Apr

02

2013

# 21+3 Side Bet in Blackjack

Side bets at blackjack come and side bets at blackjack go. Mostly they go when players discover their money is disappearing a little too rapidly. One that’s lasted, though, is 21+3, which combine blackjack with a three-card poker hand.

One reason it’s lasted is that the house edge is 3.24 percent, on the low side among side bets. Your first two cards and the dealer’s face-up card are used to make a three-card poker hand. If the resulting hand is a flush, straight, three of a kind or straight flush, you’re paid at 9-1 odds.

A while back, I had a reader suggest that maybe the player had an edge. By his calculations, the odds of three cards being the same suit were 9-1, so flushes alone would get you to break-even point and payoffs on straights and three of a kind were gravy.

“The way I figure it, the odds of two cards being the same suit would be 3-1,” he wrote. “So if the odds of two cards being the same suit are 3-1, wouldn’t the odds of three cards being the same suit be 9-1?”

He’d arrived at 9-1 by taking 3-1 odds, then squaring them. But 3-1 is the same as saying 1 chance in 4, and that’s the figure you must square. There’s a roughly a 1 in 4 chance of the first two cards being in the same suit, and if you multiply that by a 1 in 4 chance of the next one also being in that suit, you get 1 in 16, or 15-1.

That’s not exact, because each card dealt reduces the pool of cards in that suit remaining to be played. The actual odds against the three cards being the same suit are 15.47-1, with leaves plenty of room for the house to take its 3.24 percent edge.