racquet
Joined: Dec 31, 2014
• Posts: 194
March 3rd, 2018 at 6:49:49 AM permalink
Mohegan recently changed the payout on Stadium Blackjack from 3:2 to 6:5. What can they expect to profit from this change?

This is a game where all of the variables are consistent. The rate of play is determined by a clock that ticks down the time to place a bet. There's a clock that runs between every single card being played. There can be one player or a thousand - the time for a hand does not change. There's a constantly-fresh deck of cards. No true count, running count, no benefit of any index plays. I don't know them, but other variables are also fixed - splits, double downs, insurance.

Assuming 3:2 payouts on Blackjack, and a \$5 bet, what's the casino's expected return? Can that be expressed as a return in cents-per-dollar-bet?

Changing the payout from 3:2 to 6:5 increases that return. But by how much? It's the only change, so all of the difference is because of this decision.

It's easy to go from there to what an estimated drop-off in volume (probably not much) would do to the benefit.

Some one of the empty suits must have done the math.

Can someone here?
prozema
Joined: Oct 24, 2016
• Posts: 1146
March 3rd, 2018 at 7:02:55 AM permalink
3/2 = 7.5/5

7.5/5 - 6/5 = 1.5/5.

So the casino saves / makes \$1.50 for every \$5 wagered when the player gets blackjack & the dealer does not.
"A little luck never hurt any fisherman, that's all I know." - Sig Hansen
billryan
Joined: Nov 2, 2009
• Posts: 7790
March 3rd, 2018 at 8:31:12 AM permalink
People may double down on a soft 21 rather than take the 6-5 payout, so it might not be as simple as that.
prozema
Joined: Oct 24, 2016
• Posts: 1146
March 3rd, 2018 at 8:36:17 AM permalink
Quote: billryan

People may double down on a soft 21 rather than take the 6-5 payout, so it might not be as simple as that.

That player needs a comp buffet.
"A little luck never hurt any fisherman, that's all I know." - Sig Hansen
odiousgambit
Joined: Nov 9, 2009
• Posts: 8112
March 3rd, 2018 at 9:04:37 AM permalink
overall, -1.39%

typically that would raise the house edge to maybe around 2%

https://wizardofodds.com/games/blackjack/rule-variations/
the next time Dame Fortune toys with your heart, your soul and your wallet, raise your glass and praise her thus: “Thanks for nothing, you cold-hearted, evil, damnable, nefarious, low-life, malicious monster from Hell!” She is, after all, stone deaf. ... Arnold Snyder
MaxPen
Joined: Feb 4, 2015
• Posts: 3451
Thanks for this post from:
March 3rd, 2018 at 9:08:29 AM permalink
The benefit could be them having to remove the game or revert back to 3/2 if everyone stopped playing. Unfortunately the world is full of fish.
racquet
Joined: Dec 31, 2014
• Posts: 194
March 3rd, 2018 at 4:41:00 PM permalink
Maybe I'm not being clear.

All things being equal EXCEPT for the payout on a natural, what can the casino expect to gain by making the change.

I'll make up some numbers:

After one million hands at \$5 per hand, with a set of game rules that can be simulated, and a 3:2 payout on a blackjack, let's say that the casino will have made \$1,000,000, or an average of \$1 per hand played.

After one million hands at \$5 per hand, with a set of game rules that can be simulated, and a 6:5 payout on a blackjack, the casino will have made \$1,010,000, or an average of \$1.01 per hand played.

So the net benefit is a penny per hand if the casino does nothing more than change the odds on blackjack.

Let's assume that 3:2 versus 6:5 does not impact on player actions. Nobody doubles their blackjack. everybody takes the 6:5 payout. (Can you even DO that, blackjack payout notwithstanding?)

I'm thinking that maybe offering bad odds on a blackjack reduces the overall total of hands played, but that loss is more than offset by the increase in per-hand profit that accrues from 6:5.

Not that the empty suits would have bothered, or listened to anyone that did, but what's the profitability of going from 3:2 to 6:5. What exactly?
prozema
Joined: Oct 24, 2016
• Posts: 1146
March 3rd, 2018 at 5:08:55 PM permalink
It sounds like what you are asking is whether there are any estimate on the drop in total bet per period when payout on a natural changes from 3/2 to 6/5 and whether the change in total bet is offset by the increased house edge.

Is that right?

I don't have any data on this, but if you look at this from an economic point of view, 6/5 would not exist if it made less than 3/2 for the casino spreading the game.
"A little luck never hurt any fisherman, that's all I know." - Sig Hansen
odiousgambit
Joined: Nov 9, 2009
• Posts: 8112
March 4th, 2018 at 2:29:57 AM permalink
Quote: racquet

I'll make up some numbers:

why are you making up numbers? did you see the Wizard link?
the next time Dame Fortune toys with your heart, your soul and your wallet, raise your glass and praise her thus: “Thanks for nothing, you cold-hearted, evil, damnable, nefarious, low-life, malicious monster from Hell!” She is, after all, stone deaf. ... Arnold Snyder
ThatDonGuy
Joined: Jun 22, 2011
• Posts: 3738
March 4th, 2018 at 8:53:27 AM permalink
Quote: racquet

I'm thinking that maybe offering bad odds on a blackjack reduces the overall total of hands played, but that loss is more than offset by the increase in per-hand profit that accrues from 6:5.

Not that the empty suits would have bothered, or listened to anyone that did, but what's the profitability of going from 3:2 to 6:5. What exactly?

You mean, what amount? There's no way of knowing without comparing the number of people who played when it was 3:2 to the number that play under the same conditions when it is 6:5. However, as long as people think they are good enough to beat a 6:5 game by counting, something tells me the two numbers are very close to identical, especially when you are dealing with people where gambling is secondary to clubbing or shows.

However, as long as the amount is, "something greater than zero," that is all of the profitability the casino needs to make the change.

Note that this is not universal by any means; Cache Creek casino, somewhere between San Francisco and Sacramento, runs TV ads and billboards promoting that all of its blackjack games are 3:2 (although that has taken a backseat to promoting its 1700 penny slot machines).