Craps percentages and Three-Card Poker

4 January 2015

By John Grochowski

QUESTION: I’ve tried calculating the house edge at craps myself, and I keep coming up with answers that are far different than what I find in books and online.

If I make place bets on 6, I’m supposed to win five times, lose six times and have 25 pushes for every 36 rolls, right? That covers all the 36 dice combinations, with five ways to make 6, six ways to make 7 and 25 ways to make other numbers.

So if I make 36 bets of $6 each, that puts $216 on the table. I get my $6 back on the 25 pushes for $150. I get $13 on each of the five wins, $7 in winnings and the $6 bet. That’s $65, so between that and the $150, I have $215. The house keeps $1.

The way I calculate it, the house edge is the $1 the house keeps divided by the $216 in bets. That’s .0046, or 0.46 percent. But when I look it up, I see a house edge of 1.52 percent, not 0.46 percent. So where did I go wrong?

ANSWER: What you’ve calculated is the house edge per roll, which is a handy thing to know if you’re going to make one bet, then take it down, win, lose or draw. But place bets are multi-roll bets, and most players will leave the wager in action until there’s a win or loss decision.

The house edge you’ll find in most lists assumes the wager remains in play until a decision is reached. With that assumption, the 25 push rolls are irrelevant. Only the five ways to make 6 and the six ways to make 7 matter.

So to adapt your calculation, assume you’ve made 11 Place bets on 6 of $6 each, and they’re all played until either the shooter rolls another six and you win, or the shooter rolls a 7 and you lose. You risk $66 and get $13 back on each of the five winners, or $65. the house keeps $1. Divide the house’s dollar by the $66 at risk, and you get 0.0151515, which rounds to 0.0152, and that’s the same as 1.52 percent.

Most of the time, Place bets are left on the table until a decision is reached, so the 1.52 percent figure is almost always used as reference point instead of the one-roll edge of 0.46 percent.


QUESTION: I have a question about Three-Card Poker. There are two ways to bet, and an ante and bet part to play against the dealer, and the Pair Plus. One of the guys at my table was always betting twice as much on Pair Plus, with a $5 ante and $10 on Pair Plus. Somebody asked him about it, and he said that to bet equal amounts at both, he really need to bet more at Pair Plus because you make extra bets besides your ante against the dealer. Someone else pointed out that you don’t always make the extra bet after the ante, so he was really betting more at Pair Plus.

What do you think? Should you bet more at Pair Plus?

ANSWER: The house edge is higher on Pair Plus than on the ante-bet portion of the game, so no, I would not make higher bets on Pair Plus. Assuming you follow the basic strategy by matching your ante with a bet of equal size whenever your cards are Queen-6-4 or better, and folding lesser hands, the house edge on the ante-play portion is 3.37 percent of your ante, or 2.01 percent of total action once you include the follow-up bets. Those bets are part of the game, so the 2.01 percent edge is the appropriate figure fore evaluating the game.

On the Pair Plus option, you’re being paid for your card combinations and don’t have to beat the dealer. Most modern casinos use this pay table: Straight flush, 40-1; three-of-a-kind, 30-1; straight, 6-1; flush, 3-1; pair, 1-1. The house edge at that pay table is 7.28 percent.

House edges are much lower on the ante-bet play vs. the dealer than on Pair Plus. Therefore, ante-bet is where you want your money. Making bigger bets on the portion with the higher house edge is hazardous to your bankroll.

In fact, I don’t play Pair Plus at all anymore. I used to make a Pair Plus bet equal to my ante when the original pay table that paid 4-1 on flushes was common. The house edge on the 40-30-6-4-1 pay table was 2.32 percent. That’s a little higher than the ante-bet edge, but it was close enough that it was worth the entertainment value for me to play it at low limits. But in the current game, I don’t find 7.28 percent entertaining at all.