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Ask The Wizard #433

I have been trying to reproduce the house edges in your Double Down Madness Blackjack analysis by simulation. The rule wording I have seen says, “When your initial starting card is an Ace, you will only receive one card regardless of a hit or double.”

When I originally checked the page, its Version 1 strategy said to hit a lone ace against a dealer ace. In the analysis, may the player continue making decisions after hitting that ace, or must the hand stop after one additional card?

Allowing further decisions gives me results close to the published 0.95% house edge. Forcing the hand to stop gives me a higher figure. Which interpretation was used?

Zhaowei

In the analysis discussed in your question, a player who hits a lone ace may continue making decisions after receiving the next card. The one-card restriction applies to doubling on a lone ace.

The wording you quoted imposes a different restriction: one additional card after either action. Those are different rule sets, so their house edges need not agree. A simulation must match the precise rules being analyzed.

The article lists a 0.95% house edge for Version 1 with six decks and a cut card. Its first-card strategy has also been corrected since your original question: double ace against ace in Version 1; hit ace against ace in Versions 2 and 3.

See the current Double Down Madness rules, strategy, and analysis.

I am following your Bonus Deuces Wild strategy, but the practice game’s error warnings sometimes disagree with it. For example, the strategy tells me to hold a deuce with suited 6-8, while the trainer tells me to hold only the deuce. I have also received conflicting warnings about holding four cards to a flush with one deuce, including deuce plus suited 4-5-10 and 7-9-A.

I cannot find two pair in the “No Deuce Dealt” strategy. Where should it appear?

After checking more closely, I noticed that the printed strategy is for a 13/4/3 pay table, while the practice game I was playing uses 9/4/4. Is that the reason for the differences, and can you offer a practice game that matches the 13/4/3 strategy?

Carol

You found the source of the confusion. Video poker strategy depends on the exact pay table. The strategy you were reading was for 13/4/3 Bonus Deuces Wild, while the practice game you were playing used 9/4/4. Those numbers refer to the payouts for a straight flush, four of a kind, and a full house, respectively.

Deuce plus suited 6-8. For the dealt hand 2♦ 6♥ 8♥ K♣ Q♠, the expected returns per unit bet are:

Pay table Hold deuce + 6-8 Hold deuce only Better hold
13/4/3 0.997225 0.964724 Deuce + 6-8
9/4/4 0.913043 0.955182 Deuce only

The higher straight-flush payout makes the three-card draw worthwhile under 13/4/3. Under 9/4/4, holding only the deuce is better for this hand. The warning you received was consistent with the pay table you were playing.

Two pair with no deuces. Two pair does not pay by itself in this game. If you hold both pairs, eight of the 47 possible replacement cards produce a full house: the four deuces and the four remaining cards matching the two pair ranks.

  • When a full house pays 3, holding both pairs returns 24/47 = 0.510638. Holding one pair is better, so two pair is deliberately absent from the 13/4/3 strategy list.
  • When a full house pays 4, holding both pairs returns 32/47 = 0.680851. That beats holding either single pair, so two pair appears at number 12 on the 9/4/4 “No Deuce Dealt” list.

Four to a flush with one deuce. The same pay-table difference explains these warnings. On the 9/4/4 strategy list, every one-deuce four-card flush draw ranks above holding only the deuce. The 13/4/3 list is more selective, including the deuce plus suited 4-5-10 and 7-9-A combinations you mentioned.

For the 9/4/4 game, use the 9/4/4 Bonus Deuces Wild strategy. Its exceptionless strategy returns 99.4464%.

We now also offer a 13/4/3 Bonus Deuces Wild practice game, which you can use with the matching 13/4/3 strategy. Always match the strategy to the pay table displayed on the game.