Pick Em Poker Wizard Of Odds

shakhtar

The difference between Pick ‘em Poker and other forms of video poker come when you are ready to play. Once you click the Draw or Deal button, you get dealt 2 cards to the left of the screen, and 2 to the right. The cards on the left, you need to keep. The only choice you get in Pick ‘em Poker is which of the 2 cards on the right to keep.

After black friday, when stars left the US, i joined Bovada about one year ago to play poker. They run casino promos from time to time, and I read the wizards endorsement of the Pick 'em poker game, and saw that with optimum strategy, there is a 99.95% payback to the player.
So I have played Pick 'em poker (at optimum strategy) at Bovada for a full year now. Not all the time, but enough that i have played a little over 100,000 hands.
Here's what's bugging me. I HAVE NEVER MADE A STRAIGHT FLUSH. Now I know they're hard to get obviously, but considering all the draws you get to one during a years play, it really seems like the game is set up so you cant get one (or a Royal). Now under optimum play, you should get one every 30,000 hands or so, so here is the question.
How odd is it to have NEVER made a straight flush playing this game in a whole calander year with around 110,000 hands played?
I have also kept track of quads, and they are dealt below expectation as well, so I am really wondering if this game is on the level.
I keep playing from time to time cause i'd like to hit at least 1 straight flush, just to finally hit one, but I'm starting to feel like a sap, since they never hit.
JB
Administrator
A Straight Flush in Pick 'em hits about as often as a Royal Flush in regular video poker (and a Royal Flush in Pick 'em, forget about it).
The average number of Straight Flushes you will get in a 110,000-hand session of Pick 'em is 2.86, and the average number of Royal Flushes is 0.31.
Assuming your figures are correct and that you played every hand perfectly, the probability of not getting a Straight Flush or Royal Flush in 110,000 hands is 0.041857, which is slightly better than 1 in 24.
shakhtar

After black friday, when stars left the US, i joined Bovada about one year ago to play poker. They run casino promos from time to time, and I read the wizards endorsement of the Pick 'em poker game, and saw that with optimum strategy, there is a 99.95% payback to the player.
So I have played Pick 'em poker (at optimum strategy) at Bovada for a full year now. Not all the time, but enough that i have played a little over 100,000 hands.
Here's what's bugging me. I HAVE NEVER MADE A STRAIGHT FLUSH. Now I know they're hard to get obviously, but considering all the draws you get to one during a years play, it really seems like the game is set up so you cant get one (or a Royal). Now under optimum play, you should get one every 30,000 hands or so, so here is the question.
How odd is it to have NEVER made a straight flush playing this game in a whole calander year with around 110,000 hands played?
I have also kept track of quads, and they are dealt below expectation as well, so I am really wondering if this game is on the level.
I keep playing from time to time cause i'd like to hit at least 1 straight flush, just to finally hit one, but I'm starting to feel like a sap, since they never hit.

This is because you get to see what everyother player does before you have to make a playing decision.You also have the opportunity to take a free card for the turnand / or river when all of your opponents check.Once you learn how to use your position, pick your startinghands, and how to maximize your wins and minimize your losses,you’ll be well on your way to playing winning Texas holdem. https://luckyworld.netlify.app/texas-holdem-poker-pravidla-flush.html.


Well I suppose to be fair I must update this past quandary. I finally got a straight flush in Bovada pick 'em poker, and in an ironic twist, i got 2 of them within an hour. Had been running horrible in this game for while, so I was just screwing around with the cheap 5 cent machine (.25 cent per spin with 5 coin bet). Started as a typical ice cold session, blowing 500 coins fast, and then another 300 of my next 500 coin set when I suddenly got hotter than a pistol with 2 straight flushes and 6 quads in the rest of the night. So while its somewhat disappointing to have my best ever session (point wise) at the cheapest machine (i usually play .25 or .50), it was fun to finally break the straight flush collar with 2 in an hour.
teddys
Yeah, but can you get a Royal on P.E.?
I have!
'Dice, verily, are armed with goads and driving-hooks, deceiving and tormenting, causing grievous woe.' -Rig Veda 10.34.4
shakhtar

A Straight Flush in Pick 'em hits about as often as a Royal Flush in regular video poker (and a Royal Flush in Pick 'em, forget about it).
The average number of Straight Flushes you will get in a 110,000-hand session of Pick 'em is 2.86, and the average number of Royal Flushes is 0.31.
Assuming your figures are correct and that you played every hand perfectly, the probability of not getting a Straight Flush or Royal Flush in 110,000 hands is 0.041857, which is slightly better than 1 in 24.

Guns play a part soon enough too but don’t expect to find them particularly enthralling. Rambo the mobile game.


Since i revisited this thread, i became a little skeptical of your .31 royal flushes out of 110,000 hands since that would be 1 royal flush out of 354,838 hands apx. Wouldn't it actually be 1 out of 162,435 hands for a Royal? I'll put forth my math and you can tell me where I'm wrong.
WizardIn pick'em poker, you are dealt 4 cards to start. Obviously, this is 52x51x50x49 divided by 24 since sequence is not important. That would give us 270,725 possible 4 card possibilities. To make a royal, we need 3 cards A thru 10 of the same suit, and the 4rth card must not be in the royal possibilities or else we have a dead draw. That would mean AKQ,AKJ,AK10,AQJ,AQ10,AJ10,KQJ,KQ10,KJ10 and QJ10 and each one of those will be multiplied by 47 (since the 2 others needed must be taken away from the dealt 4 for us to be live). That would be 470 multiplied by 4 different suits which would give us 1880 live royal deals out of a possible 270,725. This means we should get a live royal draw 1 out of every 144 hands. Each time we draw to the royal, we are drawing 2 cards of the remaining 48 which is 1128 combinations, and only 1 of the 1128 will make the royal. So if we have 1/144 x 1/1128, aren't we 1/162,435 to make a royal flush at pick'em poker? (I realize 1880 into 270,725 is 144.0027, so thats why its 162,435 instead of 162,432)
I'm sure your math skills are light years ahead of mine. Am I wrong, or am I correct ? If I'm wrong, where did I err?
And as long as we're on this topic, the odds page on wizard of odds lists 1,832,266,800 combinations for pick em poker. How is that # arrived at? Isn't the correct # 305,377,800 ? Wouldn't it be 270,725 x1128 as actual combinations?
CrystalMath
Where C(a,b) is the combinatorial function (a!/b!/(a-b)!):
The first two cards dealt must be from te royal:
C(4,1)*C(5,2)/C(52,2)
Of the next two cards, one must be from the royal, but not the other:
C(3,1)*C(47,1)/C(50,2)
The last two cards must finish the royal:
C(2,2)/C(48,2)
Multiply these to get the probability:
4*10/1326 * 3*47/1225 * 1/1128 = 1/324870
The problem with your math was that you allowed the bad card in the first four to be in any position, but it must be located only in the second set of cards.

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JB
Administrator
What CrystalMath said, plus, if we want to get technical, the probability for a royal with perfect strategy is 5208/1832266800 = 31/10906350 ≈ 1 in 351,817.742
The reason for the smaller probability than what CrystalMath posted is because a pair of 10's or better beats 3 to a royal in some situations.
The 1,832,266,800 figure is the product of:
combin(52,2) for the left two deal cards = 1326
combin(50,2) for the right two deal cards = 1225
combin(48,2) for the two draw cards = 1128

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shakhtar
Thanks for clearing that up gentleman. I completely discarded that the first 2 cards must play. Thanks for setting me straight. I was completely sober when I did this too so I can't blame alcohol for my stupidity unfortunately.
Would I be close in this assumption? - If a player plays 825 hands per hour, he should make a Royal apx.once every 426 hours. And at the rate of 1 every 426 hours, he is close to 50% chance of making a Royal after 300 hours of play at that rate?
JB
Administrator

Would I be close in this assumption? - If a player plays 825 hands per hour, he should make a Royal apx.once every 426 hours. And at the rate of 1 every 426 hours, he is close to 50% chance of making a Royal after 300 hours of play at that rate?

Odds Of Poker Hands


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Yes, I come up with a 50.5% chance of hitting 1 or more Royals in 300 * 825 = 247,500 hands.