Double your fun?

Dec 14, 2004 4:42 AM


Obviously, many couples gamble together in the casino. I recently received a letter from a reader who told me of the many recent sessions that he and his wife had playing video poker. He seemed to feel that he was in a streak of bad luck, as it was rare for both he and his wife to win on the same night. While they frequently split (one won and the other lost), they both rarely won.

As is usually the case, this reader was most likely dealing with completely normal random occurrences. Payback only tells a part of the story. By itself it does not determine how often a player will win or lose in short sessions. While it can vary greatly from game to game, most casino games are designed so that the player will win at about 40-45 percent of the time over a two- to three-hour session.

Games like blackjack, with a high payback and relatively low volatility, will have a higher percentage of winning sessions, while more volatile games like video poker and four card poker, will have lower percentages. Games like slot machines will have some of the lowest percentages because they are both volatile AND low payback.

Let’s take a look at a relatively simple game with no strategy required, pair plus (of three card poker). Through a computer simulation, I found that nearly 60 percent of 100 hand sessions (roughly three hours of playing time) would end up as losing sessions for the player. Yet, the game has an overall payback of 97.68 percent. Mathematically, this can happen because occasionally, the player will have a large winning session, which raises the payback despite the many losing sessions.

Aces up (of four card poker) has a similar win-loss ratio despite having a payback nearly a full percentage point lower than pair plus. On the other hand, the ante/play portion of four card poker will afford the player a win percentage of 44 percent. The tradeoff for this higher win percentage is that it is more difficult to achieve large winning sessions.

How does this all translate when a husband and wife are playing together? Have you ever watched a basketball game where the game is down to the final seconds, and a player is on the foul line? You see that he’s an 80 percent free throw shooter, but how likely is he to make both free throws? Barring the pressure getting to the player, we can calculate that he is likely to make both shots 64 percent of the time (80 percent of 80 percent), miss both shots four percent of the time (20 percent of 20 percent) and make one shot the rest of the time, or 32 percent of the time.

The same math applies to our husband and wife team. Assuming each has a 40 percent chance of winning and a 60 percent chance of losing, we can expect that on average they will both win 16 percent of the time. They will both lose 36 percent of the time, and they will split (one win and one lose), the remaining 48 percent of the time.

Video poker is a relatively volatile game, and each variety will have its own win-loss percentage. Most versions will afford the player a winning three-hour session only about 35-40 percent of the time. This is not to say that at some point in the three-hour session the player will not be up significantly and would be best served by "taking the money and running."

Given these numbers, the husband and wife are even less likely to both have winning sessions of three hours. On the other hand, the more hands they play together, the more likely their overall experience will approach the theoretical payback.