Math can be madness

24 January 2016

By John Grochowski

QUESTION: I have been working to put together a strategy for 8/5 Double Double Bonus progressive video poker, and I came across a column in which you stated, “There are dozens of turning points, and they’re different on each game and pay table. … I know of no guide that already has done the number crunching for all the different games and pay tables we see on progressive video poker machines.”

I was wondering if now, a little over a year if that is still true or has some one sat down and ground out a list of turning points for the 8/5 DDB.

ANSWER: I know of no comprehensive guide to such strategy changes for all games and pay tables. I said in the column you cite that the work is painstaking, and it is. You need to go to the "analyze" feature on your video poker software and use the "select specific cards" or "select hand" option. For each hand in which the basic strategy includes discarding royal flush cards or holding more than just royal flush cards, you need to check the strategy for that hand until you find the point at which the better play is to hold just the royal cards.

Here's one example. High pairs are is higher on the 8/5 Double Double Bonus Poker strategy table than three parts of a royal, so if you're dealt king of hearts, king of spades, queen of spades, 10 of spades, 2 of diamonds, the best play with a 4,000-coin royal is to hold the two kings. Your average return per five coins wagered is 7.18 coins if you hold the pair of kings and only 6.63 if you hold the three spades.

But the potential reward for holding suited king-queen-10 increases as the royal jackpot grows. When the royal is 5,000 coins, holding the three spades brings an average return of 7.56 coins, while holding the pair of kings stays at a 7.18-coin return. The turning point actually is a little lower, at a royal of 4,595 coins, with an average return of 7.183 coins on the three spades and 7.179 coins on the pair of Kings.

A full table of turning points for progressive 8/5 Double Double Bonus means evaluating at different jackpot levels hands such as suited jack-10 vs. unsuited queen-jack, ace-king-queen-jack of mixed suits vs. suited Ace-King, a low pair vs. two suited high cards and many others.

No doubt someone with better computer skills than I have could devise a program to find the turning points at different pay tables in different games. However, I've not heard of it having been done yet.


QUESTION: I was at a craps table, $10 minimum, shooter was betting minimum pass and come, with 3x-4x-5x odds. On his comeouts, besides his pass bet he was betting $5 any 7. Terrible bet, right? He said he wanted to feel good about his winner 7s.

ANSWER: If we assume random rolls with a shooter who can’t make 7s appear in a disproportionate manner, then yes, it’s a terrible bet.

His $10 pass bets are unaffected by extra bets. Any 7 stands or falls on its own – and mostly falls. Per 36 rolls with a total risk of $180, he wins the 4-1 payoff on any 7 only six times. On each win, he wins $20 and keeps the $5 bet on, leaving him with $150 of his original $180. The house keeps $30.

In his attempt to feel good about his 7s, the shooter was spotting the house an extra edge.