Dealer paying $80 as 3 green and 3 red consistently. Is this bet now +EV?

Hi everyone!

Playing 3-card blitz last night (still no WoV page, but a playable demo here: http://inbetgaming.com/3-card-blitz)

One guy at the table was getting 5-card flushes like crazy, at $10 a bet so should pay 8:1. The dealer said “8:1” and then counted out 3 green 3 red, $90

Nobody said anything. But then she did it again when he got it a few hands later.

After the second time, I increased my flush bet from $5 to $10. Of course I never hit 5 but I was wondering how this changes the EV

Same guy hit it 3 more times during our session so he made an extra $30

Just to let you know the link you've put doesn't give the details of the bet so here is the method you can use.

Find out the House Edge of the sidebet and the chances of getting a 5-card flush and being paid one extra. The benefit in House Edge of that overpayment is the chances of getting the 5-card flush. So if that exceeds the House Edge then you would have an advantage, if not then you don't.

Quote: charliepatrick

Just to let you know the link you've put doesn't give the details of the bet so here is the method you can use.

Find out the House Edge of the sidebet and the chances of getting a 5-card flush and being paid one extra. The benefit in House Edge of that overpayment is the chances of getting the 5-card flush. So if that exceeds the House Edge then you would have an advantage, if not then you don't.

There is a playable demo but here are the numbers:
4/7 cards suited = 2:1
5/7 cards suited = 8:1
6/7 cards suited = 50:1
7/7 cards suited = 200:1

Quote: charliepatrick

Just to let you know the link you've put doesn't give the details of the bet so here is the method you can use.

Find out the House Edge of the sidebet and the chances of getting a 5-card flush and being paid one extra. The benefit in House Edge of that overpayment is the chances of getting the 5-card flush. So if that exceeds the House Edge then you would have an advantage, if not then you don't.

There is a playable demo but here are the numbers:
4/7 cards suited = 2:1
5/7 cards suited = 8:1
6/7 cards suited = 50:1
7/7 cards suited = 200:1

Confusion over 'to' or 'for' ... confusion over floor and 'eye' not noticing. Don't bank on it.

A very quick calculation (I haven't double checked it) gives, assuming it's 2 to 1 etc., 2 8 50 500 gives 2.95% and 2 9 50 500 gives 0.10%.

Quote: FleaStiff

Confusion over 'to' or 'for' ... confusion over floor and 'eye' not noticing. Don't bank on it.

If you mean confusion on my part I am certain I have the rules and payouts correct. We play this game a lot

Quote: charliepatrick

A very quick calculation (I haven't double checked it) gives, assuming it's 2 to 1 etc., 2 8 50 500 gives 2.95% and 2 9 50 500 gives 0.10%.

Thank you for doing this. The highest payout for 7/7 is 200:1, not 500. But if the .1% is correct I’ll keep an eye out for that dealer again. Too bad it only works at the $10 level.

If you get the chance I’d love a quick formula. I understand how to find house edge for craps and for roulette but when I try to do the same thing for games like this I never get the numbers quite right. I imagine I’m getting the probabilities for each different flush incorrect.

8 to 1 = 9 for 1, so you'd get $80 + your $10 back.

Quote: ChumpChange

8 to 1 = 9 for 1, so you'd get $80 + your $10 back.

Got it.

The payout for having 5 of 7 suited cards is 8 to 1. A $5 should pay $40, and a $10 should pay $80. And you get to keep your original bet. These are the rules, no doubt. Go play the demo in the link if you’d like.

This dealer was not paying 9 for 1 either because she was not removing the original $10 bet. She was leaving the original $10 in place, and then instead of grabbing 3 greens and a red, she was grabbing 3 greens and 3 reds. We watched this happen 3 times at least. I’m not sure what her source of confusion was. The layout says 8:1, she did every other payout correct

Quote: GBAM

If you mean confusion on my part I am certain I have the rules and payouts correct. We play this game a lot

Confusion on ANYONE'S part is just like drunkenness, eventually one sobers up and the windfall dries up. So I would not bank on any erroneous payout continuing.

That’s fair haha.

Quote: GBAM

Thank you for doing this. The highest payout for 7/7 is 200:1, not 500....

It makes quite a difference being 200/1 rather than 500/1.
2 8 50 200 = 4.490 629%
2 9 50 200 = 1.639 277%

Quote: charliepatrick

It makes quite a difference being 200/1 rather than 500/1.
2 8 50 200 = 4.490 629%
2 9 50 200 = 1.639 277%

Excellent. I wasn’t sure if the 500 was a typo or if you misread. Thanks so much for doing that. Not terrible either way, but wish it was 9 : 1. It’s a fun bet to hit. Wonder what the base game is

Is it P(4flush)*2 +P(5flush)*8+P(6flush)*50*P(7flush)*200 minus P(3 or 2 or 1 flush)*1

That is odds of winning* amount - odds of losing* wager
Sorry for the bad formatting


I’d love to be able to answer these questions myself

Quote: GBAM

Excellent. I wasn’t sure if the 500 was a typo or if you misread. Thanks so much for doing that. Not terrible either way, but wish it was 9 : 1. It’s a fun bet to hit. Wonder what the base game is

Is it P(4flush)*2 +P(5flush)*8+P(6flush)*50*P(7flush)*200 minus P(3 or 2 or 1 flush)*1

That is odds of winning* amount - odds of losing* wager
Sorry for the bad formatting

I’d love to be able to answer these questions myself

Okay, so the first thing that you want to do is figure out the probabilities of a flush. What we are going to start with is the fact that there are:

nCr (52,7) = 133784560

There are 133,784,560 ways to arrange seven cards out of fifty-two. (You will see we multiply by four for the matches, that's because there are four suits, but the way we are doing the combinatorial part we're acting like there is only one suit and making up for it later.)

Seven Card Match:

nCr (13,7) * nCr (39,0) = 1716 * 4 = 6864/133784560 = 0.0000513063689861

Six Card Flush:

nCr (13,6) * nCr (39,1) = 66924 * 4 = 267696/133784560 = 0.002000948390457

Five Card Flush:

nCr (13,5) * nCr (39,2) = 953667*4 = 3814668/133784560 = 0.02851351456

Four Card Flush:

nCr (13,4) * nCr (39,3) = 6534385*4 = 26137540/133784560 = 0.19537037756

You may care about two and three card flushes, but I don't, because they lose just as equally. Thus, I just want to know the overall probability of losing:

1-(0.0000513063689861+0.002000948390457+0.02851351456+0.19537037756) = 0.77406385312

Cool, now we just slap in your paytable:

((0.0000513063689861 * 200) + (0.002000948390457*50) + (0.02851351456* 8) + (0.19537037756*2)) - (.77406385312) = -0.04490628819

That means a house edge of 4.490628819%.

Now, if we change that eight to one to a nine to one:

((0.0000513063689861 * 200) + (0.002000948390457*50) + (0.02851351456* 9) + (0.19537037756*2)) - (.77406385312) = -0.01639277363

We're going to trim that House Edge to 1.639277363%

I like this online calculator for combinatorics (the nCr function):

https://web2.0calc.com/

However, you could just steal the probabilities from Wizard's High Card Flush page:

https://wizardofodds.com/games/high-card-flush/

Found under the, "Flush Bet," section, which is the same bet you're talking about with a different paytable. I used that to verify what I was doing, naturally.

So, now you know how to do it yourself cleanly and now you know how to cheat to do it!

I apologize if I say stupidly...
...but maybe there was just a game of different levels?

: )