Wrong guesses can lead to disaster
By John Grochowski
Electronic casino games have always been subject to a little mythology. You can’t see what’s driving the slot reels or watch the video poker cards being shuffled and dealt the way you can watch a blackjack dealer turn up the cards or a roulette dealer spin the wheel, so our minds fill in the gaps.
Sometimes, we fill in the gaps with wrong guesses and misinformation.
Take video poker. The odds of the game are set so they will lead to casino profits, of course. That’s the case in every game, be it live or electronic. But the game isn’t going out of its way to deal us bad cards, or to pull off some misdirection where seemingly proper game strategies actually hurt us. The random number generator does nothing but generate random numbers corresponding to cards, and every card has an equal chance of being dealt on every hand.
Still, players see patterns in short-term results, leading to questions such as this one from an East Coast reader.
“Recently while playing Double Double Bonus Poker at Taj Mahal in Atlantic City, I noticed a man on my right had four 2s with kicker, then a little later four 3s. Meanwhile I had four 6s and later four Jacks.
“His wife on my left hit four aces with a kicker. I commented that I must be doing something wrong or don’t know how to play since I seem to always have these ‘small’ four of kinds and they both are hitting the ‘big’ wins.
“The wife laughed and said, ‘That’s because you’re hitting on the sucker bets.’ She said that today, you have to think which cards will give you a bigger win. Don’t hold the pairs of 5s, 6s, 7s, 8s, 9s or 10s. Discard them and hit on everything else or discard entire hands, that’s how you get better wins.”
“Is she right about this in today’s video poker games? I usually keep all pairs in all the poker games.”
The answer is that no, she’s completely wrong. When you hold a pair of 10s and draw four of a kind, the best thing is to be happy for that 250-coin payoff and not fret that it diminishes your chances at a bigger hand. Your results on any one hand have no effect on what you’ll be dealt in other hands. The RNG just keeps on RNGing, with every hand as a fresh possibility.
If you throw away entire hands, including a pair, will that increase your chances of drawing a higher-paying four of a kind? Yes, since you go from zero chance to an extreme rarity, but you pay a high price for that chance for lightning to strike.
Let’s explore the possibilities. Say you’re dealt 10s of spades and diamonds, 8 of clubs, 5 of hearts and 3 of clubs in 9-6 Double Double Bonus Poker. Most of us would hold the pair of 10s and discard the rest. Our reader’s neighboring player was telling him he should discard all five to give himself a chance at a better four of a kind than four 10s.
If you hold the 10s, there are 16,125 possible draws. Of those, 11,559 will bring no re-turn, 2,592 will be two pairs, 1,854 will be three of a kind, 165 full houses and 45 four of a kind. There will be some return on 28.3 percent of all draws. Four of a kind is a long shot, at 0.27 percent of draws.
Bottom line for holding the 10s: Per five coins wagered, your average return will be 3.67 coins. It’s not a winning start, but the return you get helps keep you in the game.
What if you follow the woman’s recommendation and discard all five? With a complete redraw, there are 1,533,939 possible draws, and 1,175,854 non-winners. You get some return on 23.3 percent of hands, 5 percent fewer than if you start with the 10s.
Of those million and a half-plus possibilities, 240,972 are high pairs, 73,683 two pairs, 33,075 three of a kind, 5,039 straights, 2,821 flushes, 2,271 full houses, 258 four of a kinds of the most common, 250-coin pay variety, 64 four 2s, 3s or 4s, no kicker, 32 four Aces, no kicker, 22 four 2, 3 or 4 with kicker, 11 four Aces plus kicker, 15 straight flushes and four royal flushes.
Focus on the four of a kinds. If we lump all the different types together, there are 387 four of a kind possibilities. That’s 0.025 percent of all draws. By discarding the pair and starting over, we draw four of a kind less than 10 percent as often as if we held the pair.
And what about the big-paying quads? Four Aces, 2s, 3s or 4s, with or without kickers, amount to 129 draws, or 0.008 percent. Throwing away a pair gives us about a 1 in 11,891 shot at a bigger four of a kind.
Bottom line for discarding all five cards: Per five coins wagered, your average return will be 1.64 coins, less than half the average return than if you hold the pair instead.
Part of getting the most out of video poker is to make the plays that give you the best possibilities, hand by hand. You can’t chase four Aces every hand, or chase royals every hand, without making moves that will deplete your bankroll.
The idea that modern video poker favors players who turn their noses up at smaller four of a kinds is a myth. Any four of a kind is a reason for celebration, not some melancholy for a hand that woulda, coulda, shoulda been bigger.