THREE CARD POKER QUESTION

I live in New Jersey and most of the casinos here require you to make at least equal wagers on both the Pair Plus and Ante wagers. ( A $15 Pair Plus wager is not allowed unless accompanied by at least a $15 Ante wager) Now I don't play the Pair Plus wagers unless I am up a significant amount (15 wagers or more) and then I may put a small wager for a few hands hoping to catch lightening in a bottle. More times than not someone either sitting at the table or an observer will comment on it and a good amount of the time they will ask if they can piggy back my hand and play the Pair Plus wager on my hand. I don't mind it and I usually allow it. Now the last time I did this I decided that because I am giving the other person a 50% discount on his wager by allowing him to piggy back my hand ( A $15 wager on the Pair Plus would cost him $30 if he sat down and did it) I told him I would allow but I charged him a 10% commission on any hand that paid the Pair Plus wager more than even money. The pay table at the casinos I play are 1/3/6/30/40. My question is this..... Based on a $15 Ante wager and a $15 Pair Plus wager that costs me nothing but receiving a 10% commission on any hand paying better than even money approximately how much of the 3.37% house edge ( ante wager paying 1/4/5) can I shave off by doing this?

Assuming exact payoffs ($4.50 per flush, $9 per straight, $45 per trips, and $60 per straight flush), your average profit from the piggyback is $11.29 per hand.

With the ante game you lose an average of 50.6¢ per hand, so combined you make an average profit of $10.78 per hand.

If you don't fiddle with exact change and instead charge $5 per flush and $10 per straight, you are profiting $11.64 per hand on average.

Either I'm confused or those numbers can't possibly be right. I'm probably confused, can someone re-explain?

Not being a genius with numbers it does sound right. With the average per hand loss of 50 cents on the ante wager and a Pair Plus wager that I can only either win or break even on because someone else is betting it but paying a commission, an average profit every hand is not a surprise but I didn't think it was THAT much.

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Let me see if I have this right (at the risk of looking like a fool) using a 500 hand sample

HAND HIT RATE AVG. WINS HAND PAYOUT TOTAL WINS COMMISSION (10%) TOTAL COMMISSION

FLUSH 5.0% 25 45 1125 112.50 112.50
STRAIGHT 3.3% 16 90 1440 144.40 256.90
TRIPS 0.2% 1 450 450 45.00 301.90
STR.FL. 0.2% 1 600 600 60.00 361.90


361.90 / 500 = 0.723

So if this is correct then we can offset the 50.6 cents on average lost from the Ante with the 72.3 cents per hand gained from the commission for an expectation of 21.7 cents per hand?

Quote: Ibeatyouraces

I think its per win, not per hand. Doing this has been a well known advantage play for years.

Yes that is correct, my apologies. It is the average amount won per winning Pair Plus hand where a commission is charged. The average win per played hand is about 93¢, or $1.01 if the commission is rounded up to the nearest $5 increment. Both are sufficient to overcome the house edge on the ante game when betting $15 on the ante.

Should the casino be allowing you to do this? I'm pretty surprised they are.

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I don't know specifically what the rule is. Honestly I was surprised the dealer allowed it to be completely honest. But it would be interesting to hear some sort of conversation as to why you need to place both bets in New Jersey but in Pennsylvania you can play just the Pair Plus as long as it's for the table minimum. I understand that 5.32% of 30 is better than 7.68% (?) of 15 but either is better than zero.

Quote: Ibeatyouraces

Most don't.

I'm surprised to hear that, as all bets are still subject to the applicable House Edge. The piggybacker has a higher edge working against him, the player plays at an advantage, nothing changes for the casino, what's the problem?

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I suppose that makes sense, but that would be very short-sighted to stiff the piggybacker, don't you think? In fact, I'm such a moke that on one of the few occasions I played 3CP there was a player next to me playing Ante + Pair Plus who eventually asked if he could play my PP since it was clear I had no plans on doing so, I let him play it in my place without charging him anything.

I did have the positive Variance of hitting a 3OaK at one point, and he gave me $25 of the win (I didn't ask for anything), so it was all good.

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Quote: Mission146

I suppose that makes sense, but that would be very short-sighted to stiff the piggybacker, don't you think?

Sure it is, but you expect people to honor all bets? Look at the 2012 election.

And I bet with another guy on a private poker/BS forum over the Stanley Cup Final, and I still haven't got paid for it. But it's somewhat standard for people to put off paying bets there, but it annoys me that they do that. If I would have lost, he would have got his money within a week. I don't have immediate need for the money, so it's just listed in my signature there.