per round, so that this 21-cent rake now becomes slightly more than a nickel (at a 0.526% house edge).
This is easy to calculate: 2.185% house edge divided by the 4.15 units actually bet by the player = 0.526% house edge.
And it makes sense: The more you can bet at a discount whenever you can take odds (or raise when in a good position), the lower the house edge, thus the total element of risk, against you.
We can thank Mike Shackleford, the Wizard of Odds, for this element-of-risk house-edge perspective.
[This answer was provided by Dan Lubin, author of The Essentials of Casino Game Design. Our hot new book is for anyone who wants to know how casinos games are really put together and why. This is book is the real peek under the hood of all casino table games, especially the new ones you see every time you take a good long look around the pit.]
