Evaluate Simple BJ Promo
October 7th, 2021 at 3:02:27 AM
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Last night, my online Casino offered a new, very simple promotion.
I invite you to evaluate what the promo was worth to me and how best to play it, if at all.
The promo:-
Play live dealer blackjack at one specified table at a minimum of £5 per hand.
When I've been dealt a total of 5 blackjacks, they give me £10 cash.
The Blackjacks don't have to be consecutive. I can play up to two seats.
I can carry on and do this again one more time for a second £10 cash
The game in question had a RTP of 99.29% and because it's 6 deck, penetration of 50% I could not be bothered to count it.
It's that simple.
Probability of a blackjack for any one hand =2 x (1/13) x (4/13) = 0.047337 or once in 21.125 hands.
Average number of hands to see 1 BJ =21.125
Average number of hands to see 5 BJ = 5 x 21.125= 105.625
Total action needed for those wagers = £5 x 105.625 = £528.125
Total cost to the house edge = £528.125 x (1 - 0.9929) = £3.75
Total Expected Value if I wagered to completion = £10.00 - £3.75 = £6.25
BUT. And it's a big BUT. The impact of just a little bit of variance could be devastating. I would easily lose more that £10 in any three hands and I might play all night before seeing 5 Blackjacks. Of course, this is a 5h1t or bust, High risk of losing, proposition which I'd feel obligated to see through once I started.
E&OE Evidence available.
I invite you to evaluate what the promo was worth to me and how best to play it, if at all.
The promo:-
Play live dealer blackjack at one specified table at a minimum of £5 per hand.
When I've been dealt a total of 5 blackjacks, they give me £10 cash.
The Blackjacks don't have to be consecutive. I can play up to two seats.
I can carry on and do this again one more time for a second £10 cash
The game in question had a RTP of 99.29% and because it's 6 deck, penetration of 50% I could not be bothered to count it.
It's that simple.
Probability of a blackjack for any one hand =2 x (1/13) x (4/13) = 0.047337 or once in 21.125 hands.
Average number of hands to see 1 BJ =21.125
Average number of hands to see 5 BJ = 5 x 21.125= 105.625
Total action needed for those wagers = £5 x 105.625 = £528.125
Total cost to the house edge = £528.125 x (1 - 0.9929) = £3.75
Total Expected Value if I wagered to completion = £10.00 - £3.75 = £6.25
BUT. And it's a big BUT. The impact of just a little bit of variance could be devastating. I would easily lose more that £10 in any three hands and I might play all night before seeing 5 Blackjacks. Of course, this is a 5h1t or bust, High risk of losing, proposition which I'd feel obligated to see through once I started.
I played it. Starting with a credit balance of £111.26, I sat at one seat and just kept flat betting £5 per hand. I counted the hands and counted the blackjacks as the came. And they came far more rapidly than my estimate. First BJ was at 14 hands in. Next came at hands 19 and 21 !!!!! and then two more at hands 24 and 26. Amazing. I'd received my blackjacks at over 4x my expected rate! My Bankroll had grown to £128.76 and then they added my £10 to bring me to £138.76. It had taken me 25 minutes.
I pottered off and played some RNG BJ for fun and got that to just over £150
And then I returned to the live table with my £150.76 and tried again.
This time, I started out playing one seat, but soon decided to play two seats.
The Blackjacks came in at hands 4, 5, 18, 43 and 44 . The last round there, I actually had Blackjack on both my two seats!. My blackjacks had again come in at over twice the expected rate! This second round took me 17 minutes.
After the addition of the second £10 bonus, I cashed out £163.26.
I'd played this mostly for fun. The hourly rate expected value, if I'd needed to play 500 hands would have been tiny. Say 3 hours for an EV of £12.50 would give hourly EV of about £4. It was just a bit of fun before bedtime.
I pottered off and played some RNG BJ for fun and got that to just over £150
And then I returned to the live table with my £150.76 and tried again.
This time, I started out playing one seat, but soon decided to play two seats.
The Blackjacks came in at hands 4, 5, 18, 43 and 44 . The last round there, I actually had Blackjack on both my two seats!. My blackjacks had again come in at over twice the expected rate! This second round took me 17 minutes.
After the addition of the second £10 bonus, I cashed out £163.26.
I'd played this mostly for fun. The hourly rate expected value, if I'd needed to play 500 hands would have been tiny. Say 3 hours for an EV of £12.50 would give hourly EV of about £4. It was just a bit of fun before bedtime.
E&OE Evidence available.
Psalm 25:16
Turn to me and be gracious to me, for I am lonely and afflicted.
Proverbs 18:2
A fool finds no satisfaction in trying to understand, for he would rather express his own opinion.
October 7th, 2021 at 3:39:23 AM
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Cool 👍
All persons reading my posts gamble at their own risk, as I do. I don't ordinarily dispute math. I may dispute math I don't understand, or if I think it's faulty. I am not a conspiracy theorist.
October 7th, 2021 at 4:51:15 AM
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It was cool, Wellbush. I leave it there as an exercise for students of EV, such as yourself.Quote: WellbushCool 👍
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Some might come along and show where I did the maths wrong, or might show simpler ways of calculating it.
Read and learn.
You might be amused that I effectively played 3 sessions and that ignoring the bonus, I won each session.
£111 won up to £128 flat betting £5
£138 won up to £150 progressive wagering RNG Blackjack Table Min £1
£150 won up to £153 flat betting £5
So you can quote me when I say, you can walk out a winner at a -EV game whether flat betting or progressive betting.
This is what some 'believers' call hit and run session.
Hit and Run can be fun. But it's not a useful strategy at all. I was putting >100 at risk and many times I lose that 100
...
and it doesn't upset me.
Psalm 25:16
Turn to me and be gracious to me, for I am lonely and afflicted.
Proverbs 18:2
A fool finds no satisfaction in trying to understand, for he would rather express his own opinion.
