Tag: variance

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Paying to Avoid Royal Flushes

Assume you are a 5-coin dollar player playing 9/6 Jacks or Better and are dealt 3♠ A♥ K♥ T♥ 5♥.  The only two plays to consider are holding three hearts to the royal flush and holding all four hearts.

If we check out EV, we find holding three hearts is worth $6.43 and holding four is worth $6.38. That nickel’s worth of EV has always been too much for me to ignore and I go for the royal every time.

BUT, I file as a professional player and get lots of W-2Gs. Let’s say you don’t get a lot of W-2Gs. In that case, each one that you do get has some serious tax consequences. What if you held the four hearts in order to prevent the W-2G?

Once every 1,081 times on average, AKT turns into a royal flush. If you gave up a nickel each of those 1,081 times and ended up getting one fewer royal flush, it would cost you $55 (rounding slightly).

This is probably not too high a price to pay because a $4,000 royal has far more than $55 worth of tax consequences.

AKT (and AQT and AJT) are the weakest 3-card royal flush draws for two separate reasons. First, the presence of the ace eliminates all straight flush possibilities and reduces straight possibilities. Second, the presence of a ten reduces the chances for a high pair.

If we compared the preceding hand to 3♦ A♣ K♣ J♣ 5♣, holding this 3-card royal flush is better than the 4-card flush by a little more than 17¢ and avoiding the $4,000 royal flush over 1,081 opportunities will cost you $185. That’s quite a bit more than the $55 we were talking about earlier.

Going for the flush from 3♥ K♠ Q♠ T♠ 5♠ costs us $683 over the 1,081 draws, and from 3♣ K♦ Q♦ J♦ 5♦, it sets you back $770. Finally, from 3♠ Q♥ J♥ T♥ 5♥ you’ll lose a whopping $1,095 over the 1,081 hands by going for the flush every time.

So where do you draw the line? I’m not sure. I go for the 3-card royal on all of these hands. You’re going to have to decide for yourself what avoiding a W-2G is worth.

Other factors: If it were a multiple point day and/or there was another juicy promotion which gave me a considerable advantage playing this game, I would be more inclined to go for the flush. After all, time is money and it could easily take 5-20 minutes to be paid.

If I were playing in a state where royals were penalized (say Mississippi which has a 3% non-refundable tax on W-2Gs), that would make going for the flush mandatory in our first example and a closer play in the others.

If I were playing near the limit of my bankroll — either actual or psychological — I would tend to go for the flush, which is a play with a much lower variance.

On the first hand, you get skunked about 70% of the time going for the royal and “only” 68% of the time going for the flush.  If I were someone for whom today’s score mattered, I might go for the flush.   I certainly don’t recommend that you worry about today’s score, but some players just can’t help themselves.

This wouldn’t happen to me because I don’t do this, but if you were picking up someone else’s free-play and a royal flush would be awkward and you insisted on playing dollars anyway because you were in a hurry, I would go for the flush every time on these hands.

There are other hands in this game and every other game where it could make sense to avoid the possibility of a royal flush if it could be done at a low cost. But you should look at them one-at-a-time BEFORE YOU PLAY so you know which “inferior” plays are cost-effective. Trying to figure it out at the machine is very difficult. It’s easy to over-compensate when you’re doing this without study beforehand.

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Does it Matter?

You’re at your favorite casino. You’ve played a lot all month and are now there for the big drawing. Here’s the way it works:

Ten winners get called — they have a minute and a half to show up and identify themselves. If one or more spots are unclaimed after 90 seconds, more names are called. Eventually there are 10 contestants to “play the game.” Good news! You’re one of the chosen few — but I’m not going to tell you now whether you were first or last.

The way the game works is that 10 unmarked envelopes, in numbered spaces, are on a big board. Prizes total $25,000. The distribution of the prizes in the envelopes is:

First                        $10,000

Second                    $4,000

Third – Fifth                $2,000 each

Sixth – Tenth                 $1,000 each

 

Any of the players may end up with any of the envelopes. The first player drawn has the biggest choice. The last player drawn has no choice at all, but clearly it’s better to have this “no choice” rather than not to have been called at all.

Here are the questions: What’s your EV (expected value) if you get the first choice? What’s your EV if you barely make it in and you end up taking the last envelope? (We’re assuming the envelopes are indistinguishable from one another. I’ve been at drawings where actual cash was in the envelopes and the envelope with 100 C-notes inside was quite a bit fatter than the ones with “only” 10 Benjamins. In that drawing, you definitely wanted to be first to pick because visual inspection of the envelopes contained valuable information.)

The answer, of course, is “it depends.” (I like questions where this is the answer. That gives me something to write about!)

For the first player to select, the EV is clearly $2,500. A total of $25,000 is being given away to 10 players, and $25,000 divided by 10 is $2,500. This is as simple as an EV calculation gets.

For the second player, his actual EV depends on what the first player chose. If the first player selected a $1,000 envelope, then the second player’s EV is $24,000 divided by nine, which is $2,667. If the first player selected the $10,000 envelope, then the second players EV drops to $15,000 divided by nine, which is $1,667.

By the time we get down to the last player, there will be one envelope left and the EV is whatever prize hasn’t been claimed — meaning $10,000; $4,000; $2,000; or $1,000.

How do you take a weighted average of that?

Before I answer that question, let’s change this discussion a little. Assume each of the players selected an envelope but didn’t open them until the very end when they opened them together. In that case, each of the players has an EV of $2,500. There is still $25,000 in the prize pool, so far as they know, and they each have one in 10 chances to get any of the prizes.

Now, change it again. Assume you are the last person in line but you put earphones and blinders on until it’s your turn. Based on the information you have, you now have the same $2,500 EV as you would if everybody opened the envelopes at the same time!

If you are watching what happens and you’re still last, and you do this many times, on average your EV will be $2,500 — with variance!

Mathematically, on average it doesn’t matter whether you pick first or last. It can matter psychologically however. You see the $10,000 and $4,000 envelopes opened by somebody else and it’s a real downer if you’re somebody who sweats your daily scores! But sometimes getting called last will mean you see all of the smaller envelopes being opened and you’re left with the big one! On average it doesn’t matter, but if you want to feel bad about it, knock yourself out.

Since there are five $1,000 envelopes out of 10 total, half the time the last guy will end up with $1,000. (Of course, half the time the first guy — with complete freedom to choose any of the envelopes — also gets $1,000.)

When the first guy picks $10,000 (which will happen 10% of the time), it LOOKS like having the first choice was a big advantage. But it really wasn’t. He just made a lucky pick.

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Negative Variance, Juicy Count Games, and Ishniae (sp?)

In a previous post, I criticized the loser’s mentality of counters. The belief that hardening oneself to pain is a necessary and advisable part of the AP career is counterproductive. Many counters spend ridiculous amounts of time and emotional energy trying to answer the question, “How unlucky was I?” Instead of calculating how many standard deviations “below EV” you were, why not spend your time and effort trying to raise your edge? This message was lost or not well received by the counters reading my blog. Continue reading Negative Variance, Juicy Count Games, and Ishniae (sp?)

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“Doctor, it hurts when I do THIS”

“Well don’t do that!” the good doctor quips. I have always found this joke entertaining, not so much for the wisecracking humor, but for the subtle wisdom therein. Note that the doctor’s advice is not “I’ll prescribe some medical marijuana for you,” or “You need to learn to live with the pain,” or “You need a thicker skin.” Steeling oneself to endure pain is an unhealthy practice (pain is a message to you), and yet suffering card counters constantly prescribe this regimen to each other.

Continue reading “Doctor, it hurts when I do THIS”