The Math of Six Card Bonus in Three Card Poker

Three Card Poker arrived at the Bellagio in 1997 with a side bet called the Six Card Bonus. For nearly thirty years I watched that bet print money for the house while players thought they'd cracked some kind of code. They hadn't. The math was always against them. It just looked good on paper.

1997-2000: The Introduction

Derrick Glassman brought Three Card Poker to Las Vegas after developing it in the UK. The game itself is simple: you bet ante, get dealt three cards, and either fold or raise. Your hand plays against the dealer's hand. Push on ties.

Glassman knew the straight three-card version alone wouldn't pack the floor. Casinos make money on side bets. Everyone in the industry understood this by the late 1990s. Blackjack has the insurance bet. Roulette has the five-number bet (a sucker's play at 7.89% house edge). Poker games need a side angle that looks smart but plays dumb.

The Six Card Bonus was genius for this reason. You combine your three cards with the dealer's three cards and make the best five-card poker hand from those six. You're paid based on hand strength: straight or better pays even money. Trips pay 3-to-1. A flush pays 4-to-1. Trips of a kind pays 30-to-1. Straight flush pays 40-to-1. Royal flush pays 120-to-1.

Look at those payouts and your brain does something interesting. You think: I have three cards, the dealer has three cards, that's six cards total, and I'm making one hand from six. That feels like I have options. That feels like odds in my favor. Your brain is wrong.

2000-2010: The House Learned to Scale It

Casinos started tweaking the paytables. The early versions had the house edge around 10-13%. That's terrible for a side bet. The industry standard for a good side bet is 2-3%. By 2005, most casinos had bumped the edge to 14-15% by cutting the payout on straights from even money to 5-to-4. By 2010, some houses had it at 16%.

Here's the mathematics that nobody at the tables understood. You have 22,100 possible ways to be dealt six cards from a standard deck. Of those 22,100 combinations, roughly 1,900 make a straight or better. That's about 8.6%. If the game paid true odds on every hand, you'd break even. But it doesn't.

A flush from six cards hits roughly every 23 hands. You get paid 4-to-1. A straight hits roughly every 20 hands. By 2010, you got paid 5-to-4 instead of 1-to-1. The expected value on that single adjustment swings the game from bad to worse.

I watched guys at the tables who thought they were brilliant. "I'm playing the Six Card Bonus because mathematically, with six cards, I have better odds than regular poker." They were right about one thing: six cards beats three cards. They were wrong about what the house was paying. The payouts were calibrated to extract money, not to reward good odds.

2010-Present: The Standardization

By the 2010s, most casinos standardized around a 14-15% house edge on Six Card Bonus, which made it slightly better than a typical slot machine and worse than a video poker game if you play video poker correctly.

The split paytable became the norm. Straight paid 5-to-4. Three of a kind paid 3-to-1. Flush paid 4-to-1. And then you had the carnival hands: three of a kind suited or trips or a straight flush that paid 30-to-1 to 120-to-1. Those astronomical payouts serve a purpose. They're the dream hand that appears once every 10,000 or 100,000 hands. A player hits a royal flush once in a career and thinks the game is beatable. One hand in ten thousand doesn't make up for losses on the other 9,999 hands.

I can count the number of times I saw someone quit the table ahead on Six Card Bonus. I can count it on one hand, and most of those were luck outliers who got out before they gave it back.

The game is still on the floor. It still works. Players still think they've found an angle. The math hasn't changed since 1997. Only the payouts moved in one direction.