9up sidebet

Not really a sidebet as much as a game modification, but it's advertised as a sidebet. If you take the sidebet, your first card is from a limited deck that doesn't contain 2-8. It costs 20% of your initial stake, which you get back if you have BJ, otherwise it's forfeited.

It's an online game, fully shuffled after every hand. Dealer stands on S17, DAS allowed, full dealer peek, 1 split only, no surrender.

I think this "sidebet" improves the RTP, is that right?

Question: If you make the side bet, is the 9-10-Face-Ace your first card for your blackjack hand as well?

Quote: Romes

Question: If you make the side bet, is the 9-10-Face-Ace your first card for your blackjack hand as well?
link to original post

My understanding is there isn't 2 different hands. You have your initial blackjack bet and this is basically a tax paid equal to 20% of the bet to dramatically improve your first card.

Here is my attempt at an answer:

Rules: 6-deck (assumed), BJ pays 3/2 (assumed), and the rules that you mentioned in the OP.

For the first card in your initial hand, for a normal game of blackjack:
a 9 Is worth about -0.94% , so about -20.94% with the "side bet tax".
a 10 is worth about +14.34%, so about -4.12% with the "side bet tax *** "
an Ace is worth about +50.79%, so about +36.94% with the "side bet tax ^^^ "

***: With a 10 showing, you have about a 12/13 chance of NOT getting a blackjack, so 12/13 x "20% tax" = about 18.46% as the expected "tax". 14.34% - 18.46% = -4.12%, therefore -4.12% is the EV for having a 10 as your first card.

^^^: With an Ace showing, you have about a 9/13 chance of NOT getting a blackjack, so 9/13 x "20% tax" = about 13.85% as the expected "tax". 50.79% - 13.85% = +36.94%, therefore +36.94% is the EV for having an Ace as your first card.

For your first card, the chance of receiving a 9 is 1/6, a 10 is 4/6, and an Ace is 1/6, so:

(1/6 x -20.94%) + (4/6 x -4.12%) + (1/6 x 36.94%) = (-3.49%) + (-2.75%) + (+6.16%) = -0.08%

Therefore , if I have worked it out correctly, this "side bet tax" will cost you about 0.08% on top of the regular house edge of the game.

I am trying to find a demo version I can access, but no luck so far.

I really enjoy reading the rules pages on these game variants.

Caveat: I accept these are different rules to those stated, since I have my simulation set up to use UK rules and infinite splits. My simulations normally log the results by the running count, but I changed the program to do it for the player's first card. Thus technically I didn't deal the player's first card from a separate deck. As a very quick check, for all hands regardless of player's first card, the regular EV was -0.4877% and the EV when taking 20% extra for each non-BJ hand was -19.539%.

I'm not sure of the exact differences when "you can only split once" and whether "when the dealer peeks" entirely offsets this, but this could suggest it's a fairly good game to play.

Player's Card	Hands	Win (not BJ)	Lose	Tie (not BJ)	Tie (BJ)	Win (BJ)	Hands (not BJ)	Win/Lose	EV
Ace	305 475 878	132 608 215	110 525 006	23 371 243	4 292 239	89 890 909	211 292 730	114 661 026.5	.375 352
Nine	305 195 631	150 648 007	153 700 754	30 350 475	0	0	305 195 631	- 64 091 873.2	-.210 003
Picture	1 220 147 876	520 670 355	480 807 257	124 508 394	4 289 719	89 872 151	1 125 986 006	- 50 525 876.7	-.041 410
TOTAL	1 830 819 385	803 926 577	745 033 017	178 230 112	8 581 958	179 763 060	1 642 474 367	43 276.6	.000 024

Another thought is there may be a side effect of ignoring the hands which started with low cards, since by definition that removes more low cards than average before you get to an A9X hand.

What does the second figure in the box, (the 878, 215, 006 etc in Ace) mean?

Edit, never mind just realised its one number across 2 lines, thanks,

Edit again, too late :)

Quote: rumba434

What does the second figure in the box, (the 878, 215, 006 etc in Ace) mean?
link to original post

I'm not sure what's happened with the formatting but the numbers have wrapped, so these are 305475878 etc. Hopefully this version is better!

Player's Card	Hands	Win (not BJ)	Lose	Tie (not BJ)	Tie (BJ)	Win (BJ)	Hands (not BJ)	Win/Lose	EV
Ace	305475878	132608215	110525006	23371243	4292239	89890909	211292730	114661026.5	.375352
Nine	305195631	150648007	153700754	30350475	0	0	305195631	-64091873.2	-.210003
Picture	1220147876	520670355	480807257	124508394	4289719	89872151	1125986006	-50525876.7	-.041410
TOTAL	1830819385	803926577	745033017	178230112	8581958	179763060	1642474367	43276.6	.000024

Another look seems to confirm the House Edge as nearly zero (in this case -0.0122%).

I set the initial player card as fixed and did runs of 1m shoes with A,9 and 10. When the first card is a 10 the player will, fairly often, stand on two cards, whereas on other cards the chances of the player needing more cards is higher. Therefore you get more hands per shoe with a 10-upcard. In theory you should get the same number of Aces and Nines, and four times as many Pictures; so for a fairer estimate take the actual results and factor them up...
Table 1 : (A) 50504296 (9) 50429506 (Ten) 54505322 (multiplied by four for the first table).
Table 2 : Factor them to 100,100,400.

Player's Card	Hands	Win (not BJ)	Lose	Tie (not BJ)	Tie (BJ)	Win (BJ)	Hands (not BJ)	Win/Lose	EV
Ace	50504296	22001627	18399718	3879572	734384	14773924	34995988	18763597.4	.371525
Nine	50429506	24970117	25424382	5042471	0	0	50429506	-10540166.2	-.209008
Picture	218021288	93149196	85773504	22343800	768348	15986440	201266500	-8897948.0	-.040812
TOTAL	318955090	140120940	129597604	31265843	1502732	30760364	286691994	-674516.8	-.002115

Player's Card	Hands	0	0	0	0	0	Hands (not BJ)	Win/Lose	EV
Ace	100000000	43563872	36431986	7681667	1454102	29252807	69293091	37152477.9	.371525
Nine	100000000	49514895	50415687	9999049	0	0	100000000	-20900792.1	-.209008
Picture	400000000	170899267	157367209	40993795	1409675	29330053	369260272	-16324915.9	-.040812
TOTAL	600000000	263978035	244214882	58674511	2863777	58582860	538553363	-73230.1	-.000122