4 card poker promotion math

Im playing a 4 card poker promo that pays a gas card everytime you hit trips or better. i have a 200 unit bankroll and wish to see as many hands as possible. I know the house edge is lower betting the ante but i plan to play 7 spots at once. betting 3x every hand, it is possible to lose 28 units in 7 hands. if i run bad, i could easily go broke before 200 hands, which is the minimum id see if i bet the trips and hit nothing (very unlikely).

or is my 200 unit bankroll simply to small to support this type of play? should i play fewer hands at once?

thanks

Hi, Hai!

From the Wizard of Odds (see link), the probability of receiving trips or better is 61,352/2,598,960 = 0.023606366. Flipping this over means that, on average, you'll see trips or better once every 42.36145521 hands. If you have the BR to play 200 hands, I'd guess that your chance of losing all without hitting trips or better is quite small.

I ran a Poisson Distribution (more info on Wikipedia at http://en.wikipedia.org/wiki/Poisson_distribution), where the expected number of wins is 200/42.36145521 = 4.721273125, and found the following probabilities of each result:

 

Wins	Probability 

0	0.008903836 

1	0.04203744 

2	0.099235118 

3	0.156172031 

4	0.184332704 

5	0.174057008 

6	0.136961779 

7	0.092376281 

8	0.054516706 

9	0.028598696 

10	0.013502225 

That's for the reply...

However, my question was which bet would allow me to see more hands. Would I be able to see more hands playing the aces up bet or the ante bet?

Hai,

First of all, I've never played 4 card poker, so all I know of it is what I read on WoO's website. What exactly do you mean by asking which bet will allow you to see more hands? Obviously, if we ignore the effect of wins on your BR, the lower one: if one bet requires a minimum wager of $10 and the other $5, the $5 bet will allow you to see more hands.

If you can explain a bit more about what you want to know, perhaps I or someone else here can provide the answer you seek.

Dog Hand

In four card poker there are two separate bets that may be placed before the hand; the ante and the aces up bet. The ante is a bet against the dealers 4 card hand and the aces up is just a bonus bet independent of the dealers hand. You may bet both or just one, doesn't matter which bet. If u play the ante, you will need to place an additional play bet of 1-3x your ante bet after you see your cards to play against the dealer. Otherwise you fold and lose your ante bet. If you bet the aces up bet without the ante, the bet is either paid or taken at the end of the hand; you will not lose anymore than what you bet originally.

So with the ante it is possible to lose 4 units a hand. With the aces up bet you will only lose one.

Hai,

According to the Wiz's website, the house edge on the Ante wager varies between 2.8% and 3.4%, depending on what bonus paytable is in use and what strategy the player uses. So, for your game and style of play, what is the house edge on the Ante bet?

Furthermore, the sidebet house edge varies from about 2% to over 6%. Here, though, the player's strategy has no effect on the house edge. So, what paytable is being used at your casino?

Dog Hand

Hai,

Ok, now that we know the HE, we can calculate the results!

If you play the Ante bet, on average you'll lose 0.0284 units/round. With a 200-unit BR, you can thus play the Ante bet

(200 units)/(0.0284 units/round) = 7042.2535211267605633802816901408 rounds.

If you play the Aces Up bet, on average you'll lose 0.0424 units/round. With a 200-unit BR you can thus play the Aces Up bet

(200 units)/(0.0424 units/round) = 4716.9811320754716981132075471698 rounds.

Thus, your BR will last 2325.272389051288865267074142971 rounds longer by playing the Ante bet as compared to the Aces Up bet.

Hope this helps!

Dog Hand

P.S. This answer seems too easy... are you asking something else?

What I meant to ask was whether or not my bankroll can handle 7 spots at once playing the ante. I know playing one hand at a time against the dealer will end up in more hands seen, but I want to know if betting 7 hands at once ( seven individual hands against the same dealer hand) will be too risky. I'm thinking if I get unlucky playing the ante I'll go broke before I see the min hands I get playing the trips.

Hai,

To answer that question, we need to know the variance and co-variance of your hands when you play the ante bet with multiple betting spots, along with the EV for the play.

Of course, the gas cards must be worth enough to offset the -EV of the base game.

If you have the info, I (or someone else here) can probably help with the RoR calculations.

Dog Hand