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Ask the Wizard #249

Recently the Suncoast ran a promotion where every second royal flush paid double. What strategy changes would you recommend?

Arnold

According to VPfree2.com, the best game at the Suncoast is 99.92% two pair or better joker wild. The game normally pays 1000x for a royal, so every other royal would pay 2000x. I’m going to assume that time is not a factor, and the player could do this over and over, as many times as he wished. Granted, this is not a realistic assumption, because Suncoast rules required the second royal to be hit within 24 hours of the first, but it would get too complicated to factor that rule into this.

At first I thought the player should play a more aggressive strategy when going for the 2000x royal than the 1000x royal. However, that is not correct. The idea of using a single intermediate strategy for both the first and second royals was suggested to me by video poker expert, Bob Dancer. Bob tells me he thought of employing this strategy back when Flush Attack games were common. Smart players used the same intermediate strategy in both regular mode and flush attack mode, rather than switching strategies between modes. Once he made the suggestion, I ran the analysis to see if he was correct.

Let’s look at the overall expected return if the player played based on a 1000x royal for the first one and 2000x for the second one. Using my video poker calculator, we find the probability of a royal flush with a strategy based on a 1000x royal is 1 in 43,617, with a return of 0.999205. The probability of a royal flush with a strategy based on a 2000x royal is 1 in 40,776 hands, with a return of 1.022934. The overall return after two royals is (0.999205×43,617 + 1.022934×40,776)/( 43,617+ 40,776) = 1.010670.

Now let’s do the same thing, but with a strategy based on a 1500x royal the entire time. With a 1500x strategy, but with an actual royal win of 1000, the royal probability is 1 in 42,209, and the return is 0.998969. With a 1500x strategy, but with an actual royal win of 2000, the royal probability is still 1 in 42,209, but the return is 1.022661. The overall return after two royals is (0.998969×42209 + 1.022661×42209)/( 42209 + 42209) = 1.010815. 101.08% is greater than the 101.07% with the two separate strategies, confirming that a balanced strategy is the way to go. The same principle of assuming an average win of 1.5 times the normal win will apply to any video poker game under this promotion.

I know what the chart says, but I can’t make myself split eights against a dealer 9, 10 or ace in blackjack. My question is what is this doing to the house edge?

boomdog

Let’s assume six decks, the dealer stands on soft 17, and the player may re-split to up to four hands. The effect of each basic strategy change is the probability of the hand occurring and the cost of not making the correct play when it does. My blackjack appendix 9 shows both the probability of each hand and the expected value of each play. Assuming the player chooses to hit instead of split, the effect on the expected value of the game is:

Prob(8,8 vs A)×(EV(hit)-EV(split)) + Prob(8,8 vs 9)×(EV(hit)-EV(split)) + Prob(8,8 vs 10)×(EV(hit)-EV(split))
= 0.0003036 × (-0.513551 -(-0.364371)) + 0.0004404 × (-0.505707 -(-0.38995)) + 0.0016249 × (0.535361 -(-0. 475385))
= -0.019%.

So hitting 8,8 against a dealer 9, 10 or ace increases the house edge by 0.019%, or about one bet every 5,300 hands played. If the player surrenders instead of hitting, the effect drops to 0.013%. So, it is not a significant mistake. To put it in comparison, taking "even money" with a blackjack against a dealer ace increases the house edge by 0.014% in a six-deck game. If the player insures every blackjack and 20 (a common mistake), then the error cost jumps to 0.149%!

This question was raised and discussed in the forum of my companion site Wizard of Vegas.

I was playing 6-5 blackjack at a Strip casino a while back and had consumed just enough free booze that I doubled every time I got a blackjack against a dealer 2-6. Fortunately, I won every time. But, I wonder how bad my decision was. Would it make sense if blackjack paid even money?

Jumboshrimps

My blackjack appendix 9 is useful to answer questions like this. For example, assuming six decks and the dealer hits a soft 17, the expected value of doubling on a blackjack against a dealer 5 is 0.622136 and against a 6 is 0.667063. Both are much less than 1.2, costing over half a bet. Even if a blackjack only pays even money, as is unfortunately sometimes the case now, you should stand on the blackjack. The only game where you should not stand on a blackjack is in Triple Up 21, where the player should triple on a blackjack against a dealer 6.

This question was raised and discussed in the forum of my companion site Wizard of Vegas.

I have a resolution this year to try and keep as accurate a track as I can on my gambling trips. Obviously, bankroll taken and net outcome are key entries. Since I play almost 100% craps, I don’t have to worry about tracking lots of games. This log needs to have enough information so I can use it to prove losses to offset the big jackpot my wife is going to win this year.

RaleighCraps

According to page 12 of IRS publication 529 (PDF), the minimum a gambling log should include is:

  • Date and type of wager or wagering activity.
  • The name and address or location of the gambling establishment.
  • Names of other persons present during the gambling activity.
  • Amount won or lost.

In addition, you should keep other documentation, such as W2-G forms and losing tickets. Personally, I keep my log in Excel and always retain W2-G forms and losing sports tickets. The book Tax Help for Gamblers by Jean Scott & Marissa Chien has a whole chapter on this topic.

This question was raised and discussed in the forum of my companion site Wizard of Vegas.

Marissa is on Twitter at @taxpro4gamblers, where she occasionally answers tax questions to followers.