A shuffle through the Gaming mailbag:
Q. What would you hold with these two hands if you were playing Double Double Bonus Poker?:
1. Ad, Ah, 7d, 7c, 7h ?
2. Ad, As, 4h, 4d, 4c ?
A. The best play in either case is to hold the full house as long as it pays at least 8-for-1. Assuming a five-coin bet, neither the 250-coin payoff on four 7s, the 400 on four 4s nor the 800 if four 4s come with Ace, 2, or 3 as the fifth card is enough to keep us from collecting on the full house.
Let’s do this by the numbers for two pay tables: 9-6 Double Double Bonus, which returns 98.98 percent with expert play, the common 8-5 version that returns 96.79 percent, and a low-paying 7-5 game that returns 95.71 percent.
Flushes aren’t in play here, so the key figures are the 9-for-1, 8-for-1 and 7-for-1 returns on full houses.
Assuming a five-coin wager, holding the full house gives you a 45-coin payback on the 9-6 game and 40 on the 8-5 version.
With Ace-Ace-7-7-7, holding just the 7s and discarding the Aces would leave 1,081 possible draws. Of those, 968 would leave you with three of a kind for 15-coin paybacks, along with 67 full houses for 45 coins each and 46 sets of quads for 250 each.
The average return would be 26.86 coins, far less than the 45 you’d get on the full house.
It’s a little closer with Ace-Ace-4-4-4. There still would be 968 three of a kinds and 67 full houses, but the quads would include 36 that paid 400 and 10 with an Ace, 2 or 3 kicker, each paying 800.
Those higher paybacks on four 4s with and without kicker bring the average return when discarding Aces up to 36.94 coins, but that’s still not within hailing distance of the 45 on the full house.
On the 8-5 game, holding 7-7-7 would bring an average return of 26.55 coins, while holding 4-4-4 would bring 36.63 coins, decreasing to 32.77 if you held one of the Aces with the 4s. Full houses pay only 40 coins for your five-coin bet, so the play is a closer call, but game math still favors holding the full house.
The best play doesn’t reverse until you get down to a 7-for-1 payback on full houses.
Should you find yourself at a 7-5 game, it’s still better to old a full house with two Aces and three 7s. However, with Ace-Ace-4-4-4, the average return of 36.32 coins when discarding the Aces and drawing for quads is higher than the flat 35 coins on a full house.
Q. Roulette with the two zeroes has one of the highest house edges on the tables. I know really bad bets at craps are higher, but the best bets are far lower. Blackjack is lower, Three Card Poker is lower, Mississippi Stud is lower.
What if they met players halfway and paid 36-1 on single numbers? Then there wouldn’t be quite as big a gap between the 37-1 true odds and the 35-1 pays.
A.That would leave the house with a 2.63 percent edge instead of 5.26 percent. I doubt we’ll be seeing that. If casinos really wanted to lower their roulette edge, they could use single-zero wheels with a 2.7 percent edge.
Better payoffs might or might not add customers. A casino exec once told me of trying a single-zero wheel and having customers complain double-zero was their lucky number. In any case, chasing potential roulette customers doesn’t seem to be a prime concern.