For those with Math skills.

[DoctorJames]

I posted a little while ago on this topic, but i did some more research and thought a "bump" was in order.

In Wong's book he describes the Royal Match Side Bet. With 1D you are at a severe disadvantage like -3%, this bet then sucks. He then says in 6D you have an advantage of 1.3%. This assuming the payoff for first 2 cards suited was 3:1 and for Royal Match 10:1.

The last time I posted this question I got the impression that I had some "need" to make a ploppy side bet, so I should do Lucky Ladies. Fine, except that is a rare side bet in my neck of the woods, nor do I have a "need" to make a side bet. Any advantage bet in my mind is an advantage bet. So being that I seek wisdom and knowledge I ask if there is a resource (person or machine) that could calculate (or tell me how to) the advantage of the follow payoff for Royal Match. Any first two cards suited = 2.5:1; A suited natural 5:1; Royal Match (suited king/queen) 25:1.

My thought is that with those payoffs I will have a greater advantage, but I would like to know for sure. So I could calculate a needed Bankroll to cover standard deviation and such. Mathamatics I am quite poor at.

Just to put it into perspective... 1.3% in a 6D blackjack game is defiently over a TC of 1. Thus with the House Rules of the establishment I frequent, would give me a total advantage of 0.3 without counting.

I respect your thoughts and intelligence.
Thank You,
DoctorJames.

 

[Abraham de Moivre]

A Real Quick Rough Calculation

There are 13 ranks of cards and four suits.
This produces (13 x 4) x (13 x 4) = 2704 possible two card combinations.
(I'll ignore the small 1/312th effect of removal that occurs in a 6 deck shoe when you get one particular card first, your chances of getting the second identical card is less.)

Out of these 2704 combinations, 1/4 or 676 are suited for the 2.5 to 1 payoff

There are 32 combinations of suited natural, that pay 5:1, but subtract these 32 combinations from the 676 suited combinations, because that number already includes them. So we have 32@5:1, and [email protected]:1.

There are 8 suited king/queen combinations (4 K/Q and 4 Q/K, all my numbers are taking into account order, although not important, oh well - it is a quick calculation.) So we subtract these 8 suited combinations from the already counted ones, and we end up with 8@25:1, 32@5:1 and [email protected]:1.

So making the mythical 2704 $1 side bets, and the cards fall the mythical way probability suggests into the 2704 equally likely combinations:

We wager a total of $2704.
We win 8@25:1 for $208,
We win 32@5:1 for $192,
We win [email protected]:1 for $2226.

This gives us a total of $2626 won.
Subtract the $2704 wagered = -$78 net loss.

$78/$2704 = about a 2.89% house edge,
which is pretty good for a casino side bet, most have really awful edges.

 

[DoctorJames]

Re: A Real Quick Rough Calculation

Wow,

so the half a bet unit payoff change for (any first two cards suited) makes a tremendous difference ! I would have thought the greater payoff on Royal Match and the additional payoff on suited naturals would have more than compensated for the half unit. Amazing. Thank you for those calculations, I will now repeal my Royal Match bet, unless I find a system to exploit the high payouts.

Thanks again,
Doctor James.

 

[DoctorJames]

I went over your calculations and have a question.

How do we factor in then the number of Decks. In a Six Deck shoe it is obvious that it is more likely to catch a card of the same suit after the first card, because there is no longer just 4 suits there are 6 times of each suit. So then instead of there being 13 Hearts, for instance, there are 78 hearts. This is probably obvious to the mathamatically talented, but I just dont know where to plug that number in. Because i would think you would have the same 2704 possible two card combination, but I would think more than 1/4 of them would be suited in a Six Deck situation, since you have essentially mulitplied the number of same suited cards by 6 yet have not changed the fact their are 13 ranks of them. Just like you get more naturals at single deck and less at Shoe Games, I would think a similiar effect would happen here. This is mystery to me.

So now looking at your numbers it appears that this payoff system yeilds a 1% advantage over the Payoffs Wong describes on page 150 in Basic Blackjack (the newest print), For single deck he says the casino has an edge of 3.8% which looks aweful similiar to your 2.8% as you calculated with the payoff I described. Then he says with 6 decks the player has a 1.1% edge over the house, so now we are closer still to solving the puzzle. I think I am now more confused than before. =)