As you know, I’m primarily a video poker player, but I have played table games at the Palms often enough that I sometimes get mailers for their table games. For February, they sent me four “First Card is an Ace” coupons — one useable each week.
In blackjack, an ace as a first card is worth something like 57% of your bet. The exact percentage depends on the rules and the accuracy of your play, but for today’s article, 57% is close enough. The coupons need to be used on a 6-deck shoe game and I can bet anywhere from $10 to $100 with the coupons.
Since each coupon is worth $5.70 on a $10 bet and $57 if I bet $100 with it, betting the maximum amount is a no-brainer for me. There are people with bankroll considerations who might bet less, but that’s not me.
So I figured that my Expected Value (EV) for the month was $228 — which is 4 x $57. A pretty sweet mailer, especially since I also get a mailer for my video poker play and I’ll be in the casino anyway.
On Week 1, I was dealt an A5 against a dealer upcard of 6. I pulled out an extra $100 and doubled down. I received a useless 7 (giving me a 13 which is a loser unless the dealer gets 22 or more). Fortunately, the dealer cooperated and busted. That meant I was $200 ahead for Week 1. Nice start!
On Week 2, I received the ten of diamonds to go with my ace for a $150 win. In two weeks, my total win was $350.
A friend named George asked me whether it was smart to quit and just throw the other two coupons away. After all, if my expected win was $228 and I was already ahead $350, why risk losing my profit? I had already “beaten the odds” so why should I press my luck? Does this make sense to you?
I know George from the square dancing world, so it’s understandable that he’s not a particularly savvy gambler. Even so, I looked at George as though he came from another planet.
My EV for Weeks 3 and 4 totals $114 (i.e. 2 * $57). George was suggesting I throw this away so I could protect my earlier winnings. He doesn’t know me very well!
I could have been up or down as much as $400 over the first two weeks, but whatever my score was had nothing to do with my play going forward. And regardless of what happens in Week 3, I’m still going to play the ace coupon on Week 4.
EV is an expectation made at a particular point in time. You know (or should know) that it’s rare for your actual result to be identical with your EV. In the case of the ace promotion, my actual result CAN’T be the same as my EV because my result each week will either be -$200, -$100, $0, +$100, +$150, or +$200. It definitely WON’T be +$57.
I included $0 because that would be the result if I split aces and won one hand and lost the other. If the rules at the Palms allow you to re-split aces more than once (and I’m not sure what their rules allow), the scores could theoretically include plus or minus $300 or even $400 — but these are real long shots. I don’t know what happens if the dealer and I push with, perhaps, an 18 or 19. I know my score on that hand would be $0, but I’m not sure if I get to keep the ace and play it again or not. I didn’t see anything in the fine print on the coupon to indicate this one way or the other. If I push and the dealer takes my ace, I will call the supervisor over to make sure that’s house policy. If it is, I’ll live with it. This must be a common enough event when hundreds of these coupons are mailed out. I’ll choose my strongest arguments for use in battles I can possibly win — which this one wouldn’t be. But if the dealer was just making it up as he went along, I don’t want to give up the coupon because of his mistake. How these things are actually done at the Palms affects the precise value of the coupon, but the precise value of the coupons won’t affect whether or not I play them. Even under the harshest possible rulings, these are still a sweet deal.
After the first week, my expectation was +$171 (i.e. 3 * $57) for the remaining coupons. Whatever happened in Week 1 was history and was just absorbed as a bankroll adjustment. Week 1 was then as important to me as what year Grover Cleveland won the election for his second term as President. (If the bet size was a large proportion of my total bankroll, perhaps it would please me or bother me more. But these are small amounts to me and each individual result is just noise. I record it and move on.)
The fact that I am ahead or behind last week’s EV calculation is irrelevant. EV is always based on going forward — starting from zero.
In video poker, you sometimes hear players say silly things like, “I was playing 9/6 Jacks or Better and ended up losing 10% of my coin in. I wasn’t playing a 99.54% game. I was playing a 90% game.”
That is nonsense, of course. This player was playing a 99.54% game and ran bad. No big deal. Sometimes he hits a royal and the actual score comes out to 814% (or whatever) of his coin-in for a particular session rather than 99.54%. Whether he wins or loses, the EV is 99.54% (plus slot club and other benefits). As I said, EV is always based on going forward and has nothing to do with your actual results.
If you play long enough and well enough, your actual results will come out reasonably close to your expectation. But over the short run, anything can and will happen.
Being ahead of your calculations is no reason to quit. Lagging behind your calculations is no reason to panic or to change strategy.
In these cases, we can calculate EV fairly accurately before we begin. There are gambles in the casino (and in life) where you can’t know beforehand what your EV is and you have to use your best current data to get an estimate. One example would be when you get a scratcher for every 4-of-a-kind. At the outset, you may have no idea what the scratcher is worth but you gain knowledge as you go along. That’s a worthy discussion for another day.
(Author’s note: I originally wrote this article mid-way through February and planned to run it last week in this column. I bumped it to this week because I felt my comments about the ex-mayor purportedly losing $1 billion at video poker were more timely to run last week and this article could wait. Since I wrote the article I have played the last two aces — losing a total of $50. I received a blackjack one week for $150 and I split aces and lost both hands the other week.
My friend George told me that had I listened to him I would have saved $50. He now believes that he has important counsel for me if I would only listen. I, of course, believe that the actual results are largely irrelevant and that you determine the value of a promotion before the event rather than after. I am not going to take George’s advice on gambling situations because I continue to believe that he doesn’t know his ace from a hole in the ground.)