Anyone want to do the math?

A local grocery store has a gaming room. The VP is pretty poor but they have an interesting promo.
Get the exact three cards on display and get a wheel spin. Today was King,Jack and five of Hearts. I don't know if it changes Dailey but I think not.
Wheel gives anything from $10 to $1000. Not sure if it's random or weighted.
What are the chances of getting three cards like that? If you get the three on the deal, you can lose the five and draw for the Royal.

Does it have to be on the deal, or can it be after the draw?

If it has to be on the deal, there are 2,598,960 different possible five-card deals, of which 1176 contain three specified cards, so the probability is 1 in 2210.

If it can be on the draw, and play for the bonus above anything else (including discarding, in this case, A-Q-10 of hearts from a Royal Flush):
Of the 2,598,960 possible deals:
1,906,884 have none of the three cards; your chance of drawing all three is 903/1,533,939, or about 1/1700
635,628 have one of the three; your chance of drawing the two you need is 990/178,365, or about 1/180
55,272 have two of the three; your chance of drawing the third card is 1035/16,215, or about 1/15.6667.
1176 have all three
The total probability is about 1 in 278.

Quote: ThatDonGuy

...The total probability is about 1 in 278.

Does that include catching all three on the deal?

It wouldn't make sense to hold JH,5H if dealt them, correct?

Quote: billryan

It wouldn't make sense to hold JH,5H if dealt them, correct?

I think it depends on how many slots and their amounts on the prize wheel. There is an average win that may make it worth taking the shot. Plus you could still catch JoB or a flush, so it's not a total dump.

Quote: Ayecarumba

Does that include catching all three on the deal?

Yes - and, if I read the original post right, if you get all three on the deal, you can discard one or more of the cards and still collect the bonus.

I believe that's the case. I'll look closer next time. As I was asking the counter about it, someone actually hit a $1565 Royal.
Meter reset to $1500.

Quote: billryan

It wouldn't make sense to hold JH,5H if dealt them, correct?

The key question is: What is the average return on the wheel spin. Count the total number of slots on the wheel. Assuming the wheel is mostly $10 slots and has one $1000 slot, also count the number of slots that are $20, and $50, etc. We also need to how many dollars you need to put into the VP machine each time you play.

Here's the probabilities if you pursued a strategy of maximizing your chance of a wheel spin. In this strategy, if you get one of the 3 cards on the deals you keep that card and discard the other 4 and draw 4. If you get none of the 3 cards on the draw, you discard all 5 cards and draw 5, etc. It's not a realistic case, but it provides a bounding probability on how often you can get a wheel spin.


Maximum Possible Probability of Wheel Spin/ Hand

Scenario	Probability on Deal	Probability on Draw	Total Probability
3 on Deal	0.000452	1.0	0.000452
2 on Deal, 1 on Draw	0.022624	0.06383	0.001444
1 on Deal, 2 on Draw	0.288462	0.00555	0.001601
0 on Deal, 3 on Draw	0.688462	0.000617	0.000425
Tot Prob of Wheel Spin			0.003922

So, the maximum probability of a wheel spin is 0.003922 or about 1 in 255 and if the average return on the wheel is about $40/spin then the "wheel spin bonus" would amount to an average of about $0.157 per hand - almost 16 cents per hand. Of course, this is an unrealistic strategy that would greatly reduce your return from the VP part of the game. You should not discard made VP hands or any promising combination of VP cards just to chase the wheel spin bonus - thus your actual return from the wheel bonus will be significantly lower.

I think you have identified the right strategy issue. If the average wheel spin payout is $40/spin, and you have 2 of 3 cards on the deal, then drawing 3 to those 2 cards will get you a wheel spin 6.4% of the time and an average wheel bonus of $2.56 + whatever return you may be able to achieve on video poker hands. You should probably draw 3 to "2 cards" except when that involves breaking up a very strong hand.

That's great information but what is missing would be how much pursuing that max wheel strategy would lower the normal JOB payouts.
For example, JH, 8S, 9H, 5H, 5C.
Normally you would hold the fives, but your strategy would call for holding two to the three bonus cards.

Quote: gordonm888

Here's the probabilities if you pursued a strategy of maximizing your chance of a wheel spin. In this strategy, if you get one of the 3 cards on the deals you keep that card and discard the other 4 and draw 4. If you get none of the 3 cards on the draw, you discard all 5 cards and draw 5, etc. It's not a realistic case, but it provides a bounding probability on how often you can get a wheel spin.

Maximum Possible Probability of Wheel Spin/ Hand

Scenario	Probability on Deal	Probability on Draw	Total Probability
3 on Deal	0.000452	1.0	0.000452
2 on Deal, 1 on Draw	0.022624	0.06383	0.001444
1 on Deal, 2 on Draw	0.288462	0.00555	0.001601
0 on Deal, 3 on Draw	0.688462	0.000617	0.000425
Tot Prob of Wheel Spin			0.003922

Slight nitpick: your numbers on the deal appear to be off.
The number for 3 is correct.
However, your number for 2 on the draw appears to be based on "3 ways to have 2 of the 3 cards, plus (50)C(3) = 19,600 ways of having the other 3 cards from the remaining 50." Since the third card in the set cannot be in the other three cards (otherwise you would have all three cards in the set and not just two), that should be 3 x (49)C(3) = 55,272 = a probability of 0.021267.
You do the same thing for 1 on the draw; your number is based on 3 x (51)C(4) instead of 3 x (49)C(4).
The number for 0 on the draw should be (49)C(5) / (52)C(5) = 0.733710.

I appreciate the work you guys are doing, as well as the fact that you are showing it so I can attempt future calculations on my own.

When you have something on the deal (like a low pair) it becomes a closer call. On the example you provide: JH, 8S, 9H, 5H, 5C its clear that you would need to evaluate these options:

1. 5C, 5S Avg. Wheel Bonus Return = 0
2. JH, 5H Avg. Wheel Bonus Return = $2.55
3. JH, 5H, 5C Avg. Wheel Bonus Return = $1.70

You can evaluate those options on a VP calculator and add the Wheel Bonus Return to the standard VP return. The correct strategy will depend upon how much you are wagering on each VP hand - which you haven't told us. If you are wagering $1 per hand, then the wheel bonus is a dominating consideration, if you are wagering $10/hand or more, then its less significant.

Also, you said the VP payout table is poor - how bad is it is?

I'm a $1-$1.25 per hand player. One casino I frequent I play 100 pennies per hand, others I'm a five quarters person. This game is available 5 cents to $1. I believe you need max coins in at any denomination.

Are you sure it's not a four of a kind promotion?

If not, I wonder if you could just get 1 or 2 and get the spin. Smith's has the 20-1000 wheel spin for 4oak running now. The wheel is electronic and weighted though.

I'm really not sure about it. I noticed it, started to ask the boothling and this woman hit a Royal Flush which caused a commotion. Didn't even see the wheel, just a picture of it.

I'm thinking this is a 4 oak promotion and you saw the three ranks of cards that would make acceptable 4oak's. If it was Smith's, this is definitely what you saw.

Quote: MaxPen

I'm thinking this is a 4 oak promotion and you saw the three ranks of cards that would make acceptable 4oak's. If it was Smith's, this is definitely what you saw.

As I was reading, I was thinking the same thing, I'm 99.54% sure this is exactly right.

The wheel spins are definitely weighted, $27 might be a fair number to go with. Drich might know more about the wheel spin values. From what I understand and perceived in the past it can vary a bit from location to location as well.

But don't let that discourage you, Bill. The wheels were turning and that's half the battle. Keep looking, I have seen some crazy promotions in strange places that turned out to be very lucrative.

Next time we talk I will give you a few pointers that may lead to some good finds.

Also if you can find out where bartopbob is nowadays, I think he is someone who actively seeks out and finds some good hidden .25 plays around town. I think he's willing to share in private as long as you don't step on his toes or burn stuff out and share back when you find something.

Yes, that is a four of a kind promotion at the grocery stores. Hit a 4 kind anyone of the three cards listed gets you a wheel spin. The wheel is weighted and the weights are configurable. Typically averages are set between $15 and $20. Grocery stores are usually on the low end. If you are playing a multi hand game it only triggers the wheel spin on hand one.