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Please help and advice on which Swiss Pass to choose.

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Hello Everyone, Sorry about the long post. The exercise below is to figure out as to which pass should be good for me: 3 days Swiss Flexi or Swiss Half Fare Card. Please advise. If I get 3 days flex pass then what 3 days of free choice of travel I should pick based on my below planned Iternery. I think I should utilize Day 1, Day 5 and Day 6 which are fully covered by Swiss Flexi pass.

Costs: Half Fare Card: 120 CHF and 221.00 CHF for 3 days Swiss Flexi Pass Per person for a group of 4 adults and 1 toddler.

Day 0) Zurich Airport to Interlaken - full Fare 71.00 CHF = with Half Fare/Swiss Flex Card: CHF 35.50

Day 1) Lake Thun and Breinz and Bern.
1a)Lake Thun and Breinz from Interlaken - At http://www.bls.ch 1-day tickets for both lakes » 64.00 CHF = with Half Fare Card: CHF 32.
1b) Thun ThS to Bern, Hauptbahnhof - (Full Fare - CHF 15.60) -Half Fare Card: CHF 7.80
1c) Bern to Interlaken - (Full Fare - CHF 27.00) -Half Fare Card: CHF 13.50

Comments: Completely Covered with Swiss Pass or 53.3 CHF with Half Fare.

Day 2) Day trip to Jungfraujoch from Interlaken -
2a) Going up: Interlaken Ost - > Grindlewald -> Kleine Scheidegg -> Jangfrau - Full Fare = 100.80 = Half Fare = CHF 50.40
2b) Jungfraujoch - Interlaken OST -> Full Fare = 100.80 = Half Fare = CHF 50.40

Comments: Partial (25%) discount with cost 151.2 CHF (50.40 discount) with Swiss Pass or 100.80 CHF with Half Fare (50%) on the Jungfraujoch.

Day 3) Lauterbrunnen Valley from Interlaken

Lauterbrunnen Valley from Interlaken -> Interlaken to Lucerne - Below is detailed plan for a day trip to Lauterbrunnen, but I could not break it down completely to understand what's going to be the total with Half Fare Card. Half Fare from Interlaken to Lucerne is CHF 15.50. I believe using Half Fare is still good on this day and I don't have to use Swiss Pass as it doesn't fully cover trains/gandola from Lauterbrunnen.

3a) Take the train to Lauterbrunnen from Interlakan and catch the lift up to Grutchalp. = Half Fare = CHF 3.70 CHF
3b) Then train along the cliff's edge to Murren
3c) Aerial gondola down to Gimmelwald OR Walk from Murren to Gimmelwald (30 Minutes)
3d) Aerial cable car that awesomely plunges back down to the Lauterbrunnen Valley at Stechelberg
3e) Walk from Stechelberg to Trummelbach Falls OR fom Stechelberg either take postal buses take you the few miles back to Lauterbrunnen.

Day 4) Day trip to Mt Titlis from Lucerne

4a) Luzern -> Engelberg -> Bus / Train Cost ::: No charge 0$ with Swiss Flexi vs 50% (8.70 CHF) price with Swiss Half Fare.
4b) Engelberg-Titlis -> Full Fare = 86 CHF Return || 43 CHF return with Half Fare and Swiss Flexi/Pass
4c) Engelberg -> Luzern -> Bus / Train Cost ::: No charge 0$ with Swiss Flexi vs 50% (8.70 CHF) price with Swiss Half Fare.

Comments: Partially covered on the Mt Titlis with 43 CHF with Swiss Pass or (43 + 8.70 + 8.70 = 60.4 CHF) with Half Fare (50%).

Day 5 -> Ferry on Lake Geneva, Golden Pass, Château-de-Chillon Castle from Lucerne

5a) Train Luzern --> Lausanne (Full Fare - CHF 62.00) - Half Fare = CHF 31 CHF ->
5b) Ferry on Lake Geneva (Full Fare - CHF 28.00) - Half Fare = CHF 14 CHF ->
5c) Montreux -> Château-de-Chillon Castle(CHF 12.00) ->
5d) Montreux -> Golden Pass (Full Fare - CHF 31.00) - Half Fare = CHF 15.50 up to Zweisimmen ->
5e) Zweisimmen to Lucerne (Full Fare - CHF 64.00) - Half Fare = CHF 32 CHF

Comments: Completely Covered with Swiss Pass or 31 + 14 + 12 + 15.50 + 32 = 104.5 CHF with Half Fare.

Day 6) Day trip to Mt. Rigi from Luncerne (Closest city to get to Mt. Rigi is from Lucerne).

6a) Take boat to Vitznau that runs every 1 hour from the pier next to Lucerne. Boat ride is 1 hours. Depart Luzern 9:12 arrive Vitznau 10:09.
6b) Take Cog Rail in Vitznau to Rigi Kulm. Ride is 25-30 mins.
6c) take cog train from Rigi Kulm back to Vitznau (boat to Lucerne).

Comments: Completely Covered with Swiss Pass or approx 53 CHF with half fare card.

I will be back to zurich for one day and take additional benefit of Half fare on the trains on our last day, train from Lucerne to Milan Central, and train from Hotel to Zurich airport and this discount won't be available if I get flex pass as card will be expired on the last day of validity i.e. Day 6.

Downside of getting flexi pass are:
1) I will get only 25% reduction on Jungfraujoch Vs 50% with Half fare card.
2) I can get 50% discount only in between the first and the last selected day of validity i.e. Day 1 - Day 6, not covering Day 0.
3) We could switch day trips based on the weather. For example: If whether is good on Day 1 then I will prefer to visit Jungfraujoch on the day 1 and swap our day trips. In this case, I will have to activate flex card for the trip to Jungfraujoch from Interlaken as a free day of travel which won't be very beneficial.

Advantage of flex pass over Half Fare card:

1) I won't have to get in lines to buy tickets for 3 days and will have more flexibilty to travel in Switzerland travel system without restrictions with some exceptions.
2) I will not have to spend extra 53.3 (Day 1) + 104.5 (Day 5) + 53(Day 6) - 35.50 CHF (Day 0) - 50.40 (25% reduction on the Jungfraujoch for flex Vs Half Price Card) = 124.4 CHF if I get flex pass over HF Card.
3) Based on point 2, net flex pass cost over Half Fare Card is going to be 221.00 (Cost of Flex Card) - 124.4 (Money saved on 3 free travel days )= 96.6.

Thank you in advance for a valuable advice.

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