Deal or No Deal Video Poker

Yesterday I encountered Deal or No Deal Video Poker at the Red Rock. Mathematically speaking, it is like conventional video poker with a surrender feature as the cards on the draw are revealed. This surrender feature is, of course, animated as a "Banker Offer." The Banker does not bother making an offer on low-value situations. If the player has high pair, then he will. I imagine he would also with something like four to a royal.

To make matters more complicated, it adds an Ultimate X kind of feature, where any two pair or better earns a multiplier on the following hand. However, the multiplier is random. Without knowing something about how the multiplier is determined or an average, I can't quantify the odds. I can offer the following analysis on the base game, before considering the multiplier.

Outcome	Win	Combinations	Probability	Return
Royal Flush	400	41,197,187	0.000025	0.010000
Straight Flush	25	179,177,820	0.000108	0.002700
Four Aces with any 2,3,4	200	92,170,345	0.000055	0.011000
Four Aces with any J,Q,K	160	97,196,439	0.000059	0.009440
Four 2s, 3s, 4s with any A,2,3,4	80	243,969,603	0.000147	0.011760
Four Js, Qs, Ks with any J,Q,K,A	80	323,588,154	0.000195	0.015600
Four Aces	80	168,677,102	0.000102	0.008160
Four 2s, 3s, 4s	40	656,854,468	0.000395	0.015800
Four 5s thru Ks	25	2,318,325,353	0.001396	0.034900
Full House	4	18,514,375,776	0.011146	0.039011
Flush	3	18,465,575,038	0.011116	0.033348
Straight	2	18,175,925,813	0.010942	0.021884
Three of a Kind	2	125,204,238,231	0.075374	0.113061
Two Pair	1	215,634,177,909	0.129814	0.129814
Jacks or Better	0.5	349,204,617,309	0.210225	0.105113
All Other	0	911,782,476,553	0.548902	0.000000
Totals		1,661,102,543,100	1.000000	0.561591

Regarding the Banker offers, here is an analysis of a situation where I had a high pair and one card left to reveal. My bet was 60 credits. The table shows the situation was worth 36.176471 credits. The banker offer was 36, which is fair if you round down the expected value of declining the offer. I assume that the player earns the multiplier if he gets a two pair or better whether or not he accepts the Banker Offer.

Event	Wini	Cards	Probability	Return
Three of a kind	90	2	0.058824	5.294118
Two pair	60	3	0.088235	5.294118
Pair	30	29	0.852941	25.588235
Total		34	1.000000	36.176471

The banker offer was 36.

Here is a video of the game:


Direct: https://www.youtube.com/watch?v=XGjTRL-d_Fk

This game should not be confused with Deal or No Deal Poker Special.

The question for the poll is would you play Deal or No Deal video poker?

p.s. The 8th choice should have read "Why do Jake Perry's cats live so long?"

Wtf demo. KkK and they also hold A. ? What am I missing?

Quote: GWAE

Wtf demo. KkK and they also hold A. ? What am I missing?

It is a super double double bonus pay table. With a 60-coin bet, KKKKA pays 4,800 and KKKKL (where L = low card (2-10)) pays 1,500. Might be the right play.

Somebody sent me a screenshot where he held 3338 with one card to be revealed. The other three was out of the deck but all three eights were still in it. At the bet he was at, a fair offer would have been 502.94. He was offed 464.

Quote: GWAE

Wtf demo. KkK and they also hold A. ? What am I missing?

I was curious about this too. I thought maybe they were playing String Multiplier Poker !!!

Quote: Wizard

It is a super double double bonus pay table. With a 60-coin bet, KKKKA pays 4,800 and KKKKL (where L = low card (2-10)) pays 1,500. Might be the right play.

Gee this is where casinos have got to make a ton of money. I would play that game but would probably never hold the A and would be too lazy to look up the strategy.

I’m definitely intrigued by the game as it looks like it could be fun.

I wish they used different cards as it takes awhile to figure out what you have in the hand.

Quote: Wizard

Somebody sent me a screenshot where he held 3338 with one card to be revealed. The other three was out of the deck but all three eights were still in it. At the bet he was at, a fair offer would have been 502.94. He was offed 464.

I wonder if they could build some kind of AI into the system, (not that I think they did, I just find it to be an interesting possibility for the future).

The game would "learn" about it's opponent as they played. If they jump at every "deal" then it would reduce the offers accordingly.

I can't help but think that at some point a company will do this. So part II is, "could you use it to your advantage?"

Quote: Hullabaloo

"could you use it to your advantage?"

Only if it raised offers above expected EV for players that usually did not take the offer.

I have asked Gamblit for the average multiplier, but have not received an answer to that question yet, although they did reply. Waiting to hear from the right person.

Meanwhile, in case they don't tell me, if anyone plays for a while, I would appreciate a tally of how often you get each multiplier.

I nagged the people at Gamblit at the gaming show for the multiplier weights. They replied that the weights are configurable and agreed to send me them for the 99% version only, which are:

Multiper	Wini	Probability	Expected multiplier
2	492	0.085684	0.171369
3	600	0.104493	0.313480
4	2,100	0.365726	1.462905
5	2,550	0.444096	2.220481
Total	5,742	1.000000	4.168234

Let's keep in mind that the player is entitled to 1x with his bet, so he is getting an extra 3.168234 with a two pair or better. Let's also keep in mind that the multiplier multiplies the base win only, but not more multipliers.

That said, after some algebra, I find to get a correct strategy you should add the bet amount * 3.168234 * 0.56 to the win for any hand of two pair or better. Why 0.56, you might ask. That is because the immediate win is worth about 56% of the amount bet and the value of the multiplier 43%, based on the multiplier weights above.

That said, here is a return table based on putting these weighted prizes into my video poker calculator.

Outcome	Wini	Combinations	Probability	Return
Royal Flush	400	35,233,752	0.000021	0.008484
Straight Flush	25	180,308,491	0.000109	0.002714
Four Aces with any 2,3,4	200	92,242,314	0.000056	0.011106
Four Aces with any J,Q,K	160	97,568,842	0.000059	0.009398
Four 2s, 3s, 4s with any A,2,3,4	80	247,317,223	0.000149	0.011911
Four Js, Qs, Ks with any J,Q,K,A	80	316,807,768	0.000191	0.015258
Four Aces	80	168,847,716	0.000102	0.008132
Four 2s, 3s, 4s	40	667,438,461	0.000402	0.016072
Four 5s thru Ks	25	2,341,297,690	0.001409	0.035237
Full House	4	18,603,466,086	0.011199	0.039198
Flush	3	18,212,391,017	0.010964	0.032892
Straight	2	20,207,073,329	0.012165	0.024330
Three of a Kind	2	125,979,020,716	0.075841	0.113761
Two Pair	1	215,929,781,064	0.129992	0.129992
Jacks or Better	0.5	336,162,430,695	0.202373	0.101187
All Other	0	921,861,317,936	0.554970	0.000000
Totals		1,661,102,543,100	1.000000	0.559671

The probability of getting a two pair or better is 0.242657. That makes the average multiplier 0.242657 * (4.168234 - 1) + 1 * (1 - 0.242657) = 1.768795384.

Thus, the overall return of the game is 1.768795384 * 0.559671 = 0.989944062.

Gamblit also added the banker offers are worth 95% of expected value. I think he meant for the 99% version only, but I'm not sure. Screenshots I've seen on a version likely under 99% were at 92.3%.

The fact that the probabilistic weights of the multipliers are the configurable item (used to tune the player return) means that that there is no readily apparent way to tell what the return is on any given machine. The machines configured for 99% return might in fact be unicorns - they're what you show to players on the WOV forum but perhaps 100% of actual machines may be configured for 96% return.

Quote: gordonm888

The fact that the probabilistic weights of the multipliers are the configurable item (used to tune the player return) means that that there is no readily apparent way to tell what the return is on any given machine. The machines configured for 99% return might in fact be unicorns - they're what you show to players on the WOV forum but perhaps 100% of actual machines may be configured for 96% return.

That's certainly possible. If anyone plays one of these for a while, I'd appreciate a count of how often each multiplier is seen.

I just wrote up a page on Deal or No Deal Video Poker at WoO.

As always, I welcome all questions, comments, and especially corrections.

Quote: Wizard

I just wrote up a page on Deal or No Deal Video Poker at WoO.

As always, I welcome all questions, comments, and especially corrections.

I just took a quick look. I would like to play it a little first than then re-look at your analyst, in the meantime can you explain why KJss is better than QKss?

Quote: AxelWolf

I just took a quick look. I would like to play it a little first than then re-look at your analyst, in the meantime can you explain why KJss is better than QKss?

What does the "ss" stand for?

ss probably means same suit, as in the following from the basic strategy

Quote: LoquaciousMoFW

ss probably means same suit, as in the following from the basic strategy

2 to a Royal Flush	JA; JQ; JK
3 to a Straight Flush	78T; 79T
2 to a Royal Flush	QA; QK; KA

Thanks. Good question by Axel. They would seem to be of equal value to me, ignoring penalty cards. The strategy generator is not perfect.

Quote: Wizard

Quote: LoquaciousMoFW

ss probably means same suit, as in the following from the basic strategy

2 to a Royal Flush	JA; JQ; JK
3 to a Straight Flush	78T; 79T
2 to a Royal Flush	QA; QK; KA

Thanks. Good question by Axel. They would seem to be of equal value to me, ignoring penalty cards. The strategy generator is not perfect.

Again, excuse me if I didn't look close enough and missed something obvious in the paytable or rules. It seems to me that QKss would be raked higher than KJss. It's as if it puts more value on the jack.

I have the same question about AKss and AJss, It would seem to as if they should be ranked the same.

Quote: AxelWolf

It seems to me that QKss would be raked higher than KJss. It's as if it puts more value on the jack.

It seems to me they should be equal, not considering penalty cards. There are the same number of wait to make straights and straight flushes around both.

Quote: AxelWoome

can you explain why KJss is better than QKss?

I do not think the KJ is 'better' than 'KQ' ; it does not have a higher EV.

There are two hands listed between KQ and KJ, namely suited 78T and 79T and so thins is just indicating that there are cases where you would keep KJ but not KQ:
- If you have suited 78T and suited KQ, you should keep the 78T.
- If you have suited 78T and suited KJ, you should keep the KJ. (Presumably due to the presence of the J reducing the EV of the 78T since it removes a straight chance.)