How would you calculate house edge under the following situation?

This is just for fun and food for thought.

Say, a casino offers a player $100 in match plays a month. This casino is also pretty lenient to letting you play a wife or significant other's match plays as long as they are with you at the table. So, you've got $200 in match plays.

Minimum bet is $5 and you have your match plays splint into 40 $5 tickets. You only plan on playing those 40 hands and are just playing basic strategy. Essentially, every win will be a 2:1 win. Blackjack would be a 3:1 win. Further rules are this is a shoe game, 8 decks, 75% pen, stand on all 17s, split aces once with one card after split, double on any two cards, double after split, no surrender

how would the house edge be calculated on the 40 hands you intend to play?

The best way to calculate this would be by building the wizards house edge spreadsheet, but your EV calculation now has all wins paying 2:1, and BJ paying 3:1.

https://www.youtube.com/watch?v=jCF-Btu5ZCk

Assuming match play, for any given hand except a Natural, EV = (0 * Push %) + (-1 * Loss%) + (2 * Win%)

Its important that you know if you're allowed to double on your match play since that will greatly increase your EV.
(i.e. $5 chip + $5 match, can you double for the full $10)

You can double your initial bet, not the match, however.

edit: thanks for the quick reply!

Quote: DavidHasEdge

You can double your initial bet, not the match, however.

edit: thanks for the quick reply!

So your EV for doubling would be:

EV = (0 * Push %) + (-2 * Loss%) + (3 * Win%)

Quote: DavidHasEdge

...how would the house edge be calculated on the 40 hands you intend to play?

From the game you described, house edge (ignoring the match plays for now) = -.45% (https://wizardofodds.com/games/blackjack/calculator/)

If you play 40 hands at $5 per hand, this means your Expected Loss (EL) = (40)(5)(-.0045) = -$0.90.

Now, let's take a look at your expectations from the match play...
1) Every time you win, you essentially get paid an extra $5. This accounts for blackjacks and winning hands alike since we're already taking in to account the 1-1 payout for a win, and the 3/2 payout for a blackjack in our initial Expected Loss calculation.

*since doubles and splits are only on the original bet, we've already calculated for that in our initial expected loss and the match plays have no effect on our doubles/splits. On a side note, I've actually played where most places let you double for the match play as well, but never the less, this is what you asked for.

1) You're expected win rate in blackjack is 42.42% (https://wizardofodds.com/games/blackjack/appendix/4/). Thus, in 40 hands, you could 'expect' to win "on average" 40*.4242 = 17 hands (barely rounded up). So you can expect to win 17/40 hands, where the match play will thus benefit you with an extra $5 payout. Therefor I'll conclude that you can expect, on average, 17*5 = $85 extra from these match plays in your 40 hands. This, I'll call your Match Play Bonus (MPB).

Overall, your expectations for your 40 hands are... EV = EL + MPB.

EV = -.90 + 85 = $84.10

Every time you play 40 hands, with 40 match plays, you can expect to make $84.10, playing perfect basic strategy and flat betting $5 w/ $5 match plays on all 40 hands.

House Edge what?? =D

That's pretty awesome! Seems a good way to get my blackjack fix in until my counting is perfected. Thanks!

Quote: Romes

Quote: DavidHasEdge

...how would the house edge be calculated on the 40 hands you intend to play?

From the game you described, house edge (ignoring the match plays for now) = -.45% (https://wizardofodds.com/games/blackjack/calculator/)

If you play 40 hands at $5 per hand, this means your Expected Loss (EL) = (40)(5)(-.0045) = -$0.90.

Now, let's take a look at your expectations from the match play...
1) Every time you win, you essentially get paid an extra $5. This accounts for blackjacks and winning hands alike since we're already taking in to account the 1-1 payout for a win, and the 3/2 payout for a blackjack in our initial Expected Loss calculation.

*since doubles and splits are only on the original bet, we've already calculated for that in our initial expected loss and the match plays have no effect on our doubles/splits. On a side note, I've actually played where most places let you double for the match play as well, but never the less, this is what you asked for.

1) You're expected win rate in blackjack is 42.42% (https://wizardofodds.com/games/blackjack/appendix/4/). Thus, in 40 hands, you could 'expect' to win "on average" 40*.4242 = 17 hands (barely rounded up). So you can expect to win 17/40 hands, where the match play will thus benefit you with an extra $5 payout. Therefore I'll conclude that you can expect, on average, 17*5 = $85 extra from these match plays in your 40 hands. This, I'll call your Match Play Bonus (MPB).

Overall, your expectations for your 40 hands are... EV = EL + MPB.

EV = -.90 + 85 = $84.10

Every time you play 40 hands, with 40 match plays, you can expect to make $84.10, playing perfect basic strategy and flat betting $5 w/ $5 match plays on all 40 hands.

House Edge what?? =D
link to original post

Trying to figure this out for $25 match plays

If you play 40 hands at $25 per hand, this means your Expected Loss (EL) = (40)(25)(-.0045) = -$4.50.

Now, let's take a look at your expectations from the match play...
1) Every time you win, you essentially get paid an extra $25. This accounts for blackjacks and winning hands alike since we're already taking in to account the 1-1 payout for a win, and the 3/2 payout for a blackjack in our initial Expected Loss calculation.

*since doubles and splits are only on the original bet, we've already calculated for that in our initial expected loss and the match plays have no effect on our doubles/splits. On a side note, I've actually played where most places let you double for the match play as well, but never the less, this is what you asked for.

1) You're expected win rate in blackjack is 42.42% (https://wizardofodds.com/games/blackjack/appendix/4/). Thus, in 40 hands, you could 'expect' to win "on average" 40*.4242 = 17 hands (barely rounded up). So you can expect to win 17/40 hands, where the match play will thus benefit you with an extra $25 payout. Therefore I'll conclude that you can expect, on average, 17*25 = $425 extra from these match plays in your 40 hands. This, I'll call your Match Play Bonus (MPB).

Overall, your expectations for your 40 hands are... EV = EL + MPB.

EV = -4.50 + 425 = $420.50

Every time you play 40 hands, with 40 match plays, you can expect to make $420.50, playing perfect basic strategy and flat betting $25 w/ $25 match plays on all 40 hands.
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I'm getting two $25 match plays per day twice a week, plus a $20 dinner voucher twice a week. I've tried betting $12 on the PB 6 or 8 when other people throw at the craps table then run a progression on the passline when it's my turn to throw. The first time the dice went by me and I had to wait an hour for the dice to get back to me. I threw 7 winners including 2 points in a row and won both of my $25 match plays but had a craps on a $90 PL bet so I had to reset to a $12 PL bet. I colored up about $175 ahead after waiting for one more person to finish throwing (I was down $60 before I started my turn). So I figured I was up $100 from the match play because I won them both (($25 + $25) X 2 = $100). If I return, and lose both, I'll be down $50. If I win one and lose one, I'll be up $25 (+$50 - $25 = $25). So if I get 30 of these vouchers and win both 10 times, lose both 10 times, and win/lose both 10 times, I'll have $1000 + $250 -$500 = $750 in winnings. Of course variance will screw that up someway and those numbers won't pan out, but that's what I would expect. This is a different calculation than the one above for BJ which has a lower win rate. But it has me thinking I should play my match plays alone at the craps table from the Don't Pass line if I get the chance. There must be some hours when the table is deserted, but then the restaurant might not be open.

Did you account for pushes? Or better stated removed pushes fron the calculation. As nornal rules for match play is that they are not taken away in that scenario. This increases the win ratio of the match and makes it very close to 50%
Also original post didnt mention the blackjack payout for the coupon. Some do pay out 3:2 while most dont


P.S.

I dont count and are positive (money wise) playing blackjack for advantages very similar to the ones mentioned on this thread
This is for 15+ years now playing
Also without taking free drinks and food into account

Just watching someone play Spanish 21 on YouTube and trying to figure out how a Match Play would work in this situation.
Win 5 pairs of $25 match plays in a row and win $250 based on my own $25 chips and $250 based on the match plays for a total profit of $500.

If I get a double down or a split, would a second match play be allowed for that bet if I had one?

If I get a Black Jack that pays 3:2, or 2:1 or 3:1 would the Match Play pay the extra chips? I hope more play at the table will clarify whether Match Plays pay properly or just even money on Black Jacks of various forms. But since I'm betting at least $25, I'm eligible to win the $5,000 Super Bonus for 3 suited 7's against any dealer 7.

If I have to split to 4 hands and only 1 Match Play is available, I have to come up with the extra $150, and any extra $50 bets to double down with. So I'm thinking I need $800 in chips in my pocket in case both of my Match Plays turn into 4 way splits with all double downs. It may take awhile to build up that kind of bankroll. Each win puts me a $25 chip ahead of normal, but it could take me 50 Match Plays to actually get to $800 - $1,000 ahead which could be over 3 months. I could just go to the casino and play two hands and go home twice a week for 2-3 weeks and see if a winning streak pops up. I'd probably just hoard the chips and take them home and not color up and bring them back the next time so I don't have to buy in, because I need to be ready for splits and double downs.

I did play three hands already and one hand was a push and the Match Play stayed up for the next hand.

I'm only getting one meal credit per week, not two, I was mistaken, and I wound up spending 2000 points on a meal I thought was comped. Apparently a lot of people associate getting their printed match plays with getting a meal credit on their card so they think they're getting a meal credit when they already spent one earlier in the week. The restaurant is getting overwhelmed with complaints about missing meal comps. I had to drive home and check my flyer because they couldn't prove at the promotions desk what they were saying, but they were right. I have to keep a flyer in my car now in case of discrepancies.

I went and got some clarification. I can use my 2nd Match Play on a double down or split with an extra $25 chip on my first hand that is using a Match Play with a $25 chip. So that's $100 bet there and if they win, I'll be up $100 for the hand. Blackjacks pay $75 for 3:2, $100 for 2:1 and $150 for 3:1 with the $25 Match Play & the $25 chip.
There is double double down. If I get a 9 against a 6, I can bet another $50 to double down and if I get a 2 for an 11 I double double down with another $100 and hopefully I draw a face card and don't lose. That would pay $50 + $50 + $100 = $200. There's double down rescue, but I didn't ask if that applies to double double down, I suppose it does, so I'd lose $100 on the hand if I hated my draw card on the 11, but why should I, the dealer is gonna bust.

I waited while 2 people were finishing up a shoe and I got my Match Plays signed. Then the dealer dealt me a Black Jack, but the dealer dealt herself a Black Jack, but this is Spanish 21, I didn't push or take insurance and was paid $75 for my $25 & $25 Match Play. The 2nd hand was 17 against a dealer 17, a push, and my Match play wasn't taken away. The 3rd hand I was dealt a 20 and the dealer had an 8 up + Ace down for 19. I won $50. So I was up $125 in 3 hands and I was done for the night. I got to the casino kiosk at 11:56 pm after a 25 minute drive, and the kiosk stops spitting out Match Plays at 11:59 pm, so I've got to get an earlier start.

I couldn't get on the Spanish 21 table on a busy Saturday night so I had my choice of $25 or $50 Black Jack tables. I found one and waited for the shuffle. First hand I got a 9 against a dealer 4, so I tried to use my 2nd Match Play & chip for the double down, but I was told by the dealer and the pit that I couldn't, so I had to put $50 extra on the bet to double down. I pulled an Ace for a 20, but the dealer drew to a 20 and pushed, so I took my extra chips back. My 2nd hand was a loss of 1 chip. My 3rd hand was an 11 against a dealer 10 so I doubled down with an extra 2 chips, and I drew a 4 and the dealer wasn't much better but a couple cards later she was at a 19 and I lost the bet. So I was down $100.

I've got to make it clear that playing on a BJ or Spanish 21 table is like playing $50 a hand when adding in the double downs and splits. I'm gonna have to cut back to playing a Match Play on my $25 Pass Line bets at the craps table until I get far enough ahead to afford 15 or 25 $50 bets the card tables. I can probably throw the dice better.