richardsonnerd
richardsonnerd
Joined: Oct 20, 2021
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October 20th, 2021 at 7:22:15 AM permalink
I'm making a new game and it basically is a 3 card stud game. One bet, three cards you vs. the dealer. In order to get paid on the bet the dealer must have a queen or higher. According to 3 card poker data a player will win 44.91% of the time with these rules. What's the formula knowing the winning percentage and all the payout probabilities?
Mission146
Mission146
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October 20th, 2021 at 7:32:22 AM permalink
Quote: richardsonnerd

I'm making a new game and it basically is a 3 card stud game. One bet, three cards you vs. the dealer. In order to get paid on the bet the dealer must have a queen or higher. According to 3 card poker data a player will win 44.91% of the time with these rules. What's the formula knowing the winning percentage and all the payout probabilities?
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Is this just a straight up Even Money game, or are there other rules?
https://wizardofvegas.com/forum/off-topic/gripes/11182-pet-peeves/120/#post815219
richardsonnerd
richardsonnerd
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October 20th, 2021 at 8:00:37 AM permalink
I'm trying to calculate the pay tables to create the house edge then rtp. Right now I know that after hiring someone to generate our rtp, that if the pay table is as follows then our RTP is 89.57%. I'm trying to find the formula for that or the house edge so I can tweak the payouts.

Mini Royal: 30 to 1
Straight Flush: 15 to 1
Three of a Kind: 10 to 1
Straight: 3 to 1
Flush: 2 to 1
Pair: 1 to 1
High Card: 1 to 1

The dealer must qualify with a queen or better or it is a push. In order to get the payout the player must beat the dealer. I know that a dealer only qualifies 69.59% of the time. I have all the probabilities per hand and the returns. I just don't know the formula to calculate the house edge. My reverse engineering is failing.
unJon
unJon 
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October 20th, 2021 at 8:17:40 AM permalink
Quote: richardsonnerd

I'm trying to calculate the pay tables to create the house edge then rtp. Right now I know that after hiring someone to generate our rtp, that if the pay table is as follows then our RTP is 89.57%. I'm trying to find the formula for that or the house edge so I can tweak the payouts.

Mini Royal: 30 to 1
Straight Flush: 15 to 1
Three of a Kind: 10 to 1
Straight: 3 to 1
Flush: 2 to 1
Pair: 1 to 1
High Card: 1 to 1

The dealer must qualify with a queen or better or it is a push. In order to get the payout the player must beat the dealer. I know that a dealer only qualifies 69.59% of the time. I have all the probabilities per hand and the returns. I just don't know the formula to calculate the house edge. My reverse engineering is failing.
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You could do this in excel with just the combinations of each hand.

Seems to me that the RTP is too low for this to be a game players will play. And the dealer qualifier missing 3/10 is brutal too. Too many pushes will slow the game too much from casino perspective I think.

What happens if J or better qualifies, and then you can tweak the pay table a bit to make the RTP closer to three card?
The race is not always to the swift, nor the battle to the strong; but that is the way to bet.
richardsonnerd
richardsonnerd
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October 20th, 2021 at 8:48:38 AM permalink
Yeah, the RTP is low, that's why I am trying to find the formula to tweak for something in the high 90's. This bet is actually a prop bet on a larger game but this was the easiest way to simplify it.

When you say do this in excel, I'm trying to set that up using the wizard of odds ante return table to guide me. However, I'm just confused on how to derive the formulas. ( i wish i could attach a screen shot) For instance let's narrow to a straight flush. The site says this:

Player wins with straight flush: combinations: 617,044 probability: .001515
Player has straight flush, dealer doesn't qualify: combinations: 266,196 probability: .000654
Player loses with straight flush: combinations: 968 probability: .000002
Player ties with straight flush: combinations: 144 probability: .0000005

If the odds of getting a straight flush are 0.002172, then those numbers added equal that number? How did the combinations get calculated? Probability?

If I'm looking at the chart correctly then I add up all of the wins, loses, ties, no qualifies in order to find my edge. Is that correct? BTW, I appreciate your help, greatly!
richardsonnerd
richardsonnerd
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October 20th, 2021 at 10:04:48 AM permalink
Ah ha! I think I figured it out, sorta. Any ideas how I find the missing combination numbers below? I have found a few online but have no idea the formulas on how to get them.

Player Win
Mini Royal:
Straight Flush:
Three of a Kind: 665,776
Straight: 8,975,484
Flush:
Pair:
High Card:

Player Win No Dealer Qualify
Mini Royal:
Straight Flush:
Three of a Kind: 288,960
Straight: 4,001,004
Flush:
Pair:
High Card:

Player Tie
Mini Royal: 12
Straight Flush: 132
Three of a Kind: 0
Straight: 18,288
Flush:
Pair:
High Card:

Player Loss
Mini Royal:
Straight Flush:
Three of a Kind: 3,312
Straight: 270,504
Flush:
Pair:
High Card:
unJon
unJon 
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October 20th, 2021 at 10:41:59 AM permalink
I think you would need to brute force this if itís not on Wizard of Odds three card page.
The race is not always to the swift, nor the battle to the strong; but that is the way to bet.
richardsonnerd
richardsonnerd
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October 20th, 2021 at 11:10:08 AM permalink
It's not on there in the numbers I need. I have my mini royals separate from the straight flush so that blows those numbers up. And the numbers on there only go to straight. Then it groups the flushes and below since the payout is for the ante and ante bonus. Was just curious if some awesome math nerd had these handy. Thanks!
gordonm888
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gordonm888
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October 20th, 2021 at 11:12:55 AM permalink
Check out the tables here: 3 Card Poker Analysis I think all the numbers you want are on a table; specifically check out the Ante Bet Analysis Table.

To calculate yourself, you could use either combination theory to write out algebraic formulas, or you could write out all the hand combinations that are Q-high or higher.

I believe the Wizard uses a computer code that would treat this as a 6 card problem (3 cards each for dealer and player) and then automatically creates all possible combinations of six cards configured as (player hand+ dealer's hand) and accumulates the needed statistics. That's a lot of work but its how to do the calculations so that the answers are rigorously correct.

By the way, how is your game idea different than conventional Three Card Poker? They sound identical.
So many better men, a few of them friends, are dead. And a thousand thousand slimy things live on, and so do I.
ThatDonGuy
ThatDonGuy
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October 20th, 2021 at 11:14:01 AM permalink
Quote: unJon

I think you would need to brute force this if itís not on Wizard of Odds three card page.
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Here's what I get, although I am not entirely confident with the numbers:
HandWinTieLoseNot Qualified
Mini-Royal36,24412037,440
Straight Flush425,184132968384,372
3 Of A Kind500,65603312454,080
Straight6,637,98018,288270,5046,338,508
Flush9,291,17632881,260,5969,637,644
Pair24,210,86411,23211,873,52032,883,840
Garbage13,306,860149,352144,612,792144,821,556

This is a RTP of 82.92%

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