VIDEO POKER PROBABILITY
The chance of getting winning hands
By Henry Tamburin
One of the nice features of the Video Poker for Winners software program is that it will compute the probability of every winning hand for any video poker game. For example, the Table 1 shows the probability (or occurrence) for 9/6Jacks or Better.
If you glance at the table, you’ll see some interesting facts about 9/6 Jacks or Better.
- You’ll hit a royal, on average, once in every 40,390 hands.
- You are more likely to hit a full house than either a flush or straight.
- Your chance of hitting a straight is nearly the same as a flush.
- The reason you rarely hit a straight flush is because the odds are pretty steep. (Once in every 9,148 hands).
- Getting a high pair (Jacks-Aces) is a fairly frequently event. It will occur roughly once in every five hands.
Suppose you are planning to play four hours of 9/6 Jacks or Better. How many four-of-a-kinds would you expect? Care to guess? Actually, you don’t have to guess. If you assume a leisurely pace of 600 hands per hour and use the occurrence data in the above table, you would arrive at six expected four-of-a-kinds on average. (If you end up losing money after your four hour session, one reason could be that you had less than six four-of-a-kinds.) I’ve calculated in Table 2 how many of each winning hand on average you can expect in every four-hour session, assuming 600 hands per hour, and I rounded up or down).
Usually, a video poker player will end up wining money in a four-hour session when he or she gets either a royal flush, straight flush, or more than six four-of-a-kinds. Losing sessions usually occur when you get more than 1,311“no win” hands. Here are some more interesting facts to ponder based on the above data:
1.You lose more hands than you win when you play video poker. (In the above ex-ample of a typical four-hour session, you can expect to lose 1311 times for every 1091 times you win something).
2.Because you can expect more losing sessions than winning sessions when you play video poker, you can expect your bankroll to head south.
3.You will recoup your losses over time when you hit a royal flush.
4.Since a royal flush only occurs once in every 40,000 or so hands on average, you need patience and enough bankroll to sustain your play between one royal flush and the next one.
5.Playing 600 hands per hour, you can expect to get a royal flush once in every 60hours of play. That’s an average. Sometimes you’ll hit more than one royal in 60 hours of play and other times you will experience a “royal flush drought.” (That’s when it takes longer than 60 hours to hit a royal flush, which is why having enough bankroll is so important.)
Here’s another bit of information to ponder. It’s based on what video poker players frequently tell me; namely, that “they never seem to win playing a specific video poker game at Casino X but they win more times playing the same game at Casino Y. Based on this “recollection,” they incorrectly conclude that Casino Y must offer better odds at video poker than Casino X.” The facts are this: Casinos do not alter the odds in the above table for getting each winning poker hand (if they did and got caught, they could lose their gaming license).The only thing they can and often do is change the payoff odds for some of the winning hands (which is why you should always check the pay schedule on a video poker machine to be sure the game is paying the maximum amount for each winning hand, known as a full pay game). As I often tell students in my video poker classes, it doesn’t matter where you play a specific video poker game because the odds of get-ting any winning hand are the same regardless if the casino happens to be in Las Vegas, Atlantic City, the Midwest or even Timbuktu.
Bottom line: Unlike slot machines, casinos do not change the odds of getting winning hands in video poker machines (that randomly select the cards for every hand).
HOW WOULD YOU PLAY IT?
You are playing Jacks or Better and are dealt the following hand. How would you play it?
Normally you would keep a suited J-10 over an unsuited J-K but this hand also contains a 3 of hearts, which is a flush penalty card. This means if you discard the 3♥ (along with the 5 and King), your chances of getting a flush by holding the J-10 suited have been slightly reduced (because you’ve removed from play one of the flush cards when you discarded the 3). Therefore, the presence of the flush penalty card makes the Expected Value slightly greater for holding the unsuited J-K over the suited J-10. Remember: Hold suited J-10 over unsuited J-K except if there is a flush penalty card, in which case, hold the unsuited J-K.
