Four Card Poker Bad Beat Wager

Hey Wizard (or anyone),

What is your analysis of the side bet on Four Card Poker called the Bad Beat wager?
It is paid when the player's hand and the dealer's hand are of a value of at least 2 Pair. The player's hand does not have to be higher than the dealer's.
Exampes: Player 2 Pair, Dealer Trips = Bad Beat wager paid for 2 Pair value. Player Flush, Dealer Trips = Bad Beat wager paid for Trips value.

The payouts are:
2 Pair = 4:1
Straight = 6:1
Flush = 25:1
Trips = 100:1
Straight Flush = 10,000:1
4 of a Kind = 25,000:1

The game rules list that the hit frequency is 5.6% and the house edge is 20.3%. Is this correct, especially if you are playing multiple hands at once? Since the dealer is essentially playing 6 card stud (even though only 4 of the cards play), and on your charts on wizardofodds.com, it looks like the dealer should have 2 pair or higher about 20% of the time. I know the hit frequency for a player to get the Aces Up wager (pair of aces or higher) is 18.56%, so the hit frequency for the 2 pair or higher will be slightly less since a pair of Aces do not qualify for the Bad Beat wager.

I've seen a player get paid for the Trips Bad Beat wager 100:1 playing 4 spots quite often. Due to the high payouts, is Shufflemaster's estimation of a house edge of 20% and a hit rate of 5.6% accurate? How would you calculate the hit % if you are playing multiple spots? If the dealer will hit 2 Pair or higher 20% of the time, do the high payout rates make it worth playing if you are playing multiple spots?

Please post if you create an analysis of this on the Four Card Poker section on wizardofodds.com. Thanks for all the great information.

Forgot to post this part: I know the Straight Flush and 4 of a Kind hands will happen very rarely, but what about the Trips over at least Trips wager? Can you expect to get that hand more than 1 in 100 combinations? That is the hand situation that seems to happen often enough with the 100:1 payout odds that seems to hit frequently enough to make me question that the payout amount is high for the frequency of times it will occur.

Quote: brianparkes

Forgot to post this part: I know the Straight Flush and 4 of a Kind hands will happen very rarely, but what about the Trips over at least Trips wager? Can you expect to get that hand more than 1 in 100 combinations? That is the hand situation that seems to happen often enough with the 100:1 payout odds that seems to hit frequently enough to make me question that the payout amount is high for the frequency of times it will occur.

It sounds like the bad-beats are based on 5-card straights and flushes, correct?

Quote: brianparkes

Straight = 6:1
Flush = 25:1

These should be almost equal.

The fact is, in 4CP, flushes are slightly MORE common than straights, so they should pay LESS than a straight. But since the Aces Up bet pays more for the flush, this should also pay slightly more for a flush. But your numbers are out of whack.

The results are based only on the 4 cards that actually play for the player and the dealer.

The odds listed are for the Bad Beat wager only, not part of the Aces Up wagers. I only referenced the Aces Up wager because it is listed to hit around 18% of the time (so excluding the pair of aces, the other 2 pair hands and higher will happen almost as frequently for reference to how often you might be eligible for the Bad Beat wager as long as the dealer has at least 2 Pair).

The full game rules approved for this state (WA) is on page 10 of this link: http://www.wsgc.wa.gov/docs/game_rules/four_card_poker_bbb_progressive.pdf
if you want to reference it

Quote: brianparkes

Exampes: Player 2 Pair, Dealer Trips = Bad Beat wager paid for 2 Pair value. Player Flush, Dealer Trips = Bad Beat wager paid for Trips value.

Isn't the last example wrong, then? If the player has a flush and the dealer has trips, then the bad-beat should be paid for Flush value, as a Flush is less than Trips in 4-card?

The bad beat pays for the lowest of the two hands, but it does not matter who is holding it (the player or the dealer). All that matters is that both have at least 2 pair.

Now I see the confusion, I put the pay table down wrong. My Bad

2 Pair = 4:1
Straight = 15:1
Flush = 25:1
Trips = 100:1
St. Flush = 10000:1
Quads = 25000:1

Looking at the wrong chart, sorry.

Quote: brianparkes

The bad beat pays for the lowest of the two hands, but it does not matter who is holding it (the player or the dealer). All that matters is that both have at least 2 pair.

Right, I guess my point was, that if a Flush, whether your Flush or the dealer's Flush gets beat by Trips, you get paid the odds for the Flush and not for Trips- so you wouldn't get the 100 to 1. To get 100 to 1, you or the dealer would need to have Trips and get beat by a higher trips or Quads or Straight Flush.

Yup, but I've seen that happen frequently enough to wonder if the hit rate % of that is often enough that the 100:1 is a favorable payout.

Quote: brianparkes

Yup, but I've seen that happen frequently enough to wonder if the hit rate % of that is often enough that the 100:1 is a favorable payout.

I play the game semi-frequently, although usually for high-stakes and not for a large number of hands. I have had my Trips beat but it's been a while since that has occurred. Regulary, both flushes and straights get beat, though.

I'm sure SHFL's math is correct- so it's too bad they feel the need to introduce a 20% house edge side bet. Come on, guys, that's just too much...

It is ridiculously high. There is no reason for that, but that is why I was wondering if it was a mistake on their part.

the mistake is that players bet it. Until that changes, the HE will never decrease on side bets in general.

That makes me curious, and I pose this only as a philosophical question.

At what point would a side bet be considered worth playing. Some of the match bonus games (Spanish 21 and Match the Dealer blackjack) have a house edge under 4%. Is that still too high? I guess it has to be considered what your goal is. If your goal is to hit a large "jackpot" style bonus hand, that would mean the house edge would likely be fairly high to get a player to keep placing wagers to keep playing it (vs. hitting enough small ones to stay relatively even).

If you want to win a lot of them, you might expect to have a low house edge, but no real chance of a huge payout unless a lucky streak arrives.

I know most skilled players won't consider the wager unless the house edge is 1% or lower, or can be tracked in a way to flip the advantage :)
But if you were to consider "gambling", what would you consider fair?

I think you are right in that whether you want to play a side bet depends on what you are hoping to achieve in making the bet.

The other piece you need to add in to your variables is the hit rate or percentage of times the side bet pays you back any amount.

For example, if there was a side bet that paid 900 to 1 on a single event that occurred every 1000 hands and that was the only payoff, you would have a side bet with a house edge of 10%. Now let's say you had the same bet that paid 980 to 1. Well the house edge is now only 2%. But the feel of the bet to the player is still going to be that they feed the bet for 999 hands before getting paid a large amount and that is not likely to be a side bet that will make it in the marketplace.

My point is you can't look at house edge and payouts alone in understanding what a side bet will feel like to the players.

The keys to analyzing a side bet are house edge, hit rate and pay table. Each of the factors pull against each other in that if you want a low house edge and a high hit rate you typically sacrafice large payouts. It works similarly if you want large payouts and a low house edge you can't have a very high hit rate.

What seems to be used a lot is having high payouts, a 10% range hit rate with a really high house edge. I don't particularly like those types of side bets, but they are everywhere in BJ.

The key to designing a good side bet (IMHO) is to find a balance of the three variables that will appeal to a large enough set of players to make the game viable to be on the floor. I prefer higher hit rates at the sacrafice of large payouts and a house edge in the 3% range (like Lucky Lucky for BJ). But that is just my preference and other players like to have a chance at life changing types of payouts, etc. It is all up the player and ultimately the players as a whole vote with their dollars and those are the side bets that stay on the floor.

Quote: brianparkes

Yup, but I've seen that happen frequently enough to wonder if the hit rate % of that is often enough that the 100:1 is a favorable payout.

Wouldn't you know it, but this happened to me over the weekend- and thankfully, I was on the winning end! To be clear, the casino I was playing at didn't offer the bad-beat wager, but it just a situation of the dealer's trips losing:
https://wizardofvegas.com/member/thebigpaybak/blog/#post739

If they did offer it, I admit I probably would have been playing it- but man- that house edge is just ridiculous...

Greetings. Someone posted the question about the mathematics of the Bad Beat Bonus on my blog. I decided to investigate. Wow. That was some good time! But, by doing this project, I also could do the hole-card analysis of Four Card Poker, and also now have the software to analyze Crazy 4 Poker, and just about any other "four card poker" type game. So it was well worth it.

Here is my analyis of the Bad Beat Bonus side bet for Four Card Poker.

My main conclusions:

1. The house edge for the BBB is about 19.5%, not the 20.3% claimed by Shuffle Master.
2. Shuffle Master did not assume that the player hand and dealer hand were dealt from separate decks.
3. Shuffle Master's house edge for the main game of Four Card Poker is also wrong.

Fantastic work teliot. I checked out your report and it is great to see the results. I like the entire web page, too (apheat.net). Thanks for the extra work you put in to answer my question.

Quote: brianparkes

Fantastic work teliot. I checked out your report and it is great to see the results. I like the entire web page, too (apheat.net). Thanks for the extra work you put in to answer my question.

Thanks! You said 19.5% H/A in your question to me, but I can't find that result posted. Can you point me to it?

Quote: teliot

Thanks! You said 19.5% H/A in your question to me, but I can't find that result posted. Can you point me to it?

https://wizardofvegas.com/forum/questions-and-answers/math/10853-having-trouble-with-4-card-pokers-math/#post171867

Sorry to resurrect this thread. Just a quick question about BBB. Is it a dollar bet or is it an odds bet with a limit of say $100 or $500? And it only plays when you place a 'play' bet. A fold and there is no action on the BBB, correct? And finally, what casinos offer is this game with BBB?

Thanks.

Nick D

Glad to see there's an existing thread on this. I hadn't been to Motor City Casino (Detroit) in awhile, but I recently went back and saw they had the Bad Beat Bonus on the Four Card Poker table now. Not sure about everywhere else, but here, you can bet $1-5 on the bonus. And I don't believe you have to place a play bet either. I'd imagine folding is an automatic loss for the bonus. I mean, if you're folding two pair or better, I don't know what to tell ya.

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