What effect does this have on the house edge /my EV?

Recently, while waiting for a spot to open up at a Casino Royale dice table, I sat down at one of their 6:5 bj tables. Armed with one of their 2-1 blackjack coupons, I had planned on playing until I hit a blackjack or until the dice table cleared up, whichever came first. About an hour later, I was 6-7 beers deep and I still hadn't been blessed with a blackjack, although I had been lucky and was ahead. That's when several things transpired, all in rapid succession: Immediately after finishing a hand and placing my $5 bet out for the next hand, 2 impatient friends of mine tapped me on the shoulder and tried to sell me on walking over to another casino for some craps action. While arguing with them (and while not paying attention to the game I was involved in), the cocktail waitress arrived with my 7th (or was it 8th?) drink. After tipping her and calming my friends, I turned back to find $11 where there had been $5. The cards had been picked up. I had been dealt a blackjack! Instead of protesting, I simply explained to the dealer that I had a coupon and asked if I could redeem it on my NEXT blackjack. "No problem", she said. About 6 hands later, I hit that next BJ, got paid 2-1, and cashed out for a SMALL profit.

Before I ask my question, I'll add a couple more nuggets of info: Although I like a good value at the tables, I'm not a high roller, and I'm NOT an advantage player, and I'm OK with that. I go to Vegas to hang with the boys, drink, gamble, and have a blast. That said, There are few places that are better suited to doing the aforementioned activities than Casino Royale. I just wish they still had 3:2 BJ tables. But, on to the question:

What did my foregoing the 2-1 payout on my original BJ (and redeeming it on a later hand) do to my EV? Let's say I played the Casino Royale game until I hit EXACTLY 2 blackjacks? EXACLTY 3? EXACTLY N? Where would I stand from an expected win/loss standpoint?


From a "stretching out my vacation bankroll" standpoint, here's what I'm tempted to do on an upcoming trip (and I'm tempted to do this at the Casino Royale simply because I think it's a PROFOUNDLY fun place to play): Play the 6:5 game with the 2:1 coupon in hand, and live with the 6:5 payout IF I'M WINNING. If I hit a BJ while I'm losing, I redeem the coupon and I'm done.

7 or 8 beers in about an hour? That's excellent drink service!

Three cheers for the cocktail staff at Casino Royale!

Although the service was admirable, a few of those came in the form of me walking to the bar for the $1 Michelob Light bottles.

Well, since you delayed on using it for one blackjack, then you'll be expected to play an additional number of hands that it takes to get a blackjack on average. For a 6 deck game, this occurs 1 in 22.06 hands on average. The house edge on 6 to 5 BJ is about 2%. So the extra money you would expect to lose by delaying the use of the coupon by one blackjack is:

(0.02)(22.06)($5) = $2.206

Although that's correct, that ~2% house edge comes from the fact that any future bj will be paid at 6:5. If I know that my next bj will be paid at 2:1, I'm not really playing at a ~2% house edge, right?

I'm playing at some weighted average of the hands I play at a -ev (6:5) and a +ev (2:1).

Thats right, but that's not how you had played it.

You were distracted for one hand where you missed to use the coupon. And this distracted hand (despite of the positive outcome) was -EV.

If your coupon strategy is: Wait for N-1 Blackjacks, and only use the coupon on the next one, then you are playing with a weighted EV
(EV(6:5)*(N-1) + EV(2:1)) / N. But again, this is not how it was played.

Eh, you made it all back in drink E.V. :) I would have been betting $25 a hand, though. Your profit would have been less SMALL. Walking to the bar for the $1 Michelob is the better play at CR. The waitress will only serve you 6 oz. glasses of draft beer.

Quote: teddys

Eh, you made it all back in drink E.V. :) I would have been betting $25 a hand, though. .

Indeed, my drink EV that day was impressive. And, since drinking is a big part of the Vegas experience for me and my friends, that can't be overlooked. As far as the $25/hand, That's generally a no-go for me. On a long weekend in Vegas, I value the 16 extra "bullets" betting nickels affords me over betting quarters.

I suppose the nitty-gritty of my origin al question is this (and I acknowledge the answer may be somewhat subjective): given that I ENJOY gambling at the casino royale, and assuming that the last hand I play will be a 2-1 blackjack, how many 6-5 blackjacks can I endure before the overall game becomes an embarrassingly bad play? Without any numbers to back it up, my intuition is telling me it's somewhere between 1 and 2.

As much as I hate to say it, if you enjoy playing there, continue doing so. Just don't bet more than $5 at a time. You'll stand to lose $5 every hour at a full table dealing 70 hands an hour. You can easily drink that much in beers. The two-for-one coupon will get you an extra couple bucks in E.V., making it somewhat more worthwhile.

I always play there using the 2-for-1 for $25, and leave after getting the first blackjack. It's always fun to buy in for $300 at a table of red chip-betting fleas, say "all green, please," and watch their jaws drop. :)

If you really had 7 or 8 beers in an hour, you have a bigger problem then using a coupon !